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Volume 8 Number 1, 2005ISSN 1094-8848JOURNAL OF TRANSPORTATIONAND STATISTICSU.S. Department of TransportationResearch and Innovative Technology AdministrationBureau of Transportation Statistics

JOURNAL OF TRANSPORTATIONAND STATISTICSPEG YOUNG Editor-in-ChiefDAVID CHIEN Associate EditorCAESAR SINGH Associate EditorJEFFERY MEMMOTT Associate EditorMARSHA FENN Managing EditorJENNIFER BRADY Data Review EditorVINCENT YAO Book Review EditorDORINDA EDMONDSON Desktop PublisherALPHA GLASS-WINGFIELD Editorial AssistantLORISA SMITH Desktop PublisherEDITORIAL BOARDKENNETH BUTTON George Mason UniversityTIMOTHY COBURN Abilene Christian UniversitySTEPHEN FIENBERG Carnegie Mellon UniversityGENEVIEVE GIULIANO University of Southern CaliforniaJOSE GOMEZ-IBANEZ Harvard UniversityDAVID GREENE Oak Ridge National LaboratoryMARK HANSEN University of California at BerkeleyKINGSLEY HAYNES George Mason UniversityDAVID HENSHER University of SydneyPATRICIA HU Oak Ridge National LaboratoryT.R. LAKSHMANAN Boston UniversityTIMOTHY LOMAX Texas Transportation InstitutePETER NIJKAMP Free UniversityKEITH ORD Georgetown UniversityALAN PISARSKI ConsultantROBERT RAESIDE Napier UniversityJEROME SACKS National Institute of Statistical SciencesTERRY SHELTON U.S. Department of TransportationKUMARES SINHA Purdue UniversityCLIFFORD SPIEGELMAN Texas A&M UniversityPETER STOPHER University of SydneyPIYUSHIMITA (VONU) THAKURIAH University of Illinois at ChicagoDARREN TIMOTHY U.S. Department of TransportationMARTIN WACHS University of California at BerkeleyC. MICHAEL WALTON The University of Texas at AustinSIMON WASHINGTON Arizona State UniversityJOHN V. WELLS U.S. Department of TransportationThe views presented in the articles in this journal are those of the authors andnot necessarily the views of the Bureau of Transportation Statistics. Allmaterial contained in this journal is in the public domain and may be used andreprinted without special permission; citation as to source is required.

A PEER-REVIEWED JOURNALJOURNAL OF TRANSPORTATIONAND STATISTICSVolume 8 Number 1, 2005ISSN 1094-8848U.S. Department of TransportationResearch and Innovative Technology AdministrationBureau of Transportation Statistics

U.S. Department ofTransportationNORMAN Y. MINETASecretaryMARIA CINODeputy SecretaryResearch and InnovativeTechnology AdministrationERIC C. PETERSONDeputy AdministratorBureau of TransportationStatisticsRICK KOWALEWSKIDeputy DirectorWILLIAM J. CHANGAssociate Director forInformation SystemsMARY J. HUTZLERAssociate Director forStatistical ProgramsThe Journal of Transportation and Statistics releasesthree numbered issues a year and is published by theBureau of Transportation StatisticsResearch and Innovative Technology AdministrationU.S. Department of Transportation400 7th Street SW, Room 4117Washington, DC 20590USAjournal@bts.govSubscription informationTo receive a complimentary subscription:mail Product OrdersBureau of Transportation StatisticsResearch and Innovative Technology AdministrationU.S. Department of Transportation400 7th Street SW, Room 4117Washington, DC 20590USAphone 202.366.DATAinternet www.bts.dot.govInformation Serviceemail answers@bts.govphone 800.853.1351Cover and text designCover photoSusan JZ HoffmeyerGregg StansberyThe Secretary of Transportation has determined that thepublication of this periodical is necessary in the transaction ofthe public business required by law of this Department.ii

JOURNAL OF TRANSPORTATION AND STATISTICSVolume 8 Number 12005ContentsLetter from the Deputy Administrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vPapers in This IssueThe Dynamics of Aircraft Degradation and Mechanical FailureLeonard MacLean, Alex Richman, Stig Larsson, and Vincent Richman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Air Traffic at Three Swiss Airports: Application of Stamp in Forecasting Future TrendsMiriam Scaglione and Andrew Mungall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Improved Estimates of Ton-MilesScott M. Dennis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Spatial and Temporal Transferability of Trip Generation Demand Models in IsraelAdrian V. Cotrus, Joseph N. Prashker, and Yoram Shiftan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Governors Highway Safety Associations and Transportation Planning:Exploratory Factor Analysis and Structural Equation ModelingSudeshna Mitra, Simon Washington, Eric Dumbaugh, and Michael D. Meyer. . . . . . . . . . . . . . . . . . . . . . . . . 57Vehicle Breakdown Duration ModelingWenqun Wang, Haibo Chen, and Margaret C. Bell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Using Generalized Estimating Equations to Account for Correlation in Route Choice ModelsMohamed Abdel-Aty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Book Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103Data ReviewEmployment in the Airline IndustryReview of Bureau of Transportation Statistics data by Jennifer Brady. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Guidelines for Manuscript Submission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Call for Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112iii

As the first Deputy Administrator of RITA, I thank all the JTS readers fortheir continued interest in this publication. Please feel free to share this publicationwith others. We look forward to expanding our readership throughyou, our valued readers. I hope you find this publication and our new administrationa valued resource.Please do not hesitate to contact me or the JTS editorial staff with your questionsand comments about either this publication or other transportationinterests.Sincerely,ERIC C. PETERSONDeputy AdministratorResearch and Innovative Technology Administrationvi

The Dynamics of Aircraft Degradation and Mechanical FailureLEONARD MACLEAN 1, *ALEX RICHMAN 2STIG LARSSON 1VINCENT RICHMAN 31 School of Business AdministrationDalhousie UniversityHalifax, Canada B3H 3J52 AlgoPlus Consulting Ltd.Halifax, Canada B3H 1H63 Sonoma State UniversityRohnert Park, CA 94928-3609ABSTRACTThis paper looks at the predictability of system failuresof aging aircraft. We present a stochastic,dynamic model for the trajectory of the operatingcondition with use. With failure defined as theoperating condition below a critical level, thedynamics of the number of failures with accumulateduse is developed. The important factors in theprediction of mechanical failures are the number ofprevious repairs and the time since last repair.Those factors are related to repair procedures, withthe time of repair and the extent of repair (fractionof good-as-new) being variables under the controlof the operator. The methodology is then applied todata on non-accident mechanical failures affectingsafety that result in unscheduled landings.INTRODUCTIONAn aircraft is a complex machine composed ofmany interrelated parts, components, and systems.Electrical and mechanical systems are designedwith an expected life length, where length refers totime units (hours) of use. As the aircraft and systemsage and their use accumulates, they graduallyEmail addresses:*Corresponding author—L.C.MacLean@dal.caA. Richman—arichman@algoplusaviation.comS. Larsson—S.O.Larsson@dal.caV. Richman—Vincent.richman@sonoma.eduKEYWORDS: Aircraft failures, aircraft degradation andrepair, airline schedule reliability.1

degenerate until they are no longer able to performthe functions for which they were designed; that is,the system is in a failed state.A nonfunctional part, component, or system canbe upgraded through replacement or repair, inwhich case the condition of the aircraft is restoredto some degree. Maintenance can be based on thecondition; that is, items are repaired when they fail.However, failure during operation can have seriousconsequences, so detection of items with a highprobability of failure through periodic inspectionbecomes a major component of maintenance.The failure rate (the probability of failure at apoint in time) for a degenerating system increaseswith use and age. Figure 1 depicts alternative patternsof failure rates for an aircraft that undergoesperiodic maintenance (a similar figure appears inLincoln 2000). In case A, the aircraft has an increasingfailure rate with age and reaches an acceptabilitythreshold, at which point the aircraft would need tobe replaced. The failure rate declines with periodicmaintenance, but the improvement through maintenancediminishes over time. The threshold is notreached in case B, likely because of increased effortand cost put into maintaining the aircraft.The cost of maintenance required to keep aircraftairworthy (below the threshold) is a major concernof operators. Although replacement time was set bymanufacturers at 20 years for many aircraft models,this life length was extended by operators. Anassumption has been made that aircraft operatingcondition can be kept at an acceptable level beyondthe intended life through maintenance, but costs arehigh.In 1997, 46% of U.S. commercial aircraft wereover 17 years of age and 28% were over 20 years.In 2001, 31% of the U.S. commercial fleet wereover 15 years of age, and those aircraft accountedfor 66% of the total cost of maintenance per blockhour. 1 Although aging (the degeneration in operatingcondition with accumulated use) inevitablyoccurs, it is modified by a number of factors: quantityand quality of repair work; intensity of use;deferral of the schedule for planned maintenance;1 A block hour refers to flying time in hours, includingtakeoff and landing.FIGURE 1 Probability of Failure of a Single AircraftProbabilityof failureProbabilityof failureCase A: Increasing Failure RateThresholdt t t1 2 3Case B: Constant Failure RateThresholdAget t t1 2 3AgeSources: AlgoPlus, 2004, available at http://www.cislpiloti.org/Technical/GAIN/WGB; and AvSoft, 2004, available at http://www.avsoft.co.uk/.and the environment (Alfred et al. 1997). It should benoted, however, unscheduled maintenance accountsfor up to 60% of the overall maintenance workload(Phelan 2003).In addition to the possibility of maintaining anairworthy operating condition, other reasons existfor not retiring an aircraft from the fleet: the highcost of new aircraft; the increase in demand requiringan expanded fleet; and an earlier shortage ofproduction capacity for new planes (Friend 1992).These and other factors result in a large number ofaircraft in use beyond their planned retirement. Aclaim could be made that commercial aircraft arebeing strained to perform well beyond theirintended operating life. Of course, if this is true wewould expect that either the rate of aircraft failure2 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

would show a corresponding increase or the operatinghours per aircraft would decrease because planeswould be out of service for repairs more frequently.In the United States, Service Difficulty Reports(SDRs) contain records of the safety problems anaircraft experiences during operation. This database,maintained by the Federal Aviation Administration,is considered a potential source ofimportant information on aircraft failures (Sampath2000). A study comparing failure rates by carrieridentified significant factors that explain the differencesin the rate of SDRs across carriers (Kanafaniet al. 1993). Because accumulated aircraft use (age)was not included in that study, degradation with ageand differences over time in the safety of individualaircraft were not considered.A THEORY OF DEGRADATIONAND REPAIRWith age and accumulated use, the many interrelatedparts and components in an aircraft can beassumed to degrade. The operating condition orairworthiness of the aircraft is based on the status ofindividual parts, components, and systems, with theitems that are most degenerated being the maindeterminants. A certain level of degenerationimplies failure; that is, the item is no longer operational.As well, failure of certain components orcombinations of components may render the aircraftnot airworthy, which means the aircraft is ina failed state. To address the failure of operatingsystems, airline management undertakes a programof maintenance, with scheduled preventive maintenanceand unscheduled repair/replacement of failedparts, components, and systems. This section presentsa conceptual model for the degradation andrepair of aircraft. The model provides a foundationfor hypotheses about operations that can be testedwith field data.DegradationTo characterize the degradation process, considerthat the operating condition of an aircraft is capturedby an unobserved health status index. Thevalue of the index is derived from the condition ofthe various parts, components, and systems in theaircraft. Let t be the age of an aircraft, defined bythe accumulated hours of use, and letY(t) = the health status of an aircraft at age t.The status is a dynamic stochastic process, withthe change in status at any age being a random variable.Assume that the average condition declineswith age, but at any point variation in the status,based on environmental factors and operating characteristics,can occur. The dynamics of degradationat a point in time can be represented by a stochasticdifferential equation asdY() t = µ t dt + σ t dZ t(1)whereµ t < 0 is the degradation rate,σ t > 0 is a scaling factor, anddZ t is an independent random process.For example, if the random process is whitenoise, the stochastic differential equation defines aWiener process, and the distribution of the healthstatus at a given age is Gaussian (Aven and Jensen1998). So, with starting state y 0 and constantparameters µ and σ, the distribution of status aftert time periods is Normal,Yt () ∝ N⎛y 0 + µt,tσ 2 ⎞⎝ ⎠(2)Mechanical FailureIn this degradation framework, at any age (hours ofuse) the possibility exists that the status of a itemduring operation will drop below the critical level forfunctionality and the component reaches a failurestate. Degradation and failure of components lowerthe value of the health status index Y. In particular,failure of parts and components included on a minimumequipment list (MEL) indicates the aircraftremains airworthy. Beyond the MEL, moderatemechanical failures that occur during aircraft operationwould render the aircraft not airworthy.Assume that the critical health status level y∗ definesairworthiness. Then an aircraft failure occurs whenYt () < y∗ .Based on the stochastic model, the many parts,components, and systems have a probability of failureduring operation and, therefore, the aircraft hasa probability of failure. For an airworthy aircraft,the important variable is the time to failure. Let T beMACLEAN, RICHMAN, LARSSON & RICHMAN 3

the length of life (hours of use before failure) ofan aircraft, with the probability distributionFt () = Pr( T ≤ t), and the corresponding densityf(t). Thenλ()t = ------------------ft ()1 – Ft ()is the failure rate at time t (Aven and Jensen 1998).The failure time distribution is determined by thefailure rate because⎧ ⎫Ft () = 1 – exp ⎨ λ( s) ds0⎬ .⎩ ⎭In the example, where the state dynamics aredefined by a Wiener process, the failure time isinverse Gaussian with density1 ⎛ (( yft () --------------------0 – y∗) – µt) 2⎞= exp ⎜–---------------------------------------- . (3)2πσ 2 t 32σ 2 ⎟⎝ t ⎠RepairFailure during operation may precipitate unscheduledmaintenance, particularly when items beyondthe MEL fail and consequently the aircraft is notairworthy. The repair/replacement of failed items iscalled on-condition repair. On-condition repairbrings the system back to the operating statusexpected of the system given its age, that is, thesame status as just prior to failure. With these minimalrepairs (Block et al. 1985), the aircraft failurerate is unchanged since other parts, components,and systems are still in the degraded state attainedjust before repair. Typically, moderate mechanicalfailures result in such minimal repair.In addition to unscheduled maintenance, thewhole system is subject to time-based or blockrepair, where items are inspected and replaced/refurbishedbefore failure. This scheduled preventivemaintenance improves the operating condition to astatus greater than expected for its age and correspondinglyreduces the system failure rate (Brownand Proschan 1983). To incorporate repair into thedegradation model, the age variable is partitionedinto intervals based on the block repair times.Assume that the first scheduled block repair is at age(hours of use) τ , and subsequent block repairs areat regular intervals of δ hours of use, where δ ≤ τ.Then age t can be written ast = Iτ + kδ + r,where∫tI = 1 if t ≥ τ, I = 0 if t < τ;(4)t – τk = --------- if t ≥ τ,k = 0 if t < τ;δandr = t– Iτ – kδ .The notation ]x[ defines the greatest integerless than x. Equation (4) gives the age in termsof (I + k) = the number of repairs, and r = the usesince the last block repair. The intervention with ablock repair improves the health status of an aircraftabove the level expected for its age. Let theimprovement level from a block repair at age t beup to the lineyt () = α + βt , (5)where α > y∗ and β ≤ 0 .The repair line is theoretical and the importantparameter is β , which describes the repair policy toreturn the aircraft to a fraction of good-as-new atscheduled times. If β = 0 , then repair always bringsthe plane to the same health status regardless of age.To simplify the presentation, repair policies thatare equivalent in terms of the total repair effort willbe considered. LetL = the expected length of the operating life ofan aircraft.Assume that all feasible repair policies have thesame total repair over the expected life of the aircraft.That is,L( α+βt) dt= α∗L ,∫0for some constant α∗ . With this condition, therepair policy is determined by β , which also determinesthe distribution of repair over the aircraft’slifetime.The partition of age at block repairs generatesrenewal cycles for the degradation process, with thefirst cycle starting at the initial status y 0 , and subsequentcycles beginning at the status defined by therepair line:y j ( τδβ , , ) = α + βt j , (6)where t j = τ + ( j – 1)δ,j = 1...,k , . The repair policyis defined by: τ — the hours of use until the firstblock repair; δ — the hours of use between subsequentblock repairs; and β — the repair fraction.Using the definitions of t j and y j , the increase in thehealth status at each block repair from β can becalculated. The policy determines the starting state4 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 2 Aircraft Degradation and Repairy*Health statusCritical conditionAgeSources: AlgoPlus, 2004, available at http://www.cislpiloti.org/Technical/GAIN/WGB; and AvSoft, 2004, available at http://www.avsoft.co.uk/.and length of renewal phases or cycles for thedegeneration process. Figure 2 illustrates the cyclesof degradation and repair for an aircraft.NUMBER OF FAILURESIn each renewal phase of the degradation model,there is a chance that the aircraft fails; that is, its statusdrops below the critical level y∗ . Let T j = time tocritical condition y∗ in cycle j starting from y j-1 ,j = 1,2,... . The failure time distribution for T j iswritten as F j ( s τ, δ,β) , with density f j ( s τ, δ,β),where the repair policy ( τδβ , , ) determines thestarting status. Given the failure time distribution,the failure rate in the jth cycle isλ j ( s τ, δ,β)f j ( s τ, δ,β)= ------------------------------------- .1 – F j ( s τ, δ,β)(7)ConsiderN(t) = the number of aircraft failures to age tfor repair policy ( τδβ , , ). (8)BecausetBlock repair∫λ( s τ,δ,β)ds = –ln( 1 – Ft ())0the expected number of failures isENt ( ()) = I( –ln( 1 – F 1 () t ))kRepair fractionUnscheduledlandingt t t1 2 3– ∑ ln( 1 – F j + 1 ( δ))j = 1–ln( 1 – F k + 2 ( r)). (9)In the failure rate for each renewal phase, the probabilitydistribution for the time to failure has thesame form, but the starting state in each phasedeclines if β < 0 . With t j = τ + ( j – 1)δ, and thestarting state in phase j + 1 asy j = α + βt j = α∗ + β⎛τ + ( j – 1)δ –L --- ⎞ ,⎝2⎠defineψ( x,y j ) = –ln( 1 – F j + 1 ( x)). (10)Thus, ψ( x,y j ) is the expected number of failuresbetween times 0 and x in phase j + 1, with failuretime distribution F j+1 and starting state y j . ThenENt ( ()) = I ⋅ ψ( τ,y 0 )k+ ψδy ( , j ) + ψ( r,y k + 1 ). (11)∑j = 1The degradation process and repair policy aredetermined by parameter values, and those policiesdetermine the properties of the expected number offailures over time. Let ψ′ x and ψ′ y denote firstderivatives of ψ with respect to x and y, respectively.Thus, ψ′ x is the change in expected failureswith use (degradation) within a phase, and ψ′ y isthe change with respect to the phase starting state,determined by the block repair policy. The followinggeneral results establish the expectations formechanical failures when the degeneration modelapplies.Proposition 1 (degeneration): If the health statusof an aircraft degenerates with use, then betweenblock repairs, the failure rate with use increases, asdoes the expected number of failures in a fixedwidthuse interval.In the dynamic model, degeneration follows fromµ < 0 . With degradation, ψ′ x = λ > 0 , and ψ′′ x > 0 ,which implies an increasing failure rate betweenrepairs.Proposition 2 (imperfect repair): If the blockrepair is imperfect, then the failure rate with usesince the last repair is nondecreasing with the numberof previous block repairs, and the expectednumber of failures in a fixed (use since last repair)interval is nondecreasing with the number ofrepairs. If the repair fraction decreases over time,then the expected number of failures is increasing.In the model, ψ′ y > 0 . If α < y 0 , β = 0 , then theexpected number of failures in a fixed interval isMACLEAN, RICHMAN, LARSSON & RICHMAN 5

constant after the initial block repair. If β < 0 , thenthe starting state y decreases, with increasing failurerates in successive phases between block repairs.Proposition 3 (repair interval): If the imperfectrepair fraction is decreasing over time, then theexpected number of failures in a fixed-use intervalincreases/decreases as the block repair intervalincreases/decreases.Block repair increases the health status abovethat expected for accumulated use, so more blockrepairs (shorter times between block repairs) raisethe expected value of y and decrease the failure rateand number of failures.The coefficients in the approximating functionsare defined by derivatives of ψ , evaluated at( τδα , , ∗). Substituting the approximations in equations(12) and (13) into equation (11), the expectednumber of failures has the formENt ( ()) ≈ B 0 + B 1 I + B 2 k + B 3 k 2+ B 4 r+ B 5r 2 . (14)kk + k(Note that ∑2j = -------------- .)2A representation of the number of failures isshown in figure 3.)r 2 + D3( , δ , α ∗ . (13)FIGURE 3 Number of Failures in anFAILURE MODELObservation WindowNThe link between the latent state model for degradation/repairand the model for the number of failuresshows how the operating practices of airlines canmanifest themselves in mechanical failures, safetyproblems, and unscheduled maintenance. Historicaldata on failures and maintenance will have thatcomplex relationship embedded. The informationN(t 1,t 2)on failures and block repairs is available, but thedegradation rate and extent of repair (fraction ofgood-as-new) are unknown. However, from Proposition1, the time since the last block repair reflectsdegradation, and from Proposition 2, the extent ofthe repair is directly related to the number of blockrepairs. The transformation of equation (11) for theexpected number of failures to an expression interms of the number of block repairs and the timesince the last block repair is achieved by a seriesapproximation to the function for E(N(t)).From the model, the average level of repair is α∗ .Consider the first order approximation to ψδy ( , )around ( δ,α∗):0 τ t 1 τ+δ t 2 τ+2δψ( δ,y j ) ≈ C 0 ( τδα∗ , , ) + C 1 ( τδα∗ , , ) × j. (12)In the last (incomplete) phase, a second orderapproximation to the number of failures around( 0,α∗)is reasonable, assuming the failure rate isincreasing monotonically with use. Thenψ( ry , k + 1 ) ≈ D 0 ( τδα∗ , , ) + D 1 ( τ, δ,α∗)k+ D2( , δ , α ∗)rj = 1Sources: AlgoPlus, 2004, available at http://www.cislpiloti.org/Technical/GAIN/WGB; and AvSoft, 2004, available at http://www.avsoft.co.uk/.Thus, B 1 is the expected number of failures in thefirst phase. {B 2 , B 3 } capture the expected number offailures in subsequent phases, and {B 4 , B 5 } capturethe expected number in the last (incomplete) phase.The coefficients in the expected number functionthat relate to the propositions are B 3 and B 5 . If theblock repair is imperfect, then B 3 > 0 . Figure 3shows this effect with the failure function startingabove the origin at block repair times. An acceleratedfailure rate between block repairs impliesB 5 > 0 , which is shown with a steeper slope in successivephases between repairs.The approximating equation for the expectednumber of failures is in a very suitable form foranalysis. Consider an observation window (interval)(t 1 ,t 2 ), where t 2 – t 1 < δ . With t 1 = I 1 τ + k 1 δ + r 1 ,and t 2 = I 2 τ + k 2 δ + r 2 , the number of failures inthe interval (t 1 ,t 2 ) is approximatelyη = ENt ( ( 1 , t 2 )) = ENt ( ( 2 )) – ENt ( ( 1 )),6 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

so that– r 2 1 ) . (15)This change model relates the number of failures inan observation window to the degeneration andthe block repairs in the window. In equation (15),(I 2 – I 1 ) = 1 if the first repair is in the interval, andzero otherwise; (k 2 – k 1 ) = 1 if a later repair occursin the window, and zero otherwise.MODEL TESTINGWe used data from AlgoPlus (2004) to test the failuremodel on operating failures and AvSoft (2004)on aircraft use. For the purposes of this study, anoperating failure is defined as an unscheduledlanding due to mechanical problems affecting safety.Thus, an unscheduled landing is a record of anoperating condition at or below a critical or interventionlevel. In figure 2, the unscheduled landings(failures) occur when the health status drops to thecritical level, where airworthiness fails. It is alsopossible that components fail and the event does notlead to an unscheduled emergency landing. As mentionedearlier, a minimum equipment list detailswhich components may fail without the need for anunscheduled landing. In terms of the degradation/repair model, the critical condition line is below thecondition for failures on the MEL, so that reachingthe critical line implies unsafe operation and a needto interrupt the flight of an aircraft.Data2( 2η = B 1 ( I 2 – I 1 ) + B 2 ( k 2 – k 1 ) + B 3 k+ B 4 ( r 2 – r 1 ) + B 5 r( 22– k 1 2 )The record of unscheduled landings over time providesan information base for analyzing the degenerationin the operating condition of an aircraft.The AlgoPlus data contain detailed records on allunscheduled landings as reported in the ServiceDifficulty Reports for all commercial aircraft inthe United States. The AvSoft data maintainrecords on departures and flying hours for all commercialaircraft in North America. Both datasetshave the serial number, chronological age, model,and carrier/operator for each aircraft.An observation window from 1990 to 1995inclusive was chosen, and all aircraft operatingduring that time for three operators and two modelswere selected for this study. For each aircraft, thefollowing information was recorded: 1) model; 2)operator; 3) age on December 30, 1995; 4) use(block hours, cycles) by month from January 1990to December 1995; 5) dates out of service for atleast one month between 1990 and 1995; and 6)number of unscheduled landings between 1990 and1995. We interpreted the out-of-service period inthe observation window as a time when scheduledrepair was undertaken. The identification of theseperiods is within a record of otherwise continuoususe. Outside the observation window, the blockrepair (preventive maintenance) cycle was set at 10years for the first block repair and 8 years for subsequentblock repairs. This is based on the recommendationsfor D-check cycles. 2 Of course, in practicethe time of block repairs would be variable acrossaircraft and using a fixed value (outside the window)could reduce the power of the fitted models.Table 1 presents a brief description of the aircraftin the dataset. For the aircraft in the study group,table 1 shows substantial differences across modelsand operators in the age of aircraft as of December1995 and the number of unscheduled landingsbetween January 1990 and December 1995.TABLE 1 Description of the Study SampleOperator Model NumberAverageage (yrs)AverageunscheduledlandingsO 1 M 1 230 10.43 3.15M 2 34 5.17 1.82O 2 M 1 221 7.74 1.35M 2 0 — —O 3 M 1 73 10.83 0.96M 2 83 6.93 0.77The definition of age in the degradation of aircraftrefers to hours of use rather than chronologicalage. However, an aircraft operator might make littledistinction between airworthy aircraft of varyingages when making decisions on use. To considerthis point, we looked at the relationship between2 A D-check refers to the major maintenance and overhaulprograms in which the aircraft is completely strippeddown and inspected, with many parts and componentsreplaced or refurbished.MACLEAN, RICHMAN, LARSSON & RICHMAN 7

flying hours per month and chronological age inthe data for the period 1990 to 1995. The correlationin the data between monthly flying hours andage is r = 0.07. The intensity of use appears almostconstant across age, indicating that aircraft are notbeing used less as they age. With constant use perunit time, the accumulated hours of use are almosta scalar multiple of chronological age. So, calendartime was used in the model for predicting the numberof failures; that is, the time between blockrepairs and the time since the last repair will bemeasured in calendar time rather than accumulatedhours of use.Regression ModelThe formulation of a change model for the numberof failures creates a framework suitable for observationand statistical analysis. Based on the model inequation (15), consider the regression modelNt ( 1 , t 2 ) = β q 1 X 1 + β q 2 X 2 + β q 3 X 3+ βq 4 X 4 + β q 5 X 5 + ε , (16)whereN(t 1 ,t 2 ) = the number of failures between ages t 1and t 2 ,X 1 = the indicator for the first τ -repair in theinterval,X 2 = the indicator for the kth δ -repair in theinterval, k ≥ 1 ,X 3 = the difference between the squared number of2 2repairs, k 2 – k 1 ,X 4 = the difference in residual times, r 2 – r 1 ,X 5 = the difference in squared residual times,2 2r 2 – r 1 , andε = the random error.In the regression model, assume that the unscheduledlandings and item failures from degradationare directly related to the number of block repairsand the time since the last block repair. There arealso other factors such as repair skill level, maintenancephilosophy, and operational environmentinvolved in unscheduled landings (Phelan 2003). Wewill assume that these other factors are associatedwith the operator. As well, the aircraft model is afactor in failure rates. So, the coefficients in theregression model depend on the aircraft model andthe aircraft operator. This is reflected in the regressionmodel with a superscript q on the coefficients.The coefficients in the regression model are counterpartsof the coefficients in the failure model, andappropriate tests characterize the role of degradationand repair on failures for a particular modeland operator combination. Table 2 displays the relevantresearch hypotheses.TABLE 2 Research HypothesesRegression modelhypothesisqH: β 2 –qH: β 3 > 0qH: β 4 > 0qH: β 5 > 0β 1q> 0InterpretationBlock repair is incomplete; not togood-as-new.The repair fraction of good-asnewis decreasing.The failure rate increases with thetime since block repair.There is an accelerated failurerate with increasing time sincerepair.A comparison of the coefficients for differentmodel and operator combinations would reveal differencesin model degeneration rates and/or differencesin operator maintenance practices. To includecomparisons, an expanded regression equation isdefined. Consider the indicator variables:U = 1 for model M 1 and 0 otherwiseV 1 = 1 for operator O 1 and 0 otherwiseV 2 = 1 for operator O 2 and 0 otherwise.The regression equation for defining model andoperator effects is5∑Nt ( 1 , t 2 ) = β j X j + λ ij V i X jj = 12∑i = 1 j = 1+ γ j UX 3 + j+ ε . (17)j = 1An equivalent formulation, which reveals theeffect on coefficients, isTo simplify notation, consider the vectors2∑3∑3⎛2Nt ( 1 , t 2 ) = ⎜β j + λ ij V i ⎟+∑j = 1⎝∑i = 12∑ β 3 + j γj = 1⎞Xj( + jU)X 3 j +⎠+ ε. (18)8 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

β⎛⎜⎜⎜= ⎜⎜⎜⎜⎝β 1β 2β 3β 4β 5⎞ ⎛λ 11 ⎞ ⎛λ 21 ⎞ ⎛0⎞⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎟ ⎜λ 12 ⎟ ⎜λ 22 ⎟ ⎜0⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎟;λ 1 = ⎜λ 13 ⎟;λ 2 = ⎜λ 23 ⎟;γ = ⎜0⎟ .⎟ ⎜ ⎟ ⎜ ⎟ ⎜⎟ ⎜ 0 ⎟ ⎜ 0γ ⎟⎟ ⎜ 1 ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜⎠ ⎝ 0 ⎠ ⎝ 0 γ ⎟⎠ ⎝ 2⎠Table 3 shows the variations on the regressionequation.TABLE 3 Model Variationsq V 1 V 2 U Parameters1 0002 1003 0104 0015 1016 011Table 4 presents the hypotheses for testing theeffect of differences in models and operators.TABLE 4 Comparison HypothesesHypothesesH: λ 1 ≠ 0H: λ 2 ≠ 0H: γ ≠ 0Fitted ModelInterpretationRepair effect for operator O 1 differsfrom othersRepair effect for operator O 2 differsfrom othersThe failure rate since repair dependson the aircraft modelThe maintenance policies of a carrier as well as theparticular design (components and systems) in anaircraft model are major factors in the operatingcharacteristics of an aircraft. Selecting a single aircraftmodel from a single carrier removes the complicationof varying models and carriers, and thusthe assumption of constant degradation and repairparameters is reasonable. This experimental settingis ideal for focusing on the degradation of the operatingcondition with accumulated use. As such, thedata for operator O 2 were used with degradationmodel (16), because the O 2 fleet consisted only ofB737 aircraft.β 1=ββ 2 = β + λ 1β 3 = β + λ 2β 4 = β + γβ 5 = β + λ 1 + γβ 6 = β + λ 2 + γBecause the number of failures is a counting variable,the error variance is not likely to be constant.Therefore, an iteratively reweighted least squaresestimation method was used, where the weightswere reciprocals of the fitted values (McCullagh andNelder 1989). The effect of weighting was minimal,so the unweighted sums of squares are reported.The results from fitting the degradation model tothe operator O 2 data are given in table 5.TABLE 5 Fitted Failure ModelVariable Parameter Estimate T Pβ 1X 1 –1.54 –6.52 0.000β 2X 2 6.39 5.03 0.000β 4X 4 0.12 6.02 0.000β 5X 5 0.02 10.86 0.000ANOVASource SS df F PRegression 615.79 4 96.22 0.000Error 347.21 217Total 963.00 221Clearly the overall fit of the change model isstrong (F = 96.22). Furthermore, the individualcomponents in the model are highly significant.Maintenance in the observation window and timesince maintenance are important factors in predictingthe number of unscheduled landings that occurin the window. Of particular significance is theacceleration in the number of repairs (increasingfailure rate) as time since repair increasesˆ( β 5 = 0.02, T = 10.86). With reference to Proposition1, the regression provides the following result.Result 1 (degradation): The rate of unscheduledlandings increases with time since the last blockrepair.Furthermore, there is evidence that the blockrepair is not as good-as-new, because the sign onX 1 = I 2 – I 1 is negative and the sign on X 2 = k 2 – k 1 isˆ ˆpositive. A test on the difference β 2 – β 1 = 7.93 ishighly significant ( P < 0.001). However, the data didnot allow for a test of diminishing repair fraction.The aircraft in the operator O 2 fleet are relativelynew and the maximum is k = 1. The regression givesthe analogous result for Proposition 2.MACLEAN, RICHMAN, LARSSON & RICHMAN 9

Result 2 (imperfect repair): The rate of unscheduledlandings decreases after a block repair, with thedecrease greater for the initial repair than for subsequentrepairs.To consider the issue of differential effects for theaircraft model and operator, the additional termswith indicator variables were included. Table 6 presentsthe regression results. The additional sum ofsquares for models and operators indicated in table6 are considered after including other effects. Thatis, the outcome (number of unscheduled landings)was adjusted for the model effect when consideringthe operator effect, and it was adjusted for the operatoreffect when considering the model effect. Inboth cases, the effects are statistically significant(i.e., there is a differential effect for operators andmodels). In the context of the regression equation,the effect of maintenance on unscheduled landingsTABLE 6 Comparison of Models and OperatorsVariable Parameter Estimate T Pβ 1X 1 –1.46 –4.73 0.000β 2X 2 2.84 2.19 0.029β 4X 4 0.18 7.51 0.000β 5X 5 0.014 7.13 0.000γ 11V 1 X 1 2.44 6.04 0.000γ 12V 1 X 2 1.88 1.39 0.166γ 22V 2 X 2 3.52 1.57 0.116λ 1UX 4 –0.14 –3.06 0.002λ 2UX 5 0.004 0.99 0.325ANOVA (OPERATOR)AdditionalSource SS df F POperator 131.12 3 13.125 0.000Error 2,104.73 632Total 4,964.00 641ANOVA (MODEL)AdditionalSource SS df F PModel 40.91 2 6.143 0.002Error 2,104.73 632Total 4,964.00 641was not the same for the operators in the study. Aswell, the effect of the time since maintenance wasnot the same for the models selected.Result 3: The relationship between the rate ofunscheduled landings and the time since the lastblock repair and the number of block repairsdepends on the aircraft model and operator.Using the indicator variables, it is possible towrite out the fitted equation for each (operatorand model) type. The estimates for equationparameters are given in table 7. The equation foroperator O 2 (q = 3) is slightly different from theequation using only O 2 data, owing to the greatervariation in using multiple operators and models.However, it is a good reference for understandingthe changes in the equation with the operator/modelvariations. The biggest operator effect is the differenceof O 3 (q = 2,5) from the others on the estimateˆˆβ 1 . For aircraft models, the estimate of β 4 is mostaffected.TABLE 7 Comparison of EstimatesqV 1 V 2 U1 000 –1.46 2.84 0.18 0.0142 100 0.99 4.70 0.18 0.0143 010 –1.46 6.35 0.18 0.0144 001 –1.46 2.89 0.04 0.0185 101 0.99 4.70 0.04 0.018DISCUSSIONβ 1qThe operating condition of aging aircraft has been ahotly discussed topic for more than a decade. TheFederal Aviation Administration’s position is thatthe operation of older aircraft is an economic decisionand not a safety issue; that is, aircraft can berepaired to a safe operating condition and the costof those repairs is the issue.This study considers the trajectory of the healthstatus of an individual aircraft, with an emphasis onepisodes where flights are interrupted because ofmechanical failures affecting safety. In the context ofa model for mechanical failure, two experimentswere carried out. In the first experiment, a singlemodel and carrier were analyzed for the potentialimpact of aircraft age (accumulated use) and repairon schedule reliability. The study assumes that allthe selected aircraft are equivalent except for age,β 2qβ 4qβ 5q10 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

and the fleet management practices of the carrierremain consistent over time. In this setting, the variabilityin the failure rate (unscheduled landings) canbe partly attributed to the aging of the aircraft andincomplete repair during preventive maintenance.The second experiment involved multiple operatorsand aircraft models. With the same failure model,the differential effect of operational practices andaircraft design can be studied.The following can be concluded from the resultsof this study.1. The percentage of variation in unscheduledlandings that can be explained by degradationwith age and incomplete repair is high.2. Age (accumulated hours of use) has a statisticallysignificant effect on failures (unscheduledlandings), with an increasing failure rate as ageincreases.3. The improvement in the operating conditionwith planned preventive maintenance is not togood-as-new.4. The relationship between failures and degradationdiffers from model to model.5. The relationship between failures and repairdiffers from operator to operator.The clear relationship between unscheduledlandings and degradation/repair in the regressionmodel has implications for the maintenance policiesof operators. The operator has control overthe repair intervals— ( τδ , ) and the repair effortβ —the fraction of good-as-new. The dependence ofthe regression coefficients on the maintenanceparameters ( τδβ , , ) is implied in this paper, but thatconnection can be made more explicit by using theactual derivatives in the series approximations. Inthat way, changes in the values of the maintenanceparameters would translate into changes in the rateof unscheduled landings. Therefore, an operatorcould explore the outcome (in terms of unscheduledlandings) of changes in the repair parameters, forexample, the block repair interval.The purpose of our research was to establishthe feasibility of predicting unscheduled landingsfrom data on use and maintenance. An earlierstudy (Nowlan and Heap 1978) found that 89% ofaviation mechanical malfunctions were unpredictedusing operating limits or undertaking repeatedchecks of equipment. The results of this work indicatethat important problems in the operation ofaircraft can be studied with existing field data. Useof these results in the management of an airlinewould require additional study, but a step in thatdirection has been taken here.REFERENCESAlfred, L., R. Ellis, and W. Shepard. 1997. The Dynamics of AircraftAging, mimeo. Decision Dynamics Inc.AlgoPlus. 2004. Available at http://www.cislpiloti.org/Technical/GAIN/WGB.Aven, T. and U. Jensen. 1998. Stochastic Models in Reliability.New York, NY: Springer Verlag.AvSoft. 2004. Available at http://www.avsoft.co.uk/.Block, H., W. Borges, and T. Savits. 1985. Age-Dependent MinimalRepair. Journal of Applied Probability 22:370–385.Brown, M. and F. Proschan. 1983. Imperfect Repair. Journal ofApplied Probability 20:851–859.Friend, C. 1992. Aircraft Maintenance Management. Essex,England: Longman Scientific and Technical.Kanafani, A., T. Keeler, and S. Sathisan. 1993. Airline SafetyPosture: Evidence from Service Difficulty Reports. Journal ofTransportation Engineering 119(4):655–664.Lincoln, J.W. 2000. Risk Assessments of Aging Aircraft. AgingAircraft Fleets: Structural and Other Subsystem Aspects,RTO Lecture Series 218, RTO-EN-015.McCullagh, P. and J. Nelder. 1989. Generalized Linear Models,2nd ed. New York, NY: Chapman and Hall.Nowlan, F.S. and H.F. Heap. 1978. Reliability Centered Maintenance,Report No. AD-A066-579. Available from theNational Technical Information Service, Springfield, VA.Phelan, M. 2003. Health Check. Flight International163(4865):26–27.Sampath, S.G. 2000. Safety and Service Difficulty Reporting,Aging Aircraft Fleets: Structural and Other SubsystemAspects, RTO Lecture Series 218, RTO-EN-015.MACLEAN, RICHMAN, LARSSON & RICHMAN 11

Air Traffic at Three Swiss Airports: Application of Stamp inForecasting Future TrendsMIRIAM SCAGLIONE 1,*ANDREW MUNGALL 21 Institute for Economics & TourismUniversity of Applied Sciences ValaisTECHNO-Pôle Sierre 3CH 3960 SierreSwitzerland2 Ecole Hôtelière de LausanneLe Chalet-à-GobetCH – 1000 Lausanne 25SwitzerlandABSTRACTThis paper presents forecasting trends for numbersof air passengers and aircraft movements at the threemain airports in Switzerland: Zurich, Geneva, andBasel. The case of Swiss airports is particularly interesting,because air traffic was affected in the recentpast not only by the September 11, 2001, terroristattacks but also by the bankruptcy of the nationalcarrier, Swissair, that same year. A structural timeseries model (STS) is created using Stamp software tofacilitate forecasting. Results, based on readily availabledata (i.e., passengers and movements), showthat STS models yield good forecasts even in a relativelylong run of four years.INTRODUCTIONAirports are now widely recognized as having aconsiderable economic and social impact on theirsurrounding regions. These impacts go far beyondthe direct effect of an airport’s operation on itsneighbors and extend to the wider benefits thataccess to air transport brings to regional businessinterests and consumers.The economic benefits of air transport may beassessed by looking at the full extent of the industry’simpact on the overall economy, from the movementEmail addresses:* Corresponding author—miriam.scaglione@hevs.chA. Mungall—Andrew.Mungall@ehl.chKEYWORDS: Structural time series, forecast, airports,Switzerland, air traffic.13

of passengers and cargo to the economic growth thatthe industry’s presence stimulates in a local area.In this respect, Switzerland represents an interestingcase. First, half of the earnings of the Swisseconomy come from abroad. Fast, direct access tothe different markets around the world is thereforevery important, especially when Switzerland’sdependence on exports will increase in the future. Inthis economy, the industry with the highest share ofexports is metallurgy and mechanical engineering.Around 75% of its production is exported. In theSwiss tourism industry, exports represented by theexpenses of foreign tourists are also important. Of atotal tourism revenue of 22.2 billion Swiss francs(CHF) in 2003 (Swiss Federal Statistical Office2004), 12.6 billion CHF (60% of the amount) camefrom foreign tourists.Second, Swiss air transport has recently beenfacing rapid change. During the last half of the1990s, Swiss airports revisited their respective strategiesfollowing the decision made by the nationalcarrier, Swissair, in 1996 to concentrate all longhaulflights at Zurich-Unique Airport (ZRH). Alsoat this time, the Basel/Mulhouse Airport (BSL)made plans to become a European hub or a spokefor Swissair, and, therefore, decided on significantexpansion investments. This obliged GenevaInternational Airport (GVA) to adopt an openskypolicy, where foreign air carriers could benefitfrom so-called “fifth-freedom” rights, enablingthem to provide intercontinental services to andfrom Geneva. The Swissair bankruptcy in 2001changed the context, calling the expansion policyof ZRH airport into question.This study uses the data from the three mainSwiss airports—ZRH, GVA, and BSL—to show theovercapacity of two of the three by forecasting theseseries to 2006. The average share of overall aircraftmovements at the three airports was: 46% (±5),32% (±3), and 22% (±3); for passengers, the sharewas 59% (±5), 32% (±4), and 9% (±3), respectively.The structure of the paper is as follows: the nextsection describes the data used for this analysis, thenwe provide the forecasts based on three models (onefor each airport) to a horizon of 2006. All sectionsuse structural time series (STS) models and theStamp software for STS (Koopman et al. 2000). Thelast section provides conclusions based on theseresults.DATAFor our analysis, we obtained data from the statisticaldepartment of each airport studied. Each providedyearly observations from 1949 to 2003,except for GVA, whose data began in 1922. Weconsidered two principal indicators: air movementsand passengers.Traffic ForecastsWe built bivariate models for each airport using thevector of variables⎛m t ⎞y t = ⎜ ⎟ ,⎝p t ⎠where m t denoted the number of movements for agiven airport, and p t denoted the number of passengers.The choice of the bivariate model seemsappropriate, because aircraft and passengers belongto the same economic system and this kind of modelallows for interaction between the two variables.These models are called Seemingly Unrelated TimeSeries Equations (SUTSE) and are an extension ofunivariate forms, with the advantage of allowing forcross-correlation leads between variables. In Stamp,SUTSE are particularly appealing because, on theone hand, models with common factors emerge as aspecial case; on the other, the direct analysis of theunobservable components provides a more efficientforecast and inference (see appendix 1 for details).In this study, the variables are transformed to logarithmsso that the model is multiplicative. Such atransformation allows for percentage changes ratherthan absolute changes in traffic levels and also helpsto stabilize the variances of the variables.Analysis for GVAFor GVA, while annual data are available from1922, the first major facility was built in 1949.Given that the period 1949 to 1952 was one oftransition, we used data from 1953 to 2002. Theobservation for 2003 was used to evaluate theprobability of a structural break using the postpredictivefeatures of Stamp (Koopman et al. 2000,pp. 39–40).14 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Table 1 shows the hyper-parameters of the model(table A1 in the appendix provides an interpretationof these values). Table 2 shows statistics tests normallyused to evaluate the goodness-of-fit of themodel. In the case of GVA, only the Box-Ljung (testof residual serial correlation) statistic is slightly significant(p-value = 0.08) for passengers. The model isa local linear trend and a common cycle (table 3).Table 1 also provides the list of intervention variables.1 There is no intervention for passenger series,but there are two interventions in the aircraft movementcomponent. The first occurs in 1956 and is apositive level shift, probably explained by theincrease of movements owing to the start of the jetaircraft era. The outlier intervention (AO) in 1967 is1 See appendix 1 for the definition of the interventionvariables.difficult to explain; however, we retained it in themodel for consistency.The analysis of the components obtained in theSTS modeling (i.e., trend, slopes, and cycles) highlightssome interesting features of the phenomenaunder study. Figure 1 shows some of the componentsof the models. First, the slopes are parallel in logarithms,suggesting that the rates of growth, thoughdifferent, have a parallel evolution. In statisticalterms, it means that the system composed of the passengersand movements is co-integrated to an orderof (2,2) and there is a combination that is stationary(see Koopman et al. 2000, p. 86; Song and Witt2000, p. 56). As the data are in logarithms, thiscomponent represents the rate of growth and can beread as tracking its acceleration and deceleration.TABLE 1 Hyper-Parameters Given as Standard Deviations and InterventionsAirportsGVA ZRH BSLVariable Passengers Movements Passengers Movements Passengers MovementsLevel 3.95E–02 7.3E–03 nil nil 3.9E–02 2.0E–03Slope 1.2E–02 8.6E–03 1.9E–02 6.7E–03 1.8E–02 2.2E–02Cycle ρ = 0.83 ρ = 0.88 ρ = 0.982.1E–02 1.6E–02 1.2E–02 2.4E–02 3.6E–02 3.0E–02Irregular 0.0E+00 2.5E–02 1.9E–02 6.7E–03 9.8E–03 3.5E–02Interventions nil +LS 1956** +AO 1957** –AO 1957* nil nilnil +AO 1967** –LS 2002*** –LS 2002** nil nilModel LLT+cycle Smooth trend LLT+cycleCointegration C(2,2)+common cycles nil C(2,2)Key: *** = p-value < 0.01; ** = p-value < 0.05; and * = p-value < 0.1; the sign in the intervention row indicates the sign of itscoefficient.TABLE 2 Statistical Values of the Goodness-of-Fit TestAirportGVA (1953–2002) ZRH (1953–2003) BSL (1956–2002)Variable Passengers Movements Passengers Movements Passengers MovementsStandard error 5.17E–02 4.43E–02 4.39E–02 3.75E–02 7.61E–02 8.00E–02Normality 5.92 0.12 3.92 2.31 2.52 0.61Heteroskedasticity 0.51 0.37 1.62 0.51 0.44 0.31Durbin-Watson 1.98 1.92 1.89 1.89 1.51 1.78Box-Ljung 11.20* 6.45 7.59 12.84* 5.40 7.64R-squared 0.36 0.64 0.63 0.34 0.51 0.48Key: * = p-value < 0.1.Note: For definitions, see the appendix.SCAGLIONE & MUNGALL 15

TABLE 3 Cycle Parameters and Final Growth Rates for Three Swiss AirportsAirportGVA (1953–2002)ZRH (1953–2003)BSL (1956–2002)VariableAmplitude at theend of the seriesCyclesPeriod(years)CovarianceSlopeGrowth rateat the end ofthe seriesPassengers 2.2 11.90 1.0 2.9Movements 1.6 1.0Passengers 3.6 8.96 4.2E–01 –0.9Movements 7.2 1.1Passengers 18.2 9.11 9.8E–01 2.0Movements 11.1 –1.9FIGURE 1 Slope Components and Cycles for Aircraft Movements and Passengers at GVA: 1953–200216Slopecomponent1412Slope_Log (Passengers)10864Slope_Log (Movements)201955 1960 1965 1970 1975 1980 1985 1990 1995 2000642CyclecomponentCyc_Log(Movements)Cyc_Log(Passengers)0–2–4–61955 1960 1965 1970 1975 1980 1985 1990 1995 2000The growth rates gradually declined from themid-1950s to the mid-1970s and then stabilized atabout 3% for passengers and 1% for movements(see the last column in table 3). This difference inrates clearly reflects the increase in the jet aircraftera. The mid-1950s brought the prospect of commercialjet airliners in the near future, with all itwould entail in terms of longer runways and greater16 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

terminal capacity. The Swiss and French authoritiesreached an agreement concerning an exchange ofland with France. Provision was also made for asector of the future terminal to become a “FrenchAirport,” linked to Ferney-Voltaire in France by anextra-territorial connection. The agreement wasratified by the Federal Assembly in 1956 and by theFrench Parliament in 1958.Other important features summarized in table3 for GVA are the existence of a cycle of approximately12 years that is stochastic, but with a correlationof 1; this means that the two cycles(passengers and air movements) move together. Thetable also shows that the amplitude of the cycle (atthe end of the series) is less than 2.5% of the trendfor passengers and less than 2% for movements.Figure 2 shows the trend and the actual values inlogs with the contribution of the cycles.Table 4(A) shows the number of passengers forecastand observed for 2003 and 2004. The forecastsunderestimate the observed figures by about 3% for2003 and 6% for 2004. Table 4(B) shows that aircraftmovements observed and forecast are veryclose for both 2003 and 2004, both approximately1.6 hundreds of thousands.In spite of the slightly high error for passengers,table 4(A) shows that the numbers observed remaininside the confidence interval of one standard error,and therefore the model does not need to bereviewed. In 2003, GVA outperformed the 2000record for passengers; this upward tendency wasconfirmed in 2004. This increased passenger levelcan be explained by the innovative policy carriedout by the GVA authorities and the reinforcement ofthe presence of low-cost carriers that have a highpassenger load rate for their flights. As an example,on April 22, 2004, the GVA Board decided to adopta loyalty policy for both the old and new companiesoperating in the airport. Under this policy, GVAwould return up to 40% of the airport taxes(excluding the share relating to security) to all companiesthat signed a commitment to operate fromthe airport for three to five years. At the same time,GVA decided to segment its terminals. The principalterminal remains a conventional one, and GVA renovatedthe old terminal and offered to let all companies(even though low-cost companies suggested thisFIGURE 2 Trend Plus Cycle and Actual Values (inLogarithms) for Movements andPassengers at GVA: 1953–2002Log12.512.011.511.010.510.0Log16.015.014.013.012.0ActualTrendAircraft MovementsTrendActual1955196019651970197519801985199019952000Passengers1955196019651970197519801985199019952000measure) use it at a lower tax level than the principalone. Table 4 (B) shows that GVA will need morethan two years to return to the maximum level ofmovements registered in 2000 (1.71 hundreds ofthousands).Figure 3 also shows the forecasts for 2004 to2006, which indicate a strong upward trend for passengersand a slight upward trend for aircraft movements.Once more, this difference in the speed ofevolution between movements and passengers canbe explained by the aggressive GVA policy in tryingto capture the low-cost market (e.g., easyJet, whichhas an excellent aircraft occupancy rate). Thus, with25% of the market share of GVA traffic in 2003,SCAGLIONE & MUNGALL 17

TABLE 4 Forecasts of Numbers of Passengers and Aircraft MovementsA. PASSENGERS (millions)Airport Year 2003 2004 2005 2006Forecast 7.86 8.05 8.29 8.19GVA (1953–2002)Observed 8.09 8.59RMSE 0.43 0.69 1.02 1.33Error –2.84% –6.29%Forecast in sample 16.41 16.55 16.59ZRH (1953–2003)Observed 17.02 17.25RMSE in sample 1.62 2.41 3.27Error in sample –4.87%Forecast 2.85 2.84 3.07 3.49BSL (1956–2002)Observed 2.48 2.59RMSE 0.23 0.44 0.70 0.10Error 14.92% 9.65%B. AIRCRAFT MOVEMENTS (hundreds of thousands)Airport Year 2003 2004 2005 2006Forecast 1.64 1.66 1.67 1.69GVA (1953–2002)Observed 1.63 1.67RMSE 0.07 0.10 0.14 0.17Error 0.61% –0.60%Forecast in sample 2.78 2.95 3.16ZRH (1953–2003)Observed 2.69 2.67RMSE in sample 0.20 0.29 0.37Error in sample 4.12%Forecast 1.01 0.97 0.99 1.04BSL (1956–2002)Observed 1.00 0.78RMSE 0.09 0.15 0.22 0.30Error 1.00% 24.36%Key: RMSE = root mean squared error.easyJet has become, for the first time, the mostimportant carrier in Geneva. The market share ofthe national airline, Swiss, amounted only to21.3%.Analysis for ZRH AirportFor ZRH airport, we considered data from 1953,which coincided with the formal inauguration of thepresent location (also called Kloten Airport). Duringthe 1980s and 1990s, the airport experienced rapidexpansion. The number of passengers reached 12million in 1990 and 22 million in 2000. Thus, in1995 the Zürich electorate accepted a further expansionprogram for the airport, with a new terminal, anew airside center (linking the different terminals)and underground facilities. Initially, the expectationwas to complete the expansion by 2005, with thecapacity of the airport increasing from 20 million to40 million passengers per year. As a consequence ofthe events of 2001, which form the object of thisanalysis, this extension phase is being implementedmore slowly and Terminal B (capacity of about 5million passengers) has been closed down.The model calculated on the sample data from1953 to 2002 shows that the observed totals for2003 lay outside the forecast confidence interval ofone standard deviation. Therefore, the authorsreviewed the model, taking 2003 as the last observation,and a level shift intervention in the modelfor 2002. Table 1 shows that the intervention has a18 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 3 Forecast Figures for Movements andPassengers at GVA1801701601501e79e68e67e66e6Number of movements(thousands)Number of passengersMovements actualForecast1401990 1995 2000 2005Passenger actualForecastAircraft MovementsObservedvaluesObservedvaluesPassengers5e61990 1995 2000 2005significant negative coefficient for both series, passengersand movements, indicating that the shift inboth trends is decreasing. The model is a smoothedtrend with a drift.Figure 4 shows the slope, namely the rate ofgrowth for the series. For movements, the range wasabout 5% (from 6% to 1%) and was quite steady.For passengers, the range was about 19% (from18% to –1%). The figure also shows the externalshocks for both series. Indeed, the rate of growthZRH passengers becomes negative in the same yearthat Swissair went bankrupt.Analysis for BSL AirportThe analysis of BSL airport uses observations from1956 to 2002. The reason for chosing 1956 is thatat that time the facilities development process wasquite mature. When the airport reached 3 millionpassengers per year at the end of 1998, expansionseemed to be essential and urgent. Extension workon the terminal buildings will allow for furtherexpansion in the number of passengers in the future,to a capacity of 5 million per year.The model is a local linear trend, plus a cycle,having a common slope, which means a cointegration(2,2) for the two series. The estimated growthrate of the fitted stochastic trend is positive forpassengers (about 2%) and negative for movements(–2%) at the end of the sample period.Table 4(A) shows a high error in the overestimationfor passengers in 2003, which could be due tothe drastic reduction of flights by the national carrier,Swiss (elimination of 11 destinations and 7transfer flights since March 2003), which stronglyaffected the number of transit passengers. The goodperformance in the forecast of movements could beexplained, in part, by the increasing number ofcharters (over 3% against 2002) following thearrival of new carriers (EuroAirport 2004).The 2004 forecast is better for passengers than formovements, nevertheless both forecast figuresremain inside the confidence interval of one standarddeviation. On the one hand, the number of passengerson scheduled flights increased by 8% against2003, given the arrival of easyJet offering four newdestinations. On the other hand, the decrease in thenumber of movements is explained by the increasingload rate and the use of aircraft with larger capacity(EuroAirport 2005). The former fact explains theapparent contradiction of the increasing number ofpassengers despite a decreasing number of movements.Finally, this high error in the forecast suggeststhat Basel Airport is in a structural change phase(i.e., the percentage of transit passengers in 2004 was2%, whereas in the past it was approximately 28%).Nevertheless, BSL seems to be growing once againowing to a policy centered more on low-cost carriersand charters and much less on its original vocationof being a Euro-Hub.SCAGLIONE & MUNGALL 19

FIGURE 4 Slope Components for the Zurich Airport Model withExternal Shocks Chronology: 1953–2002Slope20.017.515.012.510.07.55.0Slope forpassengersCubanmissile crisisOPEC oilembargoIraqi invasionof KuwaitU.S. stockmarket crash9/11 andSwissairbankruptcy2.50–2.5Slope formovements1955 1960 1965 1970 1975 1980 1985 1990 1995 2000CONCLUSIONThe forecasts here show that neither ZRH nor BSLseems likely to return to the level of the record yearof 2000, either for passengers or for aircraft movements,by 2006. The only airport that was able tobeat the record numbers achieved in 2000 wasGVA, but only in the case of passengers.The innovative policy carried out by GVA was agood solution to overcome the 2001 crises of thebankruptcy of Swissair and the U.S. terroristattacks. This being said, GVA had begun to rethinkits strategy earlier than the other two airports,owing to the decision of the national carrier toconcentrate all long-haul flights at ZRH in 1996.The high errors in the forecast figures for BSLare a result of the structural changes taking place atthat airport since 2003; namely, an evolution awayfrom being a spoke and toward becoming a city-tocityEuropean airport. Therefore, the analysis ofthose differences could be a tool for assessing theeffectiveness of the measures undertaken by BSL. Infact, table 4(A) shows that a slightly decreasingtrend was forecast for passengers between 2003and 2004, whereas the observed figures show theopposite. This may be due, at least in part, to thesuccess of the new policy adopted by the Board ofBSL.Finally, the use of Stamp software on the series ofpassengers and movements through a SUTSE modelappears to be an interesting tool for forecasting airtransportation data. On the one hand, the forecastsare good if there are no structural changes (as in thecase of BSL); on the other hand, analysis of the components(i.e., trends, slopes, and cycles) gives a goodinsight into the dynamic of the series. Moreover, thedata used (i.e., passengers and movements) are easilyavailable.ACKNOWLEDGMENTSThe authors wish to thank the following individualsfor their invaluable support: Merrick Fall (EHL),Regula Catsantonis (Unique Airport Verkehrsdaten/Statistik), Robert Weber (Statistical Department ofAéroport International de Genève), Valérie Meny(Statistical Department of EuroAirport), and MerkJürg (Stab/Statistik Bundesamt für Zivilluftfahrt).Thanks also go to Professor Andrew Harvey (CambridgeUniversity) and to the anonymous refereesfor their helpful comments on the earlier version ofthis study.REFERENCESEuroAirport. 2004. Face à Une Situation Économique Perturbéeet à la Chute de Son Trafic, l’EuroAirport s’Adapte aux NouveauxBesoins du Marché et Affirme sa Volonté de Renoueravec la Croissance en 2004.______. 2005. Evolution Positive du Traffic à l’EuroAirport:Innovation et Adaption Réussie aux Nouveaux Besoins duMarché. En 2005: Retour de la Croissance.Harvey, A.C. 1990. Forecasting, Structural Time Models, and theKalman Filter. Cambridge, UK: Cambridge University Press.20 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Koopman, S.J., A.C. Harvey, J.A. Doornik, and N. Shepard.2000. Stamp: Structural Time Series Analyser, Modeller andPredictor. London, England: Timberlake Consultants, Ltd.Song, H. and S.F. Witt. 2000. Tourism Demand Modeling andForecasting. Amsterdam, The Netherlands: Pergamon.Swiss Federal Statistical Office. 2004. Annuaire Statistique de laSuisse. Edited by Neue Zürcher Zeitung. Zürich, Switzerland.APPENDIXThe structural time series model aims to capture thesalient characteristics of stochastic phenomena, usuallyin the form of trends, seasonal or other irregularcomponents, explanatory variables, and interventionvariables. This model can reveal the components of aseries that would otherwise be unobserved, greatlycontributing to thorough comprehension of thephenomena. We describe here only the elementsnecessary for this study; for a complete descriptionsee Harvey (1990) and Koopman et al. (2000). AnSTS multivariate model may be specified as:Observed variables = trend + cycle+ intervention + irregularThe algebraic form for the N series is:y t = µ t + ψ t + ΛI t +ε t2ε t ∼ NID( 0,Σ ε ) t = 1 ,...,T(1)Unless otherwise stated, the elements in equation (1)are (N x 1) vectors,where y t = the vector of observed variables,µµ tψ tΛ= the stochastic trend,= the cycle,= the N x K* matrix of coefficients for the interventions,andI t = the K ∗ × 1 vector of interventions.The stochastic trend is intended to capture the longtrendmovements in the series and trends other thanlinear ones, and is composed of two elements: thelevel (2) and the slope (3). The trend describedbelow allows the model to handle these.µ t =µ t – 1 + β t – 1 +η t2η t ∼ NID( 0,Σ η ) t = 1 ,..., Tβ t =β t 1 + ς– ς t2ς t ∼ NID( 0,Σ ς ) t = 1 ,..., T(2)(3)If the variances of the irregular componentsε t in(1), the disturbances of the level η t in (2), and atleast one of the slope terms ζ t are simultaneouslystrictly positive, the model is a local linear trend.When the level component is fixed and differentfrom zero, and when the two other variances arenot zero, the model is called a “smoothed trendwith a drift.”For a univariate model, the cycleψ t has the followingstatistical specification:ψ tψ * tt==ρcosλ csinλ c– sinλ c cosλ c1 ,..., Tψ t – 1ψ * t – 1(4)where λ c is the frequency, in radians, in the range*0 < λ c < 1,κ t , and κ t – 1 , are two mutually uncorrelatedwhite noise disturbances with zero means and2common variance σ κ , and ρ is the damping factor.The period of the cycle is 2π ⁄ λ c .Cycles can also be introduced into a multivariatemodel. The disturbances may be correlated; thesame, incidentally, can occur with any componentsin multivariate models. Because the cycle in eachseries is driven by two disturbances, there are twosets of disturbances and Stamp assumes that theyhave the same variance matrix (Koopman et al.2000, p. 76), that is:E⎛ κ t κ′ κ ⎞⎝t = E⎛ κ*⎠t κ* t ′ ⎞=Σ⎝ ⎠ κE t * t ′⎝⎛ κ κ⎠⎞ = 0 , t = 1 , ..., T(5)where Σ κ is a N × N variance matrix.Stamp has pre-programmed the following exogenousintervention variables used in this study:1. AO: it is an unusually large value of theirregular disturbance at a particular time. Itcan be captured by an impulse interventionvariable that takes the value of the outliers asone at that particular time, and zero elsewhere.If t ao is the time of the outlier, thenthe exogenous intervention variable I tao hasthe following form:⎧1 if t = t aoI tao = ⎨t = 1 ,..., T⎩ 0 if t ≠ t ao+κ t,κ t – 1SCAGLIONE & MUNGALL 21

2. LS: this kind of intervention handles a structuralbreak in which the level of the seriesshifts up or down. It is modeled by a stepintervention variable that is zero before theevent and one after it. If t LS is the time ofthe level shift, then the exogenous interventionvariable has the following form:OutputTable A-1 illustrates the nature of the outputs usedin the main text. The figures are taken from table 1in the text.DiagnosticsI tLS⎧0 if t < t LSI tLS = ⎨t = 1 ,..., T⎩1 if t ≥ t LSThe diagnosis test statistics for a single series in anSTS model are the following (see Koopman 2000,pp. 182–183): Normality test: the Doornik-Hansen statistic,which is the Bowman-Shenton statistic with thecorrection of Doornik and Hansen. Under thenull hypothesis that the residuals are normallydistributed, the 5% critical value is approximately6.0. Heteroskedasticity test: A two-sided F-test thatcompares the residual sums of squares for thefirst and last thirds of the residuals series. DW: The Durbin-Watson statistic for residualautocorrelation; under the null hypothesis, it isdistributed approximately as N(0,1/T), T beingthe number of observations. Box-Ljung Q-statistic: A test of residual serial correlation,based on the first P residual autocorrelationsand distributed as chi-square, with P–n+1df, when n parameters are estimated.TABLE A-1 Interpretation of the Hyper-Parameters of the Modelfor Geneva International AirportVariables Passengers Movements CommentsLevel 3.95E–02 7.3E–03 Variances of level termsSlope 1.2E–03 8.6E–03 Variances of slope termsCycleρ = 0.83 Damping factor2.1E–02 1.6E–02 Variances of cyclesIrregular 0.0E+00 2.5E–02 Variances of irregular termsInterventions nil +LS 1956** Interventions: timing and coefficient'snil +AO 1967**sign (+/–)ModelLLT+cycleCointegrationC(2,2)+common cyclesKey: ** = p-value < 0.05.22 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Improved Estimates of Ton-MilesSCOTT M. DENNISBureau of Transportation StatisticsResearch and Innovative Technology AdministrationU.S. Department of Transportation400 7th St. SW, Room 3430Washington, DC 20590Email: scott.dennis@dot.govABSTRACTThis paper describes recent improvements in measurington-miles for the air, truck, rail, water, andpipeline modes. Each modal estimate contains a discussionof the data sources used and methodologyemployed, presents a comparison with well-knownexisting estimates for reference purposes, and discussesthe limitations of the data. The resulting estimatesprovide more comprehensive coverage oftransportation activity than do existing estimates,especially with respect to trucking and natural gaspipelines.INTRODUCTIONThe Bureau of Transportation Statistics (BTS) isimproving some of its basic estimates of transportationactivity. This paper describes proposed ton-mileestimates for the air, truck, rail, water, and pipelinemodes. Each modal estimate contains a discussion ofthe data sources used and methodology employed,presents a comparison with well-known existingestimates for reference purposes, and discusses thelimitations of the data. This paper should be viewedas part of a continuing series of steps forward. Additionalplanned work will allow BTS to furtherimprove its basic estimates of transportation activity.KEYWORDS: Transportation measurement, ton-miles.23

CONCEPTTon-miles is the primary physical measure of freighttransportation output. A ton-mile is defined as oneton of freight shipped one mile, and thereforereflects both the volume shipped (tons) and the distanceshipped (miles). Ton-miles provides the bestsingle measure of the overall demand for freighttransportation services, which in turn reflects theoverall level of industrial activity in the economy. Inaddition, a ton-mile estimate is necessary in order toconstruct other estimates of transportation systemperformance, such as energy efficiency and accident,injury, and fatality rates.Domestic ton-mile estimates are usually developedby aggregating data for individual freighttransportation modes. Data for air freight, railroad,and water transportation are readily available as aresult of government provision of infrastructure orresidual economic regulation. Comprehensive pipelinedata are difficult to obtain, because a significantpercentage of pipeline traffic is “in-house” transportationfor companies that produce and refine oil.Ton-mile data for the trucking sector are even moreproblematic due to the large number of shippers,receivers, and trucking firms, as well as the substantialpercentage of in-house trucking traffic. All datasources suffer, at least to some degree, from gaps inthe desired scope of coverage.The Eno Transportation Foundation has publishedhistorical ton-mile estimates for many years(Eno 2002, p. 42), but no longer does so. In morerecent years, BTS has provided alternative estimatesin National Transportation Statistics (NTS) (USDOTBTS 2003). But due to the problems describedabove, these well-known sources do not appear toprovide complete, reliable estimates of this basictransportation measure. BTS, therefore, undertook aresearch program to address these shortcomings.This paper presents the results of this research.DATA SOURCESBTS developed its improved estimates of domesticton-miles (traffic within and between the 50 states,the District of Columbia, Puerto Rico, and the U.S.Virgin Islands) to maintain compatibility with otherU.S. Department of Transportation Strategic Plandata. These annual ton-mile estimates illustratelong-term trends. Comprehensive coverage isachieved by combining reported data from establishedsources, estimates from surveys, and calculationsbased on certain assumptions. Table 1 brieflycompares the scope of the improved BTS ton-mileestimates with the NTS and Eno estimates, whilefigure 1 presents all three estimates for all modes(also see appendix table A1). The NTS and Eno estimatesare not available for the most recent years.AirFigure 2 shows air freight ton-mile data from thethree datasets (also see appendix table A2). Theimproved BTS data are compiled in Air CarrierTraffic Statistics Monthly (USDOT BTS 1990–2003), which presents the results of the T-100reporting system, supplemented by special tabulationsof data on domestic all-cargo operators fromthe Federal Aviation Administration (FAA).The T-100 data represent the population of alldomestic freight traffic for Section 401 air carriers,which operate planes with a passenger seating capacityof more than 60 seats or a maximum payloadcapacity of more than 18,000 pounds. These datainclude the vast majority of all domestic air freighttraffic. As a result of a BTS rulemaking, data forsmaller carriers have been included in this sourcestarting with the fourth quarter of 2003. The inclusionof smaller carriers does not substantially affectthe value of the data series. Domestic all-cargo operators(Section 418 carriers) have been graduallyintegrated into Air Carrier Traffic StatisticsMonthly. The FAA data captured those carriers whohad not yet reported in Air Carrier Traffic StatisticsMonthly, thus allowing representation of the fullpopulation of domestic all-cargo operators.BTS’s proposed estimates of air freight tonmilesare essentially the same as the Eno estimates.Neither estimate includes private carriage of airfreight or air freight forwarders who do not useT-100 reporting carriers. These exceptionsaccount for well under 5% of all air freight traffic.The substantial difference between the twodata series in 2001 is due apparently to Eno’s useof preliminary data.24 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 1 Comparison of Annual Data CoverageMode Improved BTS NTS EnoAirSection 401 carriersSection 418 carriersSection 401 carriersSection 401 carriersSection 418 carriersExcludes Section 418carriersExcludes private carriageand some freightforwardersExcludes privatecarriage and somefreight forwardersExcludes private carriageand some freightforwardersTruckExcludes household,retail, service,government, and certainnoncommercial freightshipmentsExcludes intracitytrafficExcludes intracity trafficRailroad All traffic Excludes smallrailroadsAll trafficWater All domestic traffic All domestic traffic Excludes coastal trafficand traffic to and fromAlaska, Hawaii, and PuertoRicoPipelineOil and oil productspipelinesOil and oil productspipelinesOil and oil productspipelinesNatural gas pipelinesExcludes chemical andcoal slurry pipelinesExcludes natural gas,chemical, and coalslurry pipelinesExcludes natural gas,chemical, and coal slurrypipelinesFIGURE 1 All Ton-MilesTon-miles (billions)4,4004,2004,000Improved BTS3,8003,6003,4003,2003,000NTSEno2,8002,6001990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pKey: p = preliminary.DENNIS 25

FIGURE 2 Air Freight, Express, and Mail Revenue Ton-Miles16Ton-miles (billions)Eno1412NTSImprovedBTS1081990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002p2003Key: p = preliminary.TruckOak Ridge National Laboratory produced estimatesof truck ton-miles based on the 1993 and 1997Commodity Flow Surveys (CFS) (USDOT andUSDOC 1993 and 1997), supplemented with dataon farm-based shipments and imports arriving bytruck from Canada and Mexico. Transportation StatisticsAnnual Report provides this 1997 estimate oftruck ton-miles (USDOT BTS 2000, p. 124). To producethe improved BTS estimate, the 1993 and 1997estimates were updated and backdated using intercityand intracity vehicle miles-traveled (VMT) forsingle-unit and combination trucks, as reported inHighway Statistics (USDOT FHWA 1990–2003).Figure 3 presents the resulting estimates (also seeappendix table A3). The trend in both series is thesame, because the same VMT data were used toupdate each series. After making these adjustmentsfor different time periods and population coverage,the difference between the 1993 and 1997 estimatesis less than 2%. 11 The VMT data include a substantial amount of trucktraffic that is outside the scope of the CFS, e.g., shipmentsby households and retail, service, utility, and governmentestablishments (including the U.S. Postal Service); and certainnoncommercial freight shipments, e.g., constructiontraffic and municipal solid waste. The VMT data can,therefore, be taken to provide a reasonable estimate of thetrend in truck ton-miles, but not the level, and should notbe used to make inferences about operational parameterssuch as empty mileage or average load per truck.FIGURE 3 Development of Truck Ton-MileEstimates1,3001,2001,1001,0009008001990Ton-miles (billions)1992Key: p = preliminary.19941997 base19961993 base1998200020022003 pThe CFS captures export movements, as well asmovements of imports once they reach their firstdomestic destination, such as a warehouse. In orderto provide a more complete estimate of truck traffic,the data in figure 3 were further adjusted to reflecttruck ton-miles from maritime movements prior toreaching their first domestic destination. Thenumber of loaded 20-foot equivalent unit (TEU)containers shipped through U.S. ports is reportedin U.S. Waterborne Container Traffic by Port (U.S.Army Corp of Engineers WCSC 2003). These figureswere then divided by 2.4 to convert them to an26 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

equivalent number of 48-foot trucks. Estimates ofthe percentage of import traffic, the truck share ofimport traffic, miles to the first domestic destination,and tons per truck for East, Gulf, and WestCoast ports were obtained through interviews withport personnel in New York, Houston, and LosAngeles, respectively. The resulting estimates addedbetween 7 billion and 12 billion truck ton-mileseach year. This represents approximately 1% of alltruck ton-miles currently estimated.Figure 4 shows trucking ton-mile estimates (alsosee appendix table A4). The improved BTS estimatesare based on the Oak Ridge National Laboratorysupplement to the 1997 study, which is the morerecent of the two studies. The improved BTS estimateis about 10% higher than the NTS and Enoestimates, each of which reflects only intercity trucktraffic. Therefore, the improved BTS estimate providesa more comprehensive estimate of truck traffic.The CFS data used to construct the improvedtrucking ton-miles estimate exclude shipments byhouseholds and retail, service, utility, and governmentestablishments (including the U.S. Postal Service);and certain noncommercial freight shipments,such as construction traffic and municipal solidwaste. The existing NTS and Eno estimates do notinclude intracity traffic. Therefore, it appears that asignificant percentage of truck VMT and a somewhatsmaller percentage of truck ton-miles are notincluded in any of these estimates. Clearly morework is needed in this area.RailroadBTS developed its improved railroad ton-miles estimatesusing data from the Carload Waybill Sample(USDOT STB 1990–2003). The population estimatein this source is based on a 500,000 recordsample of all traffic terminating on all railroads inthe United States. The sample implicitly includestraffic originating on U.S. railroads and terminatingon Mexican railroads, because almost all such trafficis rebilled to U.S. border crossings. 22 Traffic originating on U.S. railroads and terminating onMexican railroads is treated for accounting purposes as ifit terminated at the U.S. border crossing, and is thereforeincluded in the Carload Waybill Sample. This practice isknown as rebilling.FIGURE 4 Truck Ton-MilesTon-miles (billions)1,3001,2001,1001,00090080070019901992Key: p = preliminary.1994Improved BTS19961998NTS, Eno200020022003 pPopulation data on the tonnage of railroadshipments originating in the United States and terminatingin Canada come from Transportation inCanada (Transport Canada 1990–2002) for yearsprior to 2003. The average length of haul for U.S.railroad shipments was applied to this tonnage toobtain an estimate of U.S. railroad ton-miles forshipments terminating in Canada. This assumptionseems reasonable, because even though much of thistraffic originates in states bordering Canada, moredistant states such as California, Texas, and Georgiaare also among the 10 largest originating states. TheCarload Waybill Sample’s improved coverage ofCanadian terminations of rail shipments originatingin the United States allows estimates of all railroadton-miles for 2003 and subsequent years.Figure 5 illustrates the railroad ton-mile estimates(also see appendix table A5). From 1998 to 2001(the most recent years for which all three estimatesare available), the improved BTS estimates areabout 5% greater than the NTS estimates, whichinclude only Class I railroads; about 1% greaterthan the Waybill estimates, which do not includeCanadian terminations; and almost identical to theEno estimates, which include both non-Class I railroadsand Canadian terminations. The increase inthe improved BTS estimates relative to the other estimatesis probably due to better coverage of the rapidlygrowing railroad shipments originating in theUnited States and terminating in Canada. Further,DENNIS 27

FIGURE 5 Railroad Ton-MilesTon-miles (billions)1,7001,600Improved BTS1,5001,4001,300EnoNTS1,2001,1001,0001990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002p2003Key: p = preliminary.while Eno’s ton-mile estimates for non-Class I railroadsare based on financial survey data, theimproved BTS estimates are based on actual tonmiledata and should be considered more reliable.Finally, railroad ton-mile data may not includeshipments originating in Mexico and terminating inCanada. Based on data from Transport Canada, itappears that these shipments account for less thanone tenth of one percent of all U.S. railroad traffic.WaterDomestic waterborne ton-mile estimates are presentedin figure 6 (also see appendix table A6). Thecurrent NTS estimates of annual water transportationton-miles were taken from Waterborne Commerceof the United States (U.S. Army Corps ofEngineers 2003). Data in this source are developedfrom lock data and individual trip reports that mustbe filed with the U.S. Coast Guard. Therefore, thissource represents the entire population of all domesticwater traffic, including inland waterways, coastwise,Great Lakes, and intraport traffic, along withtraffic to and from Alaska, Hawaii, and PuertoRico. The NTS and Eno estimates differ substantially,because NTS includes coastwise (domesticocean) traffic and Eno does not. Thus, the currentNTS data, which are proposed for use here, aremore comprehensive than Eno’s estimates.PipelineFigure 7 shows pipeline ton-miles (also see appendixtables A7(a) and A7(b)). Annual oil and oilproducts pipeline ton-miles were obtained fromShifts in Petroleum Transportation (Association ofOil Pipelines 2003). These data represent the entirepopulation of crude petroleum and petroleumproducts carried in domestic transportation byboth federally regulated and nonfederally regulatedpipelines. Both NTS and Eno currently use thesedata, which we also propose for use here.FIGURE 6 Waterborne Ton-Miles900800700600500400300Ton-miles (billions)19901992EnoKey: p = preliminary.19941996Improved BTS,NTS19982000p2002200328 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 7 Pipeline Ton-MilesTon-miles (billions)700Improved BTS, NTS,and Eno oil pipeline60050040030020019901992Key: p = preliminary.1994Improved BTSnatural gas199619982000Natural gas pipeline ton-miles are also presentedin figure 7. These new estimates are based on naturalgas deliveries reported in the Annual EnergyReview (USDOE 2003a). BTS first converted thegas deliveries, measured in cubic feet, to metric tonsand then to tons using a standard conversion factorof 48,700 cubic feet per metric ton as reported inthe International Energy Annual (USDOE 2001).There are no data available on the length of haulfor natural gas shipments, because natural gas isdrawn from a common pipeline rather than shippedto a specific consignee. Origination and terminationdata indicate that natural gas has a distribution patternsimilar to oil and oil products (USDOE 2003band 2003c). The oil and natural gas pipeline networksare also very similar. Therefore, the length ofhaul for oil and oil products was applied to the tonnageof natural gas to estimate natural gas ton-milesin transmission lines. 3Natural gas ton-miles in distribution lines (i.e.,local utilities) were estimated using 5% of transmissionlength of haul, which is approximately half thediameter of a major metropolitan area. Natural gaston-miles in gathering lines (i.e., from well to processingplant) were estimated using the same lengthof haul as in distribution lines. The ton-miles forgathering, transmission, and distribution lines were3 The 2000 to 2003 oil pipeline length of haul data aresomewhat suspect; thus, the average length of haul from1990 to 1999 was used in place of these data.p20022003then summed to provide an estimate of total naturalgas ton-miles. Natural gas ton-miles, which havenot to our knowledge been previously estimated,represent nearly as much traffic as that carried onthe inland waterway system. These new estimatesfill a substantial gap in the existing ton-mile data.The natural gas pipeline data do not include gasused to repressurize gas fields or power the pipelineitself, because these uses do not represent gascarried in revenue transportation. The pipelinedata also exclude coal slurry, ammonia, and othertypes of pipelines. There are only a few such pipelines,which tend to have either short haul or lowvolume, and appear to account for well under 1%of all pipeline ton-miles. BTS will investigate therecent decline in the oil pipeline ton-mile data andthe resulting reduction in the estimate of naturalgas ton-miles in order to improve the most recentestimates.CONCLUSIONThe improved ton-mile estimates for the air, truck,rail, water, and pipeline modes described in thispaper are both more comprehensive and more reliablethan well-known existing estimates. Theimprovements are most noticeable with respect totrucking and natural gas pipelines. Additional workwill allow BTS to further improve these basic estimatesof transportation activity.BTS has already incorporated these improvedestimates of domestic freight ton-miles into theTransportation Statistics Annual Report (USDOTBTS 2004, p. 213). 4 BTS plans to extend theimproved estimates back to 1980 in the fall 2005update to National Transportation Statistics. 5Future research will be conducted to further extendthe improved estimates back to 1960 where data areavailable.REFERENCESAssociation of Oil Pipelines. 2003. Shifts in Petroleum Transportation.Washington, DC. Table 1.Eno Transportation Foundation. 2002. Transportation inAmerica. Washington, DC.4 Estimates presented in this paper reflect subsequent revisionsin the source data.5 Available on the BTS website at www.bts.dot.gov.DENNIS 29

Transport Canada. 1990–2002. Transportation in Canada.Ottawa, Ontario, Canada. Addendum, table A6-10.U.S. Army Corps of Engineers. 2003. Waterborne Commerce ofthe United States. Washington, DC. Part V, Section 1, Table1-4, Total Waterborne Commerce.U.S. Army Corps of Engineers, Waterborne Commerce StatisticsCenter (WCSC). 2003. U.S. Waterborne Container Trafficby Port. Washington, DC.U.S. Department of Energy (USDOE), Energy InformationAdministration. 2001. International Energy Annual. Washington,DC. Table C-1._____. 2003a. Annual Energy Review. Washington, DC. Table6.5._____. 2003b. Natural Gas Annual. Washington, DC. Table 12._____. 2003c. Petroleum Supply Annual, Volume 1. Washington,DC. Table 33.U.S. Department of Transportation (USDOT), Bureau of TransportationStatistics (BTS). 2000. Transportation StatisticsAnnual Report. Washington, DC._____. 2003. National Transportation Statistics. Washington,DC. Table 1-44._____. 2004. Transportation Statistics Annual Report. Washington,DC.U.S. Department of Transportation (USDOT), Bureau of TransportationStatistics (BTS), Office of Airline Information.1990–2003. Air Carrier Traffic Statistics Monthly. Washington,DC. Freight, Express, and Mail Revenue Ton-Milestable, p. 2, line 3.U.S. Department of Transportation (USDOT), Bureau of TransportationStatistics and U.S. Department of Commerce(USDOC), Economics and Statistics Administration, U.S.Census Bureau. 1993. Commodity Flow Survey. Washington,DC.______. 1997. Commodity Flow Survey. Washington, DC.U.S. Department of Transportation (USDOT), Federal HighwayAdministration (FHWA). 1990–2003. Highway Statistics.Washington, DC. Table VM-1.U.S. Department of Transportation (USDOT), Surface TransportationBoard (STB). 1990–2003. Carload Waybill Sample.Washington, DC.30 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

APPENDIXTABLE A1 All Ton-MilesImproved BTS Ton-Miles(billions)Mode 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pAir 10 10 11 12 12 13 14 14 14 15 16 13 14 15Truck 854 874 896 936 996 1,042 1,071 1,119 1,149 1,186 1,203 1,224 1,255 1,264Railroad 1,064 1,042 1,098 1,135 1,221 1,317 1,377 1,391 1,448 1,504 1,546 1,599 1,606 1,604Water 834 848 857 790 815 808 765 707 673 656 646 622 612 606Coastwise 479 502 502 448 458 440 408 350 315 293 284 275 264 279Lakewise 61 55 56 56 58 60 58 62 62 57 58 51 54 48Internal 292 290 298 284 298 306 297 294 295 305 303 295 293 278Intraport 1 1 1 1 1 1 1 1 1 1 1 1 1 1Pipeline 822 824 844 856 860 882 905 904 902 899 874 859 879 868Oil and oil 584 579 589 593 591 601 619 617 620 618 577 576 586 590productsNatural gas 238 245 255 263 269 281 286 288 283 281 297 283 293 278TOTAL 3,584 3,597 3,706 3,727 3,904 4,061 4,131 4,136 4,186 4,259 4,285 4,317 4,366 4,357Key: p = preliminary.NTS Ton-Miles(billions)Mode 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001DENNIS 31Air 9 9 10 11 12 13 13 14 14 14 15 13Intercity truck 735 758 815 861 908 921 972 996 1,027 1,059 1,074 1,051Class I railroad 1,034 1,039 1,067 1,109 1,201 1,306 1,356 1,349 1,377 1,433 1,466 1,495Water 834 848 857 790 815 808 765 707 673 656 646 622Coastwise 479 502 502 448 458 440 408 350 315 293 284 275Lakewise 61 55 56 56 58 60 58 62 62 57 58 51Internal 292 290 298 284 298 306 297 294 295 305 303 295Intraport 1 1 1 1 1 1 1 1 1 1 1 1Pipeline 584 579 589 593 591 601 619 617 620 618 577 576Oil and oil 584 579 589 593 591 601 619 617 620 618 577 576productsNatural gas — — — — — — — — — — — —TOTAL 3,196 3,233 3,337 3,364 3,527 3,648 3,725 3,682 3,710 3,781 3,778 3,757(continued on next page)

32 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005TABLE A1 All Ton-Miles (continued)Eno Ton-Miles(billions)Mode 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001Air 10 10 11 12 12 13 14 14 14 15 16 15Intercity truck 735 758 815 861 908 921 972 996 1,027 1,059 1,074 1,051Railroad 1,091 1,100 1,138 1,183 1,275 1,375 1,426 1,421 1,442 1,499 1,534 1,558Water 353 345 353 340 356 366 355 356 357 362 360 348Rivers/canals 292 290 298 284 298 306 297 294 295 305 303 297Great Lakes 61 55 56 56 58 60 58 62 62 57 58 51domesticPipeline 584 579 589 593 591 601 619 617 620 618 577 576Oil and oil 584 579 589 593 591 601 619 617 620 618 577 576productsNatural gas — — — — — — — — — — — —TOTAL 2,774 2,792 2,906 2,989 3,142 3,276 3,386 3,404 3,459 3,552 3,561 3,548TABLE A2 Airline Freight, Express, and Mail Revenue Ton-Miles(billions)1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pAir (improved 10.420 9.960 10.990 11.540 12.030 12.720 13.760 13.900 14.140 14.500 15.810 13.288 13.837 15.096BTS) 1,2Air (NTS) 3 9.064 8.860 9.820 10.675 11.803 12.520 12.861 13.601 13.840 14.202 14.983 13.088Air (Eno) 4 10.420 9.960 10.990 11.540 12.030 12.720 13.760 13.900 14.140 14.500 15.810 15.1801U.S. Department of Transportation, Bureau of Transportation Statistics, Office of Airline Information, Air Carrier Traffic Statistics Monthly (Washington, DC: 1990–2003), Freight, Express, and MailRevenue Ton-Miles table, p. 2, line 3.2 Federal Aviation Administration, supplementary statistics.3U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation Statistics (Washington, DC: 2003), table 1-44.4Eno Transportation Foundation, Transportation in America (Washington, DC: 2002).Key: p = preliminary.

TABLE A3 Development of Truck Ton-Mile Estimates1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pOak Ridge National Lab910 1,109estimate (billions) 1Single-unit truck VMT 52 53 54 57 61 63 64 67 68 70 71 72 76 78(billions) 2Combination truck VMT 94 97 100 103 109 115 119 125 128 132 135 137 139 138(billions) 2Total truck VMT (billions) 146 150 153 160 170 178 183 191 196 203 206 209 215 216Truck VMT index,0.915 0.935 0.959 1.000 1.065 1.114 1.144 1.197 1.228 1.268 1.285 1.307 1.342 1.3501993 baseEstimated truck traffic, 1993 832 851 873 910 968 1,014 1,041 1,089 1,117 1,153 1,169 1,189 1,221 1,228base (billion ton-miles)Truck VMT index,0.764 0.782 0.802 0.836 0.890 0.931 0.956 1.000 1.026 1.059 1.074 1.092 1.122 1.1281997 baseEstimated truck traffic, 1997base (billion ton-miles)848 867 889 927 987 1,033 1,060 1,109 1,138 1,175 1,191 1,212 1,244 1,2511 U.S. Department of Transportation, Bureau of Transportation Statistics, Transportation Statistics Annual Report (Washington, DC: 2000), p. 124.2 U.S. Department of Transportation, Federal Highway Administration, Highway Statistics (Washington, DC: 1990–2003), table VM-1.Key: p = preliminary; VMT = vehicle-miles traveled.TABLE A4 Truck Ton-Miles(billions)DENNIS 331990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pIntercity truck(NTS, Eno) 1, 2 735 758 815 861 908 921 972 996 1,027 1,059 1,074 1,051All truck, 1997 base(improved BTS)854 874 896 936 996 1,042 1,071 1,119 1,149 1,186 1,203 1,224 1,255 1,2641U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation Statistics (Washington, DC: 2003), table 1-44.2 Eno Transportation Foundation, Transportation in America (Washington, DC: 2002), p. 42.Key: p = preliminary.

34 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005TABLE A5 Railroad Ton-Miles(billions, unless otherwise noted)1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pWaybill ton-miles, U.S. 1,055 1,033 1,089 1,124 1,208 1,303 1,362 1,374 1,433 1,490 1,530 1,581 1,587terminations 1U.S.-Canadaterminations (millionmetric tons) 2 11.479 10.398 11.362 12.482 14.502 15.391 16.474 18.403 17.099 15.175 17.624 19.813 19.606Conversion to short 12.654 11.462 12.525 13.759 15.986 16.966 18.160 20.286 18.849 16.728 19.427 21.840 21.612tons (millions)Average U.S. length 726 751 763 794 817 843 842 851 835 835 843 859 853of haul (miles) 3Ton-miles, U.S.-Canada 9.183 8.611 9.550 10.927 13.057 14.295 15.285 17.261 15.740 13.966 16.383 18.750 18.435terminationsWaybill ton-miles,1,621all trafficWaybill tons, all traffic2,078(millions)Waybill tons, traffic1,965within U.S. (millions)Mileage in Canada 150Canadian ton-miles 17Railroad ton-miles 1,064 1,042 1,098 1,135 1,221 1,317 1,377 1,391 1,448 1,504 1,546 1,599 1,606 1,604(improved BTS)Class I ton-miles1,034 1,039 1,067 1,109 1,201 1,306 1,356 1,349 1,377 1,433 1,466 1,495(NTS) 4Railroad ton-miles 1,091 1,100 1,138 1,183 1,275 1,375 1,426 1,421 1,442 1,499 1,534 1,558(Eno) 51 U.S. Department of Transportation, Surface Transportation Board, Carload Waybill Sample (Washington, DC: 1990–2003).2 Transport Canada, Transportation in Canada (Ottawa, Ontario, Canada: 1990–2002), Addendum, table A6-10.3 Association of American Railroads, Railroad Facts (Washington, DC: Various years), p. 36.4U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation Statistics (Washington, DC: 2003), table 1-44.5 Eno Transportation Foundation, Transportation in America (Washington, DC: 2002), p. 42.Key: p = preliminary.

TABLE A6 Waterborne Ton-Miles(billions)1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 PWater (NTS,834 848 857 790 815 808 765 707 673 656 646 622 612 606improved BTS) 1Coastwise 479 502 502 448 458 440 408 350 315 293 284 275 264 279Lakewise 61 55 56 56 58 60 58 62 62 57 58 51 54 48Internal 292 290 298 284 298 306 297 294 295 305 303 295 293 278Intraport 1 1 1 1 1 1 1 1 1 1 1 1 1 1Water (Eno) 2 353 345 353 340 356 366 355 356 357 362 360 348Rivers/canals 292 290 298 284 298 306 297 294 295 305 303 297Great Lakes,domestic61 55 56 56 58 60 58 62 62 57 58 511 U.S. Army Corps of Engineers, Waterborne Commerce of the United States (Washington, DC: 2003), Part V, Section 1, Table 1-4, Total Waterborne Commerce.2 Eno Transportation Foundation, Transportation in America (Washington, DC: 2002), p. 42.Key: p = preliminary.DENNIS 35

36 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005TABLE A7(a) Oil and Oil Products Pipeline Ton-Miles(billions)1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pOil pipeline (NTS,improved BTS, Eno) 1, 2 584 579 589 593 591 601 619 617 620 618 577 576 586 590TABLE A7(b) Natural Gas Pipeline Ton-Miles(billions, unless otherwise noted)1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 pTotal consumption, 19.174 19.562 20.228 20.790 21.247 22.207 22.609 22.737 22.246 22.405 23.333 22.239 23.018 21.894cubic feet (trillion) 3Lease and plant fuel, 1.236 1.129 1.171 1.172 1.124 1.220 1.250 1.203 1.173 1.079 1.151 1.119 1.114 1.123cubic feet (trillion) 3Pipeline fuel,cubic feet (trillion) 3 0.660 0.601 0.588 0.624 0.685 0.700 0.711 0.751 0.635 0.645 0.642 0.625 0.667 0.635Gas to consumers,cubic feet (trillion)17.278 17.832 18.469 18.994 19.438 20.287 20.648 20.783 20.438 20.681 21.540 20.495 21.237 20.136Gas to consumers, tons 4 0.391 0.404 0.418 0.430 0.440 0.459 0.467 0.471 0.462 0.468 0.488 0.464 0.481 0.456Oil pipeline ton-miles 1 584 579 589 593 591 601 619 617 620 618 577 576 586 590Oil pipeline tons 2 1.057 1.048 1.061 1.067 1.064 1.081 1.114 1.108 1.116 1.131 — — — —Length of haul (miles) 553 552 555 556 556 556 556 556 555 546 554 554 554 554Gas transmission216 223 232 239 245 255 260 262 257 256 270 257 267 253pipeline ton-milesGas gathering pipeline 11 11 12 12 12 13 13 13 13 13 14 13 13 13ton-miles (estimated) 5Gas distributionpipeline ton-miles(estimated) 5 11 11 12 12 12 13 13 13 13 13 14 13 13 13Total gas pipeline tonmiles(improved BTS)238 245 255 263 269 281 286 288 283 281 297 283 293 2781 Association of Oil Pipelines, Shifts in Petroleum Transportation (Washington, DC: 2003), table 1.2 Eno Transportation Foundation, Transportation in America (Washington, DC: 2002), p. 42.3 U.S. Department of Energy, Energy Information Administration, Annual Energy Review (Washington, DC: 2001), table 6.5.4 Conversion factor from U.S. Department of Energy, Energy Information Administration, International Energy Annual (Washington, DC: 2001), table C-1.5 Estimated at 5% of transmission ton-miles.Key: p = preliminary.

Spatial and Temporal Transferability of Trip GenerationDemand Models in IsraelADRIAN V. COTRUS 1JOSEPH N. PRASHKER 2YORAM SHIFTAN 2,*1 Department of Civil EngineeringTechnion, Israel Institute of TechnologyHaifa 32000, Israel2 Transportation Research InstituteTechnion, Israel Institute of TechnologyHaifa 32000, IsraelABSTRACTThis research investigates the transferability ofperson-level disaggregate trip generation models(TGMs) in time and space using two model specifications:multinomial linear regression and Tobit.The models are estimated for the Tel Aviv andHaifa metropolitan areas based on data from the1984 and 1996/97 Israeli National Travel HabitsSurveys. The paper emphasizes that Tobit modelsperform better than regression or discrete choicemodels in estimating nontravelers. Furthermore,the paper notes that variables and file structures inhousehold surveys need to be consistent. Results ofthe study show that the estimated regression andTobit disaggregate person-level TGMs are statisticallydifferent in space and in time. In spite of thetransferred forecasts, the aggregate forecasts werealso similar.INTRODUCTIONTrip generation models (TGMs) are used as a firststep in classical four-step travel demand modelingand, therefore, any over- or underprediction of tripgeneration rates can cause errors throughout theentire transportation planning process. Inappropriatedecisionmaking due to these types of errors canEmail addresses:* Corresponding author—shiftan@tx.technion.ac.ilA. Cotrus—cotrus@walla.co.ilJ. Prashker—prashker@netvision.net.ilKEYWORDS: Trip generation, transferability, multinomiallinear regression, Tobit model.37

account for premature investments in infrastructurein the case of overprediction and loss of laborhours, pollution, and low levels of service in thecase of underprediction.TGMs are usually estimated based on periodicsurveys of the travel habits of individuals or households.They are expensive and difficult to performand are not conducted often. For our research, weused the last Israeli National Travel Habits Surveyscollected in 1984 and 1996/97. Transportationplanners use models previously estimated andsometimes in different contexts. The planners canperform forecasts for the same areas and, if justifiable,transfer the models to other areas. Hence, it isimportant to know whether these models can betransferred in time and in space.Recently, researchers and planning agenciesbegan to implement tour-based activity modelingsystems rather than trip-based modeling systems. 1The advantage in using an activity modelingapproach is the ability to model each individual’stours. However, in this paper, we were only able toinvestigate the stability of individual predictions oftrips. This research presents the characteristics oftrip generation in Israel and tries to answer the questionof whether linear regression and Tobit TGMscan be transferred in time and space, given thedynamic changes in metropolitan areas and socioeconomiccharacteristics. The TGMs estimated andanalyzed in this research include only vehicular trips.We estimated the models for the geographicallydiverse metropolitan areas of Haifa and Tel Aviv inIsrael and tested them for transferability in spaceand in time. The topography of Haifa is hilly, withthe core of the city poorly connected to the rest ofthe metropolitan area. Tel Aviv lies on level topography,with a well connected road network. The metropolitanareas also differ structurally: Tel Aviv isinterconnected like a spider web, including severalminor cores with high-density population andemployment concentrations. On the other hand,Haifa’s less connected road network and rolling terraingive it a lower level of accessibility. When comparingthe areas by land use, the Tel Aviv1 Tours refer to a sequence of trips usually starting andending at home. Trips refer to just the movement betweenan origin and destination.metropolitan area consists of neighborhoods thatcombine residential shopping and personal businessareas. Haifa, on the other hand, contains highly separatedareas with each area consisting of a uniformland use.Given the difference in accessibility and land use,the calibrated models were restricted to demographicand socioeconomic variables. The averagenumber of daily trips per person was higher in theHaifa metropolitan area (2.14 in 1984, and 2.03 in1996/97) than in the Tel Aviv metropolitan area(1.83 in 1984, and 1.91 in 1996/97). The differencein the average trip rates may be explained based onthe variation in land uses. The lack of mixed landuses in Haifa may encourage the generation of moretrips. Furthermore, Haifa’s hilly topography mayencourage more vehicular trips than in Tel Aviv,where shorter trips are probably done on foot. Thecomparison between these metropolitan areas andthe calibrated models is possible due to the similarityof the distribution of most demographic andsocioeconomic variables. (See table 1 for a partialpresentation of the comparison.) A more detailedcomparison of Haifa and Tel Aviv characteristics ispresented in Cotrus (2001).LITERATURE REVIEWOver the last few decades, several papers have discussedthe transferability of trip generation models.The debate among researchers, in general, focusednot only on the transferability of models in spaceand time but also on the model specification andlevel of aggregation. The aggregation levels are usuallydefined as area (zonal), household, and person.Estimating the models (see, e.g., Ortuzar and Willumsen1994) at more disaggregate levels improvesthe transferability of TGM.Atherton and Ben-Akiva (1976) emphasized thatdisaggregated models tend to maintain the varianceand behavioral context of the response variableand, therefore, are expected to give better estimateswhen transferred. Downes and Gyenes (1976)pointed out that when the explanatory power ofthe model is of interest rather than the aggregateforecasts, the disaggregate level should be selected.Wilmot (1995) indicated that disaggregate modelsare preferred because of their independence from38 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 1 Demographic Characteristics by Metropolitan Area and YearHousehold and personalcharacteristicsHaifaTel Aviv1996 1996In terms In termsIn terms In termsof 1996 * of 1984 * 1984 of 1996 * of 1984 * 1984HOUSEHOLDSTotal (thousands) 245 160 130 766 678 522Persons in household (%)1 15.8 17.3 20.7 16.7 17.3 18.82 25.6 29.9 29.3 24.3 25.4 26.03–4 36.0 37.1 32.6 35.5 35.2 34.15–6 18.4 14.4 14.8 20.3 19.4 18.27+ 4.3 1.2 2.6 3.1 2.7 3.0Car availability0 38.4 36.7 51.6 34.3 33.8 51.11 42.0 40.7 40.3 40.0 39.9 39.12 11.4 12.3 7.4 17.5 17.5 9.43+ 1.6 1.9 — 2.6 2.8 —Not known 6.6 8.4 — 5.6 6.0 —Households with vehicles (%) 55.0 54.9 48.4 60.1 60.2 48.9TOTAL POPULATIONTotal (thousands) 803 470 380 2,477 2,145 1,632Age (%)0–7 13.5 11.0 14.8 13.7 13.0 14.88–17 18.5 15.8 15.7 17.3 16.8 17.618–29 18.0 17.7 16.3 18.2 18.3 17.730–64 38.2 40.1 39.4 39.5 39.8 37.965+ 11.8 15.4 13.8 11.4 12.0 12.0POPULATION AGED 8+Total (thousands) 695 419 324 2,138 1,866 1,390Sex (%)Men 48.5 48.1 47.9 48.3 48.2 49.7Women 51.5 51.9 52.1 51.7 51.8 50.3Years of schooling (%)0–8 31.3 24.2 34.7 26.5 25.8 39.29–12 37.9 37.8 40.7 41.0 41.0 40.113+ 25.1 30.1 24.6 27.4 27.6 20.7Not known 5.7 7.9 — 5.0 5.5 —POPULATION AGED 15+Total (thousands) 589 367 281 1,833 1,609 1,177Employed (%)Total 47.3 46.8 49.1 51.3 51.2 50.3Men 57.8 55.1 61 54.1 53.5 61.5Women 42.2 44.9 39 45.9 46.5 38.5POPULATION AGED 17+Total (thousands) 559 351 270 1,752 1,540 1,127Those having a driver’s license (%) 53.0 54.2 46.6 59.8 60.0 49.8Men (%) 63.0 59.7 64.8 58.6 57.9 66.0Women (%) 37.0 40.3 35.2 41.4 42.1 34.0* In terms of 1984 refers to the geographic definition of the metropolitan area in that year. In term of 1996 refers to the geographicdefinition of the metropolitan area that year.COTRUS, PRASHKER & SHIFTAN 39

zonal definitions. In Supernak et al. (1983) andSupernak (1987), the person level was preferred forTGM because of the identity of the response factor(trip) and the generative (the person). One advantageof disaggregate person-level models is the reducedamount of data required for model estimation. (Formore details, see Fleet and Robertson 1968; andOrtuzar and Willumsen 1994.) Other types of modelspecification techniques include cross-classification,regression, logit-based models, artificial neural networks,fuzzy logic, and simulations.A number of studies found spatial transferabilityof models satisfactory (Wilmot 1995; Atherton andBen-Akiva 1976; Supernak 1982, 1984; Duah andHall 1997; Walker and Olanipekun 1989; Rose andKoppelman 1984; Caldwell and Demetsky 1980;and Kannel and Heathington 1973). On the otherhand, Smith and Cleveland (1976) and Daor (1981)found spatial transferability unsatisfactory. Weshould emphasize that Smith and Cleveland pointedout that although the explanatory variables are distinctive,their effects vary in space. A number ofresearchers found the transferability of models intime (i.e., their temporal stability) satisfactory(Downes and Gyenes 1976; Yunker 1976; Walkerand Peng 1991; Kannel and Heathington 1973; andKarasmaa and Pursula 1997). Unsatisfactoryresults, however, were obtained in other studies(Doubleday 1977; Smith and Cleveland 1976; andCopley and Lowe 1981).While several international studies exploredmodel transferability in time and space, in Israel thetransferability of discrete mode choice models hasbeen the main focus (Prashker 1982; Silman 1981).This study deals with the investigation of trip generationcharacteristics but also provides local estimatesof TGMs and their validation for transferability intime and space. The study also explores the implementationof Tobit models in TGM.We often approach trip generation from an economicviewpoint, where trips are defined as theproduct and the person/household as the customer.The strongest argument to model trips on a disaggregatelevel is that any zonal outcome is based onthe aggregation of several customers, ignoring theheterogeneity among them. The explanatory variablesfor the power of consumption of each person/household can be found in several categories includingdemographic, geographic, and economic.As discussed above, several approaches exist tomodel trip generation, including regression-basedmodels such as multiple linear regression (Wilmot1995) and cross-classification (Walker and Olanipekun1989); discrete choice models such as probit,logit, and ordered probit (Zhao 2000); simulationssuch as Smash, Amos, and the Starchild System;fuzzy logic models; and artificial neural networks(Huisken 2000). Clearly, the issue of trip generationcan be approached from several directions andtested for transferability in time and space. Therefore,researchers will choose the modeling approachbased on the size of the database at hand, the natureand structure of the variables, the aggregation leveldesired, as well as other considerations. The mainproblem with using a regression model is the treatmentof trip rates as continuous rather than discretevariables. Discrete choice models and spatiallyordered response models may better account for thebehavioral process of trip generation. However, dueto practical reasons, in most models to date, thedependent variable is treated as a continuous variable.For this reason, we perform our analysis onsuch models.METHODOLOGYIn this research, we first estimated regression modelsfor each metropolitan area for each year, taking intoaccount the inconsistency of the household surveys(table 2). We then estimated Tobit TGMs based onthe same variables and tested whether these modelsare suitable for trip generation estimation and fortransferability. The regression model form is presentedin equation 1.y i = α + β 1 • x 1, i + β 2 • x 2, i ...+β k • x ki +∀i= 1 ,...,n, ζ iwherey i = trip rate generated by individual i,x k,i = explanatory variable k for individual i,n = the number of observations,k = number of explanatory variables, and= error term of the ith observation.ζ i∀k=1,2 ,...,k(1)40 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 2 Differences Among the 1972, 1984, and 1996/97 Traveling Habits SurveysNo. Topic 1972 survey 1984 survey 1996/97 survey1 Trip modes surveyed Motorized trips only,although data on travel onfoot were also gathered2 Survey population Permanent residents ofIsraelIsraeli residents abroad forless than 1 yearPotential immigrants:persons who were eligible forimmigrant cards and wishedto stay in Israel for more than3 monthsTourists, volunteers, andtemporary residents in Israelfor more than 1 yearExcluding diplomats and UNpersonnelMotorized and nonmotorizedtripsPermanent residents of IsraelIsraeli residents abroad forless than 2 monthsImmigrants and potentialimmigrants who arrived inIsrael before June 1983Same as in 1972Only motorized tripsPermanent residents of Israel,including Jews domiciled inJudea, Samaria, and Gaza.Israeli residents abroad for lessthan 1 yearImmigrants who reached Israelbefore the survey dateTourists, volunteers, andtemporary residents in Israelfor more than 3 monthsSame as in 1972 Same as in 19723 Age 5+ 8+ 8+4 Tenants ofinstitutionsIncluding institutions where 5or more persons spend thenightInstitutions not includedIncluding students dormitories,immigrant-absorption centers,and sheltered housing5 Gross sample size 56,000 households 5,000 households 17,700 households6 Geographic spreadand locality typeCountrywide (excludingJudea, Samaria, and Gaza)Localities with populations of10,000+Small localities directlyrelated to the conurbation7 Investigation period November 1972–June 1973;not including summermonths and holidays8 Number ofinvestigation daysOne 24-hour day, starting at14:00 on day precedingenumerator’s visit andending at time of visit9 Investigation days Sunday–Thursday; the entireperiod from Thursdayevening to Sunday noon wasnot investigated; holidayeves were not investigated;Sundays were investigatedat the previous day level, andThursday at the current daylevelTwo expanded conurbationsand Jerusalem and itssurroundingsNot including Arab localities inJudea DistrictNot including kibbutzim andvillagesJanuary 1984–May 1985; 2month interruption: July–August 19841.5 24-hour days, starting onday preceding enumerator’svisit and ending at time of visitSame as in 1972CountrywideNot including Druze localitieson the Golan Heights,institutional local cities, andareas outside settled area,including Bedouin tribes in theNegevIncluding kibbutzim andvillagesMarch 1996–February 1997;supplementary period: March–August 1997.3–4 investigation days, startingat beginning of day precedingenumerator’s visit and endingat end of day afterenumerator’s visitAll days of the week; holidayswere investigated; Thursdayswere not investigated at theprevious day level; Sundayswere not investigated at thenext-day level; and Friday–Saturday were not investigatedat the current-day level(continues on next page)COTRUS, PRASHKER & SHIFTAN 41

TABLE 2 Differences Among the 1972, 1984, and 1996/97 Traveling Habits Surveys (continued)No. Topic 1972 survey 1984 survey 1996/97 survey10 InvestigationvariablesDemographic and economicvariables of household andindividualTravel-related variables:origin, destination, hour, etc.Variables related to vehiclesavailable to household:number of vehicles, type ofvehicles, etc.11 Investigation method Questionnaire filled in byenumerator12 Geographic regions Tel Aviv and HaifaconurbationsTel Aviv conurbation: 27localitiesHaifa conurbation: 8localities13 Trips Several actions—switchingvehicles, stopping andexiting vehicle, switchingdrivers, and changing travelroutes—were defined ashaving created two separatetrips14 Means of transport One means of transport pertripSame as in 1972 Same as in 1972Same as in 1972 Same as in 1972Same as in 1972Same as in 1972Tel Aviv and Haifaconurbations and Jerusalemand its surroundingsTel Aviv conurbation: 41localities (4 more were addedduring the survey, for a total of45)Haifa conurbation: 14localities; Jerusalem and itssurroundings: 12 localitiesA trip was defined by its mainpurpose even if there werestops on the wayReaching the destination bytwo means of transport oralong two routes wasconsidered one tripPossibility of more than onemeans of transport per tripSame as in 1972, plusvariables related to parkingQuestionnaire filled in byenumerator and diary left withrespondents to fill inDivision into geographicregions performed only atsurvey data analysis phase:Tel Aviv metropolitan area,Haifa metropolitan area,planned metropolitan area ofBeer Sheva, and Jerusalemand its surroundingsTel Aviv metropolitan area: 259localitiesHaifa metropolitan area: 101localitiesPlanned metropolitan area ofBeer Sheva: 130 localitiesSame as in 1972Same as in 1972Source: Israeli Ministry of Foreign Affairs, Central Bureau of Statistics, 1996/97 Household Survey: Description of Survey (English inorigin).Hald (1949) first presented the model that, in itsfinal form, is called the Tobit model (1958). Tobitmodels differentiate from regression models by theincorporation of truncated or censored dependentvariables. Tobit analysis assumes that the dependentvariable has a number of its values clustered at alimiting value, usually zero. The Tobit model can bepresented as a discrete/continuous model that firstmakes a discrete choice of passing the thresholdand second, if passed, a continuous choice regardingthe value above the threshold. This approach isappropriate for trip generation, as an individualmust decide whether to make any trips and, if so,how many trips to make.Tobit analysis uses all observations when estimatingthe regression line, including those at the limit(no trips) and those above the limit (those who choseto travel). As shown by McDonald and Moffitt(1980), Tobit analysis can be used to determine thechanges in the value of the dependent variable if it isabove the limit, as well as changes in the probabilityof being above the limit. Since the surveys include42 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

observations at the limit (i.e., persons that are nottraveling), it was also interesting to find out howwell the Tobit model can predict persons doing notravel at all. The Tobit model form is presented inequation 2:y i = X i • β + ζ i if X i • β + ζ i > 0y i = 0if X i • β + ζ i ≤ 0∀i= 1, 2, 3 ,...,( N – 1) , N(2)whereN = number of observations,y i = trip rate generated by observation i,X i = vector of independent variables,β = vector of coefficients, andζ = independently distributed error term ∼ 0,σ 2 .⎝⎛ ⎠⎞Because Tobit models have not been used previouslyin the context of trip generation, this research investigatestheir suitability for that purpose. We alsocompared the predictions obtained using regressionmodels with those produced using the analogousTobit model. The best specification of the regressionmodel is not necessarily the best specification of theTobit model. However, in order to allow for basiccomparisons of the model parameters, we estimatedthe regression models first; then, after the determinationof the final variables in the model, we estimatedTobit models with the same variables.All models were estimated at the disaggregateperson level. At the person level of modeling, wemaintained the heterogeneity among observationsand kept a good identity between the consumer ofthe product (the person) and the outcome (numberof daily trips taken by the person). As discussedabove, disaggregate models tend to show bettertransfer results than aggregate models and alsoincorporate the power to understand and controlthe production of trips. The models were estimatedfor a 24-hour period 2 and tested for transferabilityin space and in time. Figure 1 presents the sequenceof the analysis.Statistical tests were conducted to determine thespatial and temporal stability of the estimated modelsby assessing the transferability of the coefficientsfrom one area to another, and for each metropolitan2 The 1984 household survey contained 1.5 days of datafor each person; the 1996/97 survey contained 3 to 4 daysof data for each person.area between the two survey years. Transferabilitywas also tested by comparing the overall aggregateprediction obtained by the transferred model withthe local model. Furthermore, we analyzed theability of Tobit models to represent and evaluatenontravelers, that is, people who do not generatetrips based on the given survey data.Data Sources and DescriptionsThe Israeli Central Bureau of Statistics (CBS) conductedsome limited scope 3 Traveling Habits Surveysin the 1960s. Comprehensive National TravelingHabits Surveys have been conducted by CBS every12 years since 1972. Because the 1972 survey is notavailable on magnetic media, it was not possible todo a computer-based statistical analysis. Therefore,we based this research on the 1984 and 1996/97household surveys.The main problems we encountered in doing thisresearch were related to the inconsistency in theinvestigated variables, the structure of the surveys,the definition of variables, the period of investigation,the geographic deployment, and the databasestructure (see table 2 again). The 1984 and 1996/97household surveys differ in several ways: the geographicdeployment (number and size of jurisdictionsin the survey), the size of the survey (number ofhouseholds), the definitions of the investigationperiod, and the variables that were excluded fromthe surveys. For example, income is included in the1984 survey but is omitted from the 1996/97 survey.Despite definition and database differences inthe two surveys (1984 was an activity survey and1996/97 was a trip survey), we were able to bringthe variables in the models to a common basis. Inparticular, the 1984 survey included bicycle andwalking trips among the means to accomplish theactivities, while the later survey excluded them. Toresolve this difference, we excluded walking andbiking trips from the 1984 database; only motorizedtrips were considered for each person.The 1984 survey files included data for 5,420persons in the Tel Aviv metropolitan area and4,056 persons in the Haifa metropolitan area. Thefinal files used for model calibration after sieving3 These surveys were restricted to work-related activitiesonly.COTRUS, PRASHKER & SHIFTAN 43

FIGURE 1 Research Sequence of StagesHaifa metropolitan areadatabaseTel Aviv metropolitanarea databaseHouseholdlevelHouseholdlevelPersonlevelPersonlevelActivitylevelActivitylevelSTEP 1: Missing data—missing fieldsSTEP 2: Comparison of grand means with previous publicationsSTEP 3: Outliers—extreme valuesSTEP 4: Omitting observations/variablesDatabaseModelcalibrationMLR modelcalibrationTobit modelcalibrationHaifa1984Temporal transferabilityHaifa1996/97SpatialTLV1984Temporal transferabilityTLV1996/97Spatial44 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

incomplete and anomalous observations totaled4,385 and 3,258 persons, respectively. The 1996/97files included data for 20,436 persons in the TelAviv metropolitan area and 6,417 persons in theHaifa metropolitan area. The final files used formodel calibration totaled 15,729 and 5,041 persons,respectively.RESULTSThe selected trip generation models included six categoricalvariables: age, car availability, possession ofa driver’s license, employment, education, and statusin the household. Data fell into five age categories:8–13, 14–17, 18–29, 30–64, and 65 and over.Ortuzar and Willumsen (1994) found that life cyclevariables were an important factor for explainingtrip generation. Different trip rates can be expectedfor households and people at various stages of life.Furthermore, age should correlate with employment,having a driver’s license, and marital status. Caravailability included three categories: 0, 1, and ≥ 2cars in the household. Clearly, households with morecars available will generate more trips. The driver’slicense category has only one variable: whether theperson has a license (including motorcycle) or not.The employment variable indicates whether theperson was employed or not. Employed personswere expected to generate more trips, because theyusually make at least two trips: to and from work.Household status refers to whether the persondefines himself or herself as the head of the household.This variable indicates the responsibility andavailability of household resources as an incentivefor consumption of trips.Finally, four education categories were definedbased on the number of years of study (0, 1–8, 9–12, and 13 or more). The literature shows good correlationbetween education and income. In theabsence of a pure economic indicator, education isused also as a proxy for income. Respondents withhigher education (hence higher income) wereexpected to generate more trips. All variables werefound significant and the coefficients correspondedwith our expectations.Table 3 shows the estimation results for theregression models for 1984 for both metropolitanareas. As can be seen from the table, all coefficientswere found to be significant at the 95% level. Thenumber of observations remaining in the estimationprocess resulted from the limited scope of this surveyand the elimination of incomplete observations inthe original database.Estimation results for these models show that allvariables affected trip generation as expected. Theeducation coefficients show that people with highereducation generated more trips. This can beexplained not only by the assumption of the relationshipbetween education and income but also byassuming that a person with higher education ismore likely to pursue culture and perhaps leisureactivities. Also, as expected, persons with driver’slicenses and employed persons tended to generatemore trips than the equivalent nonworking and/ornondriving persons. Heads of household tended togenerate more trips, as assumed, because of theresponsibility and availability of resources. Thecoefficients of the age categories indicate that personsaged 14 to 17 travel more than people withsimilar characteristics of other age groups, probablybecause they are young and active and have lesshousehold or work responsibilities.The overall R 2 of the 1984 models was 0.33 forthe Tel Aviv model and 0.34 for the equivalentHaifa model. These R 2 values are modest but notanomalous for trip generation modeling. Theyindicate that a substantial portion of trip generationcan be explained by nonhousehold factors,such as relative location of residence, employment,and other parameters. Statistical Z tests (assumingknown variances, normal distributions, and independenceof populations) for the transferability ofthe coefficients (without updating) show that, at a95% level of confidence, the coefficients differ,except for the coefficient defining the head ofhousehold. To verify the results we also conductedChow tests for the transferability of the models.The calculated statistic was 7.86 in comparisonwith the critical 1.72 F-value (at a 95% level ofconfidence), and yield the same conclusion that the1984 models are not transferable in space.Table 4 shows the results of transferring the modelsin space by showing the predictions from theestimated models and the 1984 database, eachapplied for both metropolitan areas. The tableCOTRUS, PRASHKER & SHIFTAN 45

TABLE 3 Regression Models by Metropolitan Areas: 1984HaifaTel AvivVariableCoefficient t statisticStandarderror Coefficient t statisticStandarderrorRegression intercept 4.10 30.26 0.13 3.51 32.47 0.11Age8–13 0.60 4.32 0.14 0.35 3.22 0.1114–17 0.72 4.98 0.14 0.80 6.75 0.1218–29 0.39 3.19 0.12 0.53 5.33 0.0930–64 0.24 2.33 0.10 0.42 4.89 0.0865+ 0.00 — — 0.00 — —Number of cars perhousehold0 –0.83 –7.74 0.11 –0.80 –10.25 0.081 –0.39 –4.22 0.09 –0.46 –6.71 0.072+ 0.00 — — 0.00 — —Driver’s licenseNo license –0.99 –11.23 0.09 –0.67 –9.80 0.07License 0.00 — — 0 — —EmployedNot employed –1.06 –13.17 0.08 –1.00 –15.58 0.06Employed 0.00 — — 0.00 — —Household statusHead (0 = no) –0.24 –3.13 0.07 –0.24 –3.82 0.06Head (1 = yes) 0.00 — — 0.00 — —Education0 years –0.77 –3.98 0.19 –0.87 –6.50 0.131–8 years –0.69 –6.80 0.10 –0.68 –8.57 0.089–12 years –0.24 –2.95 0.08 –0.36 –5.50 0.0713+ years 0.00 — — 0.00 — —Overall R 2 0.34 0.33Number ofobservations used 3,243 4,356Notes: Chow test for 1984 model transferability:Ess 1 = error sum of squares of Haifa setEss 2 = error sum of squares of Tel Aviv setEss 3 = error sum of squares of combined setK = number of parameters in the model including the constantN i = number of observations in model i1 2H 0 : β i = β i ∀iH 1 = else α=0.05Ess 3 – ( Ess 1 + Ess 2 ) N---------------------------------------------------- 1 + N 2 – 2 • K-------------------------------------KEss 1 + Ess 2F( k , N1 + N 2– 2 • K) = F ( 13, ∞ ) = 1.72 ⇒ H 1• =------------------------------------------------------------20124 – ( 9351 + 10505 ) 3243 + 4356 – 2 • 13• ------------------------------------------------- = 7.86139351 + 1050546 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 4 Aggregate Estimation Results Using Regression Models: 1984Average trips perperson per dayHaifa data Tel Aviv dataTel Aviv HaifaHaifa Tel Avivmodel model Actual model model Actual1.84 2.18 2.18 2.19 1.84 1.84Negative estimations 24 0 — 0 32 —Minimum trip rate –0.07 0.20 0 0.20 –0.07 0Maximum trip rate 4.04 4.49 11 4.49 4.04 10Total 5,973 7,060 7,059 9,525 8,007 8,019Difference betweenmodel estimationand actual values–15.37 0.00 — 18.79 –0.15 —Standard deviation 1.10 1.21 2.08 1.18 1.07 1.90shows that the Haifa model overpredicts the actualtrip rate when applied to the Tel Aviv database, incomparison with the Tel Aviv model applied to theHaifa database. This was expected, as the Haifa triprate is higher than that for Tel Aviv.Table 5 presents the estimation results for the1984 Tobit models using the 1984 household surveydata. When we transferred the estimated Tobitmodels in space and used them to predict the averagetrip rate in the other city, we found that theHaifa Tobit model overestimated the trips in TelAviv by 21.9% (table 6). When we used the estimatedTel Aviv Tobit model to predict the averagetrip rate for Haifa, we found that it underestimatedthe total trips by 27.5%. However, transferability t-tests at a 95% level of confidence showed that mostof the coefficients are not significantly different inspace, except for the license variable and the 8–13and 30–64 age category variables. On the otherhand, χ 2 tests at the 95% level of confidencestrengthen the alternative hypothesis, that the2models vary in space ⎛χ 13,0.95 = 22.36 < 91.198⎞.⎝⎠An important issue was to find out whether theTobit model could explain and capture the nontravelersin the population. As can be seen in table 7,the results are not consistent for the two models.The Haifa 1984 model correctly estimated only13.5% of the observed nontravelers in the Haifadata and 18.5% in the Tel Aviv data. The Tel Avivmodel obtained better results estimating correctly41.9% of the observed nontravelers in the Tel Avivdata and 34.7% in the Haifa data. These resultsencourage further research.Table 8 presents the estimation results of the1996/97 regression models. As can be seen, the1996/97 coefficients differ substantially from thoseof 1984, and most of the coefficients are significantat the 95% confidence level. The best model specificationfor 1984 was found to be also the bestspecification for the 1996/97 model, indicatingthat the most important variables affecting tripgeneration are similar in both models. The mainproblem raised during the basic comparison wasthe difference in the geographic scope (definitionof the metropolitan survey area) for the two.The overall R 2 of the 1996/97 models, 0.21 forthe Tel Aviv model and 0.23 for the equivalentHaifa model, are even smaller than the valuesachieved for the 1984 models. But they are still notanomalous in the field of trip generation modeling.Statistical Z-tests conducted at the 95% level ofconfidence show that none of the coefficients are thesame for the two metropolitan areas; that is, thecoefficients differ in space. To verify the results, weconducted Chow tests for the transferability of themodels. The calculated statistic was 6.91 in comparisonwith the 1.72 tabular F-value (at a 95% level ofconfidence), thus yielding the same conclusion, thatthe 1996/97 models are not transferable in space.COTRUS, PRASHKER & SHIFTAN 47

TABLE 5 Tobit Models by Metropolitan Areas: 1984HaifaTel AvivVariable Coefficient t statistic Coefficient t statisticRegression 3.91 41.67 3.15 40.23Age8–13 1.25 7.79 0.81 6.0114–17 1.46 7.97 1.76 10.7418–29 0.95 6.95 1.30 11.0830–64 0.63 6.36 0.99 11.4365+ 0.00 — 0.00 —Number of cars perhousehold0 –1.10 –11.30 –1.11 –12.761 –0.48 –4.91 –0.57 –6.772 0.00 — — —Driver’s licenseNo license –1.12 –13.24 –0.89 –11.92License 0.00 — 0.00 —EmployedNot employed –1.65 –19.80 –1.67 –22.20Employed 0.00 — 0.00 —Household statusHead (0 = no) –0.36 –4.29 –0.42 –5.85Head (1 = yes) 0.00 — 0.00 —Education0 years –1.70 –5.36 –1.70 –7.041–8 years –1.06 –9.82 –1.02 –11.149–12 years –0.32 –3.38 –0.41 –4.7913+ years 0.00 — 0.00 —Standard error of U 2.40 2.50Overall pseudo R 2 0.33 0.32Number ofobservations used3,243 4,356Log likelihood –5,742.89 –7,173.62Log likelihoodconstant only–6,453.65 –8,134.6148 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 6 Aggregate Estimation Results Using Linear Tobit Models, by YearHaifa dataTel Aviv data1984 data and modelsTel AvivmodelHaifamodel ActualHaifamodelTel Avivmodel ActualAverage trips per person per day 1.84 2.18 2.18 2.18 1.84 1.84Observations with negativeestimates24 0 — 0 0 —Minimum trip rate 0 0 0 0 0 0Maximum trip rate 4.43 5.21 11.00 5.21 4.86 10.00Total 5,115 7,321 7,059 9,772 7,883 8,019Difference between model –27.54 3.71 — 21.85 –1.69 —estimation and actual valuesStandard deviation 1.30 1.52 2.08 1.50 1.48 1.90Haifa dataTel Aviv dataTel Aviv HaifaHaifa Tel Aviv1996/97 data and modelsmodel model Actual model model ActualAverage trips per person per day 1.93 2.02 2.07 2.21 2.06 2.07Observations with negativeestimates 0 0 — 0 0 —Minimum trip rate 0 0 — 0 0 —Maximum trip rate 4.30 4.57 11.00 5.05 4.41 11.00Total 9,672 10,184 10,414 34,797 32,363 32,455Difference between modelestimation and actual values–7.13 2.20 — 7.21 –0.28 —Standard deviation 1.28 1.42 2.08 1.42 1.29 1.99TABLE 7 Tobit Model Estimation of Nontravelers: 1984Estimatednontravelers (persons)Observednontravelers predictedas nontravelersTel AvivmodelHaifa dataHaifamodelObserved752 277 1,655(37.99% of totalobservations)HaifamodelTel Aviv dataTel AvivmodelObserved244 635 1,014(31.27% of totalobservations)575 224 — 188 425 —Right estimation (%) 34.7 13.5 — 18.5 41.9 —Common observed 76.5 80.6 — 77.0 66.9 —and estimated (%)Key: Right estimation = observed nontravelers predicted as nontravelers / observed * 100 ;common = observed nontravelers predicted as nontravelers / estimated * 100.COTRUS, PRASHKER & SHIFTAN 49

Table 9 presents the predicted average daily tripsusing the 1996/97 data for each model and eachmetropolitan area. As in 1984, the 1996/97 Haifamodel overpredicts trips compared with the Tel Avivmodel, however, the differences are smaller. Oneshould remember that in regression models, theregression line always passes through the average(center of gravity of the observations). Since theobserved average number of trips (in Tel Aviv andHaifa) was equal in the 1996/97 metropolitan files,the estimation difference was expected to be smaller.However, the similar predicted aggregate trip ratesindicate overrepresentation of particular sections ofthe population. For example, the calculated averagecar availability per household in metropolitan TelAviv was higher in the 1996/97 surveys than inmetropolitan Haifa (0.60 > 0.55), but in 1984 theaverage car availability per household was almostthe same (0.489 ≈ 0.484). Statistically, differentdefinitions of the sampling areas could affect thetransferability of the estimated modelsTable 10 shows the Tobit model results for 1996/97. A comparison with table 8 shows the resemblancein the effect of the explanatory variables andthe difference in the magnitude of the coefficientsbetween the Tobit and the regression models.Transferring the models in space and evaluatingthe estimated average trip rate from the models, for1996/97, we found that the Haifa Tobit model overestimatedthe trips in the Tel Aviv file by 7.2% andthe Tel Aviv Tobit model underestimated the trips inthe Haifa file by 7.1% (table 6). These values arequite similar to the over- and underprediction ofthe equivalent regression models shown in table 9.Spatial transferability t-tests held at the 95% levelof confidence show that most of the coefficients arenot significantly different between the metropolitanareas, except age categories and the education“non-educated” category. χ 2 tests for the spatialtransferability of the models at the samelevel of confidence reach the same conclusion2⎛χ 13,0.95 = 22.36 <

TABLE 8 Regression Models by Metropolitan Area: 1996/97HaifaTel AvivStandardStandardVariable Coefficient t statistic error Coefficient t statistic errorRegression coefficient 3.34 29.67 0.11 3.30 55.10 0.06Age8–13 0.19 1.62 0.12 0.14 2.11 0.0714–17 0.73 5.70 0.13 0.40 5.55 0.0718–29 0.45 4.65 0.10 0.36 6.54 0.0530–64 0.55 6.35 0.09 0.34 7.00 0.0565+ 0.00 — — 0.00 — —Number of cars per household0 –0.81 –9.50 0.08 –0.73 –16.76 0.041 –0.40 –5.52 0.07 –0.35 –9.96 0.032+ 0.00 — — 0.00 — —Driver’s licenseNo license –0.79 –10.51 0.07 –0.68 –16.59 0.03License 0.00 — — 0.00 — —EmployedNot employed –0.84 –11.93 0.07 –0.78 –20.74 0.04Employed 0.00 — — 0.00 — —Household statusHead (0 = no) –0.33 –5.28 0.06 –0.34 –10.12 0.03Head (1 = yes) 0.00 — — 0.00 — —Education0 years 0.39 3.39 0.11 0.15 2.29 0.071–8 years –0.40 –4.25 0.09 –0.39 –7.16 0.059–12 years –0.06 –0.90 0.07 –0.19 –5.32 0.0413+ years 0.00 — — 0.00 — —Overall R 2 0.23 0.21Number of observationsused5,027 15,689Notes: Chow test for 1984 model transferability:Ess 1 = error sum of squares of Haifa setEss 2 = error sum of squares of Tel Aviv setEss 3 = error sum of squares of combined setK = number of parameters in the model including the constantN i = number of observations in model i1 2H 0 : β i = β iH 1 = else α=0.05Ess 3 – ( Ess 1 + Ess 2 ) N---------------------------------------------------- 1 + N 2 – 2 • K-------------------------------------KEss 1 + Ess 2F( k , N1 + N – 2 • K) = F ( 13, ∞ ) = 1.72 ⇒ H 12• =---------------------------------------------------------------65202 – ( 16635 + 48285 ) 5027 + 15689 – 2 • 13• ---------------------------------------------------- = 6.911316635 + 48285COTRUS, PRASHKER & SHIFTAN 51

TABLE 9 Aggregate Estimation Results Using Regression Models: 1996/97Haifa dataTel Aviv dataTel AvivmodelHaifamodelActualHaifamodelTel AvivmodelActualAverage trips per person per day 1.93 2.07 2.07 2.22 2.07 2.07Observations with negativeestimates 0 0 — 0 0 —Minimum trip rate 0.37 0.16 — 0.16 0.37 —Maximum trip rate 3.67 3.89 11.00 4.28 3.80 11.00Total 9,748 10,450 10,414 34,788 32,341 32,455Difference between model –6.39 0.35 — 7.19 –0.35 —estimation and actual values (%)Standard deviation 0.91 1.00 2.08 1.01 0.92 1.99from the two models for the same year were not significantlydifferent. The distinction cannot be wellexplained, but it might be due partially to geographic,demographic, socioeconomic, and spatialstructure differences between the two metropolitanareas. The smaller sample size and scope of the1984 household survey compared with the 1996/97household survey (as shown in table 2) did notallow us to represent the ethnicity of the surveyparticipants, a variable believed to be related to tripgeneration. Also, the incorporation in the models ofa pure economic variable such as income was notpossible, because it was not included in the 1996/97survey.We ascribed the temporal instability of the estimatedmodels to changes in the structure anddevelopment of the metropolitan areas of Tel Avivand Haifa, changes in lifestyle and socioeconomicvariables that are not all accounted for in the model,as well as the inconsistency of the two surveys. Apartial explanation may be that 1984 was an economicallyunstable year, featuring high inflationrates and uncertainty, while 1996/97 was consideredto be economically stable.An important conclusion based on our results isthat in order for trip generation models to be transferablethey need to account for variables notincluded in the current models: income, land use andspatial structure, the economy, the transportationsystem and accessibility, and more detailed socioeconomicand life style variables. If we could estimate aperfect disaggregate model accounting for all factorsthat affect trip generation and with appropriate segmentation,it would likely be transferable. With thisdata lacking, models are not transferable, becauseunobserved variables affect coefficients of observedvariables with which they are correlated.Another conclusion is that household surveysconducted on a regular basis will be more useful ifthe design stays constant. Differences in the structure,variables, range, investigation period, definition ofthe variables, and database structure affect thetransferability of the estimated models.We also would emphasize the need for furtherresearch on the implementation of Tobit models inthe context of trip generation. Tobit models tend torepresent the mechanism of trip generation morerealistically, capturing and estimating (partially)nontravelers. As a combination of regression anddiscrete choice models, the Tobit model may bemore suitable for implementation in TGM thandiscrete choice or regression models, particularlybecause Tobit is better formulated to differentiatenontravelers from travelers. The underestimation ofnontravelers may be partly due to the fact that wedid not necessarily estimate the best Tobit model.For the linear regression models, almost all variableswere significant at the 95% confidence level,but the coefficients were shown to vary in time andspace. For the Tobit model, while almost all variableswere significant at the 95% confidence level, thecoefficients of the models of the two metropolitanareas were statistically similar but they differed intime for each city.52 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 10 Tobit Models by Metropolitan Areas: 1996/97HaifaTel AvivVariable Coefficient t statistic Coefficient t statisticRegression intercept 3.00 36.84 3.04 68.47Age8–13 0.62 3.69 0.46 5.0314–17 1.53 8.93 0.85 9.1418–29 1.02 8.83 0.76 12.1430–64 1.07 12.10 0.68 14.2065+ 0.00 — 0.00 —Number of cars per household0 –1.20 –12.68 –1.07 –20.421 –0.52 –6.09 –0.47 –10.402+ 0.00 — 0.00 —Driver’s licenseNo license –1.08 –12.89 –0.97 –21.38License 0.00 — 0.00 —EmployedNot employed –1.36 –17.25 –1.27 –29.96Employed 0.00 — 0.00 —Household statusHead (0 = no) –0.56 –7.42 –0.48 –11.66Head (1 = yes) 0.00 — 0.00 —Education0 years 0.50 4.21 0.21 3.141–8 years –0.77 –7.27 –0.60 –10.069–12 years –0.12 –1.34 –0.19 –4.2113+ years 0.00 — 0.00 —Standard error of U 2.85 2.67Overall pseudo R 2 *Number ofobservations used0.23 0.215,026 15,689Log likelihood –9,060.98 –28,376.08Log likelihoodconstant only–9,806.57 –30,515.70* Pseudo R 2 is a measure of goodness of fit similar to R 2 in ordinary least squares. The residuals are calculatedbased on the maximum likelihood estimators. For details of its calculation, see the EasyReg manual, available athttp://econ.la.psu.edu/~hbierens/EasyRegTours/ TOBIT_Tourfiles/TOBIT.PDF.COTRUS, PRASHKER & SHIFTAN 53

TABLE 11 Tobit Estimation of Nontravelers by Metropolitan Areas: 1996/97Nontravelers(persons)HaifamodelHaifa dataTel AvivmodelObserved293 90 1,769(35.19%)Tel AvivmodelTel Aviv dataHaifamodelObserved722 505 5,167(32.93%)Observed nontravelerspredicted as nontravelers209 67 — 504 353 —Right estimation (%) 11.81 3.78 — 9.75 6.83 —Common observed and 71.33 74.44 — 69.80 69.90 —estimated (%)Key: Right estimation = observed nontravelers predicted as nontravelers / observed * 100;common = observed nontravelers predicted as nontravelers / estimated * 100.TABLE 12 Temporal Transferability Results of the 1984 Models in the 1996/97 FilesTEL AVIVREGRESSIONAverage trips perperson per day1984 Tel AvivmodelHaifa data1996/97Tel AvivmodelActual1984 Tel AvivmodelTel Aviv data1996/97Tel AvivmodelActual1.76 1.94 2.07 1.92 2.06 2.07Negative estimations 545 — — 1,464 — —Minimum trip rate –0.40 0.37 0 –0.40 0.16 0Maximum trip rate 4.04 3.67 11 4.04 3.80 11Total 8,850 9,748 10,414 30,190 32,341 32,455Difference betweenmodel estimation andactual values (%)–15.01 –6.4 — –6.98 –0.35 —Standard deviation 1.27 0.91 2.07 1.28 0.92 1.991996/97Tel Avivmodel1996/97Tel AvivmodelHAIFA REGRESSION1984 Tel AvivmodelActual1984 Tel AvivmodelActualAverage trips per21.30 2.08 2.07 2.31 22.20 2.07person per dayNegative estimations 0 0 — — 0 —Minimum trip rate 0.11 0.16 0 0.11 0.16 0Maximum trip rate 4.49 3.89 11 4.49 4.28 11Total 10,710 10,450 10,414 36,287 34,788 32,455Difference betweenmodel estimation andactual values (%)2.84 0.35 — 11.80 7.19 —Standard deviation 1.34 1.00 2.07 1.35 1.01 1.99(continues on next page)54 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 12 Temporal Transferability Results of the 1984 Models in the 1996/97 Files (continued)Haifa dataTel Aviv dataTEL AVIV TOBIT1984 Tel Avivmodel1996/97Tel Avivmodel Actual1984 Tel Avivmodel1996/97Tel Avivmodel ActualAverage trips per1.83 1.92 2.07 2.06 1.98 2.07person per dayMinimum trip rate 0 0 0 0 0 0Maximum trip rate 4.86 4.30 11 4.41 4.84 11Total 9,203 9,671 10,414 32,363 31,155 32,455Difference betweenmodel estimation andactual values (%)–11.60 –7.12 — 0.28 –4.00 —Standard deviation 1.58 1.28 2.07 1.30 1.61 1.991996/97Tel Avivmodel1996/97Tel AvivmodelHAIFA TOBIT1984 Tel AvivmodelActual1984 Tel AvivmodelActualAverage trips per2.39 2.03 2.07 2.22 2.32 2.07person per dayMinimum trip rate 0 0 0 0 0 0Maximum trip rate 5.20 4.57 11 5.05 5.20 11Total 12,036 10,184 10,414 34,796 36,381 32,455Difference betweenmodel estimation andactual values (%)15.58 2.20 — 7.22 12.09 —Standard deviation 1.28 1.42 2.07 1.43 1.75 1.99The nature of the local household surveys raises aneed to validate the results of this study in futureresearch. In particular, further research can identifywhat makes two study areas “similar enough” tojustify transferring a model from one to the other.We also suggest further research incorporating Tobitmodels in TGM and for investigating the characteristicsof nontravelers.REFERENCESAtherton, T. and M. Ben-Akiva 1976. Transferability andUpdating of Disaggregate Travel Demand Models. TransportationResearch Record 610:12–18.Caldwell III, L.C. and M.J. Demetsky. 1980. Transferability ofTrip Generation Models. Transportation Research Record751:56–62.Copley, G. and S.R. Lowe. 1981. The Temporal Stability of TripRates: Some Findings and Implications. TransportationAnalysis and Models: Proceedings of Seminar N. London,England: PTRC Education and Research Services, Ltd.Cotrus, A. 2001. Analysis of Trip Generation Characteristics inIsrael for the Years 1984, 1996/7 and Spatial and TemporalTransferability of Trip Generation Models, Ph.D. thesis,Technion, Israel Institute of Technology, Haifa, Israel.Daor, E. 1981. The Transferability of Independent Variables inTrip Generation Models. Transportation Analysis and Models:Proceedings of Seminar N. London, England: PTRCEducation and Research Services, Ltd.Doubleday, C. 1977. Some Studies of the Temporal Stability ofPerson Trip Generation Models. Transportation Research11:255–263.Downes, J.D. and L. Gyenes. 1976. Temporal Stability andForecasting Ability of Trip Generation Models in Reading,TRRL Report 726. Crowthorne, Berkshire: Transport andRoad Research Laboratory.Duah, K.A. and F.L. Hall. 1997. Spatial Transferability of anOrdered Response Model of Trip Generation. TransportationResearch A 31:389–402.COTRUS, PRASHKER & SHIFTAN 55

Fleet, C. and S. Robertson. 1968. Trip Generation in the TransportationPlanning Process. Highway Research BoardRecord 240:11–31.Hald, A. 1949. Maximum Likelihood Estimation of Parametersof a Normal Distribution Which is Truncated at a KnownPoint. Skandinavisk Aktuarietidskrift 32:119–134.Huisken, G. 2000. Neural Networks and Fuzzy Logic toImprove Trip Generation Modeling, paper presented at the79th Annual Meetings of the Transportation ResearchBoard, Jan. 9–13, 2000, Washington, DC.Kannel, E.J. and K.W. Heathington. 1973. Temporal Stability ofTrip Generation Relations. Highway Research Record472:17–27.Karasmaa, N. and M. Pursula. 1997. Empirical Studies of Transferabilityof Helsinki Metropolitan Area Travel ForecastingModels. Transportation Research Record 1607:38–44.McDonald, J.F. and R.A. Moffitt. 1980. The Uses of Tobit Analysis.The Review of Economics and Statistics 62(2):318–321.Ortuzar, J. and L.G. Willumsen. 1994. Trip Generation Modeling.Modeling Transportation, 2nd ed. New York, NY:Wiley.Prashker, J. 1982. Transferability of Disaggregate Modal-SplitModels—Investigation of Models in the Metropolitan Areaof Tel Aviv, manuscript, p. 91. Israel Institute of Transportation.Rose, G. and F.S. Koppelman. 1984. Transferability of DisaggregateTrip Generation Models. Proceedings of the 9th InternationalSymposium on Transportation and Traffic Theory.Utrecht, Netherlands: VNU Press.Silman, L.A. 1981. The Time Stability of a Modal-Split Modelfor Tel Aviv. Environment and Planning A 13:751–762.Smith, R.L. and D.E. Cleveland. 1976. Time Stability Analysisof Trip Generation and Predistribution Modal—ChoiceModels. Transportation Research Record 569:76–86.Supernak, J. 1982. Transportation Modeling: Lessons from thePast and Tasks for the Future. Transportation Analysis andModels, Proceedings of Seminar Q. London, England: PTRCEducation and Research Services, Ltd.____. 1984. Disaggregate Models of Mode Choices: An Assessmentof Performance and Suggestions for Improvement.Proceedings of the 9th International Symposium on Transportationand Traffic Theory. Utrecht, Netherlands: VNUPress.____. 1987. A Method for Estimating Long-Term Changes inTime-of-Day Travel Demand. Transportation ResearchRecord 1138:18–26.Supernak, J., A. Talvitie, and A. DeJohn. 1983. Person-CategoryTrip Generation Model. Transportation Research Record944:74–83.Tobin, J. 1958. Estimation of Relationships for Limited DependentVariables. Econometrica 26:24–36.Walker, W.T. and O.A. Olanipekun. 1989. Interregional Stabilityof Household Trip Generation Rates from the 1986 NewJersey Home Interview Survey. Transportation ResearchRecord 1220:47–57.Walker, W.T. and H. Peng. 1991. Long Range Temporal Stabilityof Trip Generation Rates Based on Selected Cross-Classification Models in the Delaware Valley Region.Transportation Research Record 1305:61–71.Wilmot, C.G. 1995. Evidence of Transferability of Trip GenerationModels. Journal of Transportation Engineering 9:405–410.Yunker, K.R. 1976. Tests of the Temporal Stability of Travel SimulationModels in Southeastern Wisconsin. TransportationResearch Record 610:1–5.Zhao, H. 2000. Comparison of Two Alternatives for Trip Generation,paper presented at the 79th Annual Meetings of theTransportation Research Board, Jan. 9–13, 2000, Washington,DC.56 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Governors Highway Safety Associations andTransportation Planning: Exploratory Factor Analysis andStructural Equation ModelingSUDESHNA MITRA 1,*SIMON WASHINGTON 1ERIC DUMBAUGH 2MICHAEL D. MEYER 21 Department of Civil and Environmental EngineeringArizona State UniversityPO Box 875306Tempe, AZ 85287-53062 School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlanta, GA 30332-0355Email addresses:* Corresponding author—mitra_sudeshna@yahoo.comS. Washington—Simon.Washington@asu.eduE. Dumbaugh—EDumbaugh@aol.comM.D. Meyer—mmeyer@ce.gatech.eduABSTRACTThe Intermodal Surface Transportation EfficiencyAct (ISTEA) of 1991 mandated the considerationof safety in the regional transportation planningprocess. As part of National Cooperative HighwayResearch Program Project 8-44, “IncorporatingSafety into the Transportation Planning Process,” weconducted a telephone survey to assess safety-relatedactivities and expertise at Governors Highway SafetyAssociations (GHSAs), and GHSA relationshipswith metropolitan planning organizations (MPOs)and state departments of transportation (DOTs).The survey results were combined with statewidecrash data to enable exploratory modeling of therelationship between GHSA policies and programsand statewide safety. The modeling objective was toilluminate current hurdles to ISTEA implementation,so that appropriate institutional, analytical, andpersonnel improvements can be made. The studyrevealed that coordination of transportation safetyacross DOTs, MPOs, GHSAs, and departments ofpublic safety is generally beneficial to the implementationof safety. In addition, better coordination ischaracterized by more positive and constructive attitudestoward incorporating safety into planning.KEYWORDS: Transportation planning, transportationsafety, structural equation modeling.57

INTRODUCTIONThe Intermodal Surface Transportation EfficiencyAct (ISTEA) of 1991 is, in many ways, a benchmarkof federal transportation legislation. Along with thesubsequent 1998 Transportation Efficiency Act forthe 21st Century (TEA-21), not only did it definethe post-interstate transportation program, it alsobroadened the types of issues that were to be consideredas part of the transportation planning process.By mandating the consideration of a broaderrange of issues to address in planning, the projectsand strategies surviving the planning and programmingprocesses should relate to those issues. Thereare challenges in meeting this mandate, however,due in part to “institutional inertia” in many statedepartments of transportation (DOTs) and metropolitanplanning organizations (MPOs) to continuethe programming emphasis on capital-intensiveprojects. ISTEA reinforced the change in focus awayfrom capital-intensive projects with the requirementfor six management systems, one of which targetedsafety. By introducing a process to identify systemdeficiencies, analyze and evaluate prospectiveimprovement strategies, and monitor implementedprojects and strategies, it is possible to determinewhether anticipated effects occurred.Major stakeholders in the transportation andsafety fields are varied and have no tradition ofinteracting within the context of the planning process.Our interest here is whether MPOs and DOTsinteract with their respective Governors HighwaySafety Association (GHSA) representatives, who areoften the focal point for state initiatives dealingwith issues such as drunk driving, seat belt use, andteenage driving. Furthermore, it is important toknow whether GHSA and MPO/DOT coordinationmakes a difference in terms of statewide safety.The inspiration for GHSA dates back to theHighway Safety Act of 1966, which establishedstate offices of highway safety. In an effort to shareinformation among state safety offices, the NationalConference of Governors’ Highway Representativeswas created. GHSA grew out of this and, in 1974, itincorporated. GHSA includes highway safety programmanagers from all 50 states, the District ofColumbia, Puerto Rico, the Northern Marianas, allU.S. territories, and the Indian Nation. The memberagencies are tasked to develop, implement, andoversee highway safety programs using behavioralstrategies such as training and educating motorists,pedestrians, bicyclists, and school children on safebehavior, and by addressing impaired driving,speeding, aggressive driving, and safety restraintuse. Given the mission of the GHSAs, their impacton statewide safety is vital, and their cooperationand coordination with MPOs and DOTs may play apivotal role in the ultimate success of incorporatingsafety into the transportation planning process.This paper presents the results of a telephone surveydesigned and administered to state GHSA officesto capture the characteristics, attitudes, and activitiesof these agencies. (The survey was part of NationalCooperative Highway Research Program (NCHRP)Project 8-44, “Incorporating Safety into Long-RangeTransportation Planning.”) Specific objectives of thesurvey include:1. understanding if and how the agencies’mission statements, goals, and/or objectivesaddress various safety issues;2. characterizing the nature of the implementedprograms;3. determining whether an agency consideredintegrating the state safety program withspecific transportation-related activities; and4. the extent of GHSA participation in regionaltransportation planning and interaction withMPOs and DOTs.Two research questions of particular interest arosefrom the survey.1. Are the depth and breadth of programs commensuratewith statewide safety? In otherwords, does the safety level within a statedrive the adoption of programs? Will a statewith a poorer safety record have broader andmore extensive safety programs, for example,and does that indicate that GHSA activitiesand funding are out of step with safety or arelagging?2. Do GHSA perceptions of the benefits oftransportation planning influence programmingefforts and/or statewide safety levels?In other words, does cooperation betweenGHSAs, DOTs, and MPOs lead to more58 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

extensive statewide safety programmingand/or improved safety?We used latent variable models to look for answersto these research questions in a quantitatively rigorousway. We chose this type of model because ofthe type of data in the study—many variables arenot directly observable (latent), and thus theirproxies (variables we can measure directly) sufferfrom measurement errors.While latent variables and measurement errors oftheir proxies are widespread in social scienceresearch, they are relatively uncommon in transportationresearch. Latent variables refer to unobservableor unmeasured variables, such as intelligence,education, social and political classes, and attitudes.Often proxies can be used to indirectly measurelatent variables, such as IQ score and grade pointaverage, as measures of the latent variable intelligence.Certain effects of these latent variables onmeasurable variables are observable, along withsome random or systematic errors, collectively calledmeasurement errors. Everitt (1984) pointed out thatit was indeed one of the major achievements in thebehavioral sciences to develop methods that assessand explain the structure in a set of correlated,observed variables, in terms of a small number oflatent variables.In this study, the variables indicating attitudes ofGHSA personnel, their planning and programmingefforts, and coordination with MPOs and DOTs arenot directly measurable. While the survey responsesaim to measure these underlying latent variables,some of their dimensions may remain unexplored.This paper presents various latent variable analysistechniques used to examine and extract relationshipsin the data, including factor analysis (exploratory)and structural equation modeling.THE SURVEYDuring fall 2002 and spring 2003, the researchteam conducted telephone surveys of GHSA personnelin the 50 states and the District of Columbiato capture their planning attitudes, types of programs,goal-setting criteria, coordination efforts,and perceived influence on transportation planning.Respondents were asked a series of formal surveyquestions aimed at understanding the relationshipsbetween planning efforts and safety issues, as wellas several open-ended questions intended to capturethe unique viewpoints, activities, and perspectivesof each of the individual agencies. The surveyinstrument was pre-tested in two states, and thefinal survey instrument was revised based on thepretest results. The survey instrument appears in theappendix of this paper.While individuals designated as the Governor’sRepresentative for Highway Safety in a specific statewere initially targeted as the appropriate agencyrespondents, conversations with actual governors’representatives soon revealed that the individualsactually managing the development and implementationof GHSA programs were often not thedesignated representatives themselves, who weretypically high-level personnel in other state agencies.Instead, in many cases, individuals hired for theexpress task of managing these programs wereinterviewed.The respondent recruitment effort consisted ofmultiple attempts to contact each of the respondentsvia telephone, followed by an email contactto encourage each individual’s participation. Ultimately,telephone surveys, averaging 20 minutesin length, were completed for 43 of the 51 potentialrespondents. Two of the states completed the surveyelectronically, bringing the total number of statessurveyed to 45. Despite an exhaustive effort toreduce survey nonresponse, responses for six stateswere not obtained. However, among the 45 completedsurveys, item nonresponse was not a problem.The survey was designed to capture six majorcharacteristics of a GHSA. the types of planning-related activities undertaken; attitudes toward planning as reflected by GHSAefforts to include specific safety issues in transportationplanning activities, as well as howmuch GHSA participated in the regional transportationplanning process; whether the GHSA office is affiliated withanother state agency; the extent of coordination with other agencies; the planning time horizons of the agency; and the number of agency staff.MITRA, WASHINGTON, DUMBAUGH & MEYER 59

SUPPLEMENTAL STATE-LEVEL DATAIn addition to the survey responses, state-level safetydata were obtained. These data from the NationalHighway Traffic Safety Administration (NHTSA)included total fatalities, alcohol-related fatalities,and pedestrian and bicycle-related fatalities for calendaryear 2001 (USDOT 2001). To compensatefor exposure to risk, crash rates were taken intoaccount rather than the total crash statistics. Inother words, a state with a large population andrelatively higher vehicle-miles traveled (VMT) canbe expected to experience a greater number ofcrashes than a smaller state. Hence, to minimizebias imposed by population size, fatality rates per100 million VMT were considered for total as wellas alcohol-related crashes. We used fatality ratesper 100,000 population for pedestrian and bicyclecrashes. The crash rates are used as observedendogenous variables and served as proxies for thelatent variable RISK (motor vehicle safety-relatedrisk) across states. Better metrics for pedestrian andbicycle exposure are theoretically possible but arenot generally available.In addition to these data, this research utilizedvarious other sources of information, includingenacted legislation in the states covering seat beltlaws, laws related to impaired driving, helmetlaws, child restraint laws, and so forth (IIHS2004). Despite a priori expectations, these variableswere not found to be statistically significant in themodeling efforts. Table 1 presents the descriptivestatistics of various observed variables employed inthe final model.TABLE 1 Summary of Survey ResponseVariablenameQuestion numberVariabletypeScalerange Average Minimum Maximum VariancePEDS2 Q-2a Yes/No 0–1 0.67 0 1 0.227BIKE2 Q-2b Yes/No 0–1 0.60 0 1 0.245DRIVED2 Q-2c Yes/No 0–1 0.27 0 1 0.200SCHOOLED2 Q-2d Yes/No 0–1 0.47 0 1 0.254ENFORCE2 Q-2e Yes/No 0–1 0.84 0 1 0.134COOPDOT2 Q-2f Yes/No 0–1 0.67 0 1 0.227COCPLOC2 Q-2g Yes/No 0–1 0.71 0 1 0.210COOPPLAN2 Q-2h Yes/No 0–1 0.40 0 1 0.245SAFDES2 Q-2i Yes/No 0–1 0.27 0 1 0.200SAFOPS2 Q-2j Yes/No 0–1 0.22 0 1 0.177DATA2 Q-2k Yes/No 0–1 0.80 0 1 0.164STAFF3 Q-3 Ratio scale NA 8.36 0 19 22.916ENG4 Q-4a Yes/No 0–1 0.18 0 1 0.149PLAN4 Q-4b Yes/No 0–1 0.33 0 1 0.227OPS4 Q-4c Yes/No 0–1 0.31 0 1 0.219ENF4 Q-4d Yes/No 0–1 0.76 0 1 0.188EDU4 Q-4e Yes/No 0–1 0.76 0 1 0.188MKTG4 Q-4f Yes/No 0–1 0.67 0 1 0.227PERFMS5 Q-5 Ordinal 1–5 4.84 4 5 0.134SHAREPM6 Q-6 Yes/No 0–1 1.02 0 9 3.249PERFTGT7 Q-7a Yes/No 0–1 0.98 0 1 0.022TGTYEAR7 Q-7b Ratio scale NA 5.02 1 30 20.11360 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 1 Summary of Survey Response (continued)VariablenameQuestion numberVariabletypeScalerange Average Minimum Maximum VarianceAGYHZN8 Q-8 Ratio scale NA 5.38 1 30 26.331PEDEDU9 Q-9a Yes/No 0–1 0.64 0 1 0.234PEDCRWK9 Q-9b Yes/No 0–1 0.40 0 1 0.245PEDSCHL9 Q-9c Yes/No 0–1 0.62 0 1 0.240BIKEDU10 Q-10a Yes/No 0–1 0.69 0 1 0.219BKHELM10 Q-10b Yes/No 0–1 0.53 0 1 0.254BKLITE10 Q-10c Yes/No 0–1 0.29 0 1 0.210BKBRK10 Q-10d Yes/No 0–1 0.09 0 1 0.082DOT12 Q-12a Ordinal 0–4 3.96 3 4 0.043SPOLCE12 Q-12b Ordinal 0–4 3.82 0 4 0.695LPOLCE12 Q-12c Ordinal 0–4 3.96 2 4 0.088PLAN12 Q-12d Ordinal 0–4 1.80 0 4 2.300LEGS12 Q-12e Ordinal 0–4 2.67 0 4 2.363GOV12 Q-12f Ordinal 0–4 2.84 0 4 1.907HWY12 Q-12g Ordinal 0–4 0.62 0 4 1.695ENGNR12 Q-12h Ordinal 0–4 1.24 0 4 2.098SCHOOL12 Q-12i Ordinal 0–4 2.87 0 4 2.345LOCAL12 Q-12j Ordinal 0–4 3.22 0 4 1.722SDWLK13 Q-13a Yes/No 0–1 0.33 0 1 0.227CRSWLK13 Q-13b Yes/No 0–1 0.42 0 1 0.249BIKE13 Q-13c Yes/No 0–1 0.51 0 1 0.255SPEED13 Q-13d Yes/No 0–1 0.58 0 1 0.249TURN13 Q-13e Yes/No 0–1 0.47 0 1 0.254RDSIDE13 Q-13f Yes/No 0–1 0.53 0 1 0.254MONITR13 Q-13g Yes/No 0–1 0.58 0 1 0.249MPO14 Q14a Yes/No 0–1 0.38 0 1 0.240RURAL15 Q15a Yes/No 0–1 0.24 0 1 0.188STP16 Q16a Yes/No 0–1 0.67 0 1 0.186INFLU17 Q17 Ordinal 0–2 0.69 0 1 0.674TOLFTVMTALCFTVMTPEDFTPOPBIKFTPOPTotal fatality rate per100 million VMTAny alcohol-relatedfatality rate per 100million VMTPedestrian fatality rateper 100,000 personsBike-related fatalityrate per 100,000personsRatio scale NA 1.59 0.96 2.32 0.128Ratio scale NA 0.66 0.29 1.27 0.042Ratio scale NA 1.48 0.47 2.98 0.331Ratio scale NA 0.22 0 0.77 0.025Key: VMT = vehicle-miles traveled.MITRA, WASHINGTON, DUMBAUGH & MEYER 61

METHODOLOGYAn exploratory factor analysis followed by structuredequation modeling (SEM) was used to modelstructured relationships between latent variables.Latent variable models have been widely applied invarious fields, but rarely in transportation; forexample, in sociology by Amato and Alan (1995),in psychology by Östberg and Hagekull (2000)and Rubio et al. (2001), and in construction managementby Molenaar et al. (2000).While few applications exist in transportation,Ben-Akiva et al. (1991), working in the area ofpavement management, introduced the concept oflatent performance in terms of several observableperformance indicators and used measurement aswell as structural models to model relationships.The results of this model were then used for decisionson, for example, optimal maintenance andinspection policies, expected number of inspectionsfor the optimum policies, and the minimumexpected cost of inspecting and maintaining a facilityover various planning time horizons. Anotherimportant study in transportation by Golob andRegan (2000) used confirmatory factor analysis tolook at the interrelationship among the latent policyevaluations through several exogenous variablesdefining differences in freight operations.In statistical modeling, applying knowledge of theunderlying data-generating process is a critical stepwhen developing a “starter specification.” However,in the absence of well developed theories, it is oftendifficult for an analyst to specify a priori whichobserved variables affect which latent variable. Inthis context, Loehlin (2004) discussed exploratoryfactor analysis (EFA) as a method to discover anddefine latent variables as well as a measurementmodel that can provide the basis for a causal analysisof relationships among the latent variables.Methodological DetailsAs described in Washington et al. (2003), EFA is nota statistical model and there is no distinctionbetween dependent and independent variables in thisanalysis. For the EFA is to be useful, there are K < nfactors or principal components, with the first factorgiven asZ 1 = a 11 x 1 + a 12 x 2 + ....... + a 1q x q+ ....... + a 1( p – 1)y ( p – 1)+ a 1p y p(1)which maximizes the variability across individuals,subject to the constraint2a 112a 122a 13+ + +2+ ....... + a 1( p – 1)+2....... + a 1q2a 1p= 1(2)where observed variables are denoted by ( p × 1)column vector y, and ( q × 1)column vector x, andinfluence the latent endogenous and exogenousvariables, respectively. Thus, VAR[Z 1 ] is maximizedgiven the constraints in equation (2), with the constraintsimposed to ensure determinacy. A secondfactor, Z 2 , is then sought to maximize the variabilityacross individuals, subject to the constraints2 2 222+ + + ....... a + = 1a 21a 22a 23+ 2( p – 1)a 2pand COR[Z 1 ,Z 2 ] = 0, and so on, such thatCOR[Z 1 , Z 2 .......Z K ] = 0 for up to K factors. In thispaper, the various survey responses are theobserved variables, and they are used to identify theunderlying latent variables. Manly (1986), Johnsonand Wichern (2002), and Washington et al. (2003)provide additional details of EFA.After identifying useful factors from EFA, SEMsare developed. A SEM is defined with two components,a measurement model and a structural model.SEMs are a natural extension of factor analysis andare used to identify structural relationships betweenlatent as well as observed variables. The measurementmodel portion of a SEM correlates theobserved variables with latent dependent, as well asindependent, variables. Observed variables influencinglatent endogenous and exogenous variables aredenoted by a ( p × 1)column vector of y and( q × 1)column vector of x, such thaty = Λ y η + εx = Λ x ξ + δ(3)(4)whereΛ y ( p × m) and Λ x ( q × n)are the coefficient matricesthat show the relation of y to η and x to ξ,respectively, and ε( p × 1) , and δ( q × 1)are theerrors of measurement for y and x, respectively(Washington et al. 2003). For example, if statewidesafety is a latent dependent variable of interest, it is62 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

denoted as η and all the observed variables, such asalcohol-related fatalities, pedestrian and bicyclerelatedfatalities, etc., would constitute the y vector.The structural component of a SEM is given asη = Bη + Γξ + ς(5)whereη is an ( m × 1)vector of latent endogenous randomvariables,ξ is a vector of ( n × 1)latent exogenous randomvariables,B is an ( m × m)coefficient matrix reflecting theinfluence of the latent endogenous variables on eachother,Γ is an ( m × n)coefficient matrix for the effects ofξ on η, andς is the vector of regression errors for which[ E( ς) = 0] and is uncorrelated with ξ . In addition,the error terms of the measurement models areassumed to be uncorrelated with ξ and ς.From the previous simultaneous equation (5),and treating all the observed variables as dependentvariables in the model, the covariance matrix isgiven asΣ( θ) = GI ( – β) – 1 γϕγ( I – β)(–1) ′ G′(6)where G is the selection matrix containing eitherzero or one to select the observed variables fromall the dependent variables in η . Once the SEMmodel is identified (statistically), the parameters areestimated using a discrepancy function based on thehypothesized model Σ = Σ( θ), where Σ is estimatedby the sample covariance matrix S. The roleof this discrepancy function is to minimize the differencebetween the sample variance-covariancematrix and the model-implied variance-covariancematrix, and is given asF= F( S,Σ ( θˆ))(7)It is important to note that the observed variablesin this study are mainly categorical in nature andare not approximated well by normal distributions.According to Bollen (1989), the weighted leastsquares (WLS) estimator has the desirable propertyof making minimal assumptions about the distributionof observed variables, unlike maximumlikelihood estimators (MLEs), which presupposethe underlying data to be approximately normallydistributed. Hence, we used the WLS estimatorinstead of MLE for this research. The fitting functionfor WLS isF WLS = [ s – σθ ( )]′W – 1 [ s – σθ ( )](8)wheres is a 1/2(p + q)(p + q + 1) vector containing thepolychoric and polyserial correlation coefficients forall pairs of latent endogenous and observed exogenousvariables,σθ ( ) is the corresponding same-dimension vectorfor the implicated covariance matrix, andW is a consistent estimator of the asymptotic covariancematrix of s.Goodness-of-Fit MeasuresTo evaluate the overall goodness of fit of the estimatedmodels, χ 2fit, the root mean square error ofapproximation (RMSEA), normed fit index (NFI),and Tucker-Lewis index (TLI) were calculated andused to guide final model selection. In this context,it is important to mention that goodness of fit inSEM is an unsettled topic for which manyresearchers have presented a variety of viewpointsand recommendations. While a detailed explanationof them is beyond the scope of this paper, a briefdescription about each measure of fit used in thispaper is provided.As described by Washington et al. (2003), a usefulfeature of discrepancy functions is that they canbe used to test the null hypothesis H 0 : Σ ( θ) = Σ ,and (n – 1) times the discrepancy function evaluatedat θˆ is approximately χ 2 distributed. The degrees offreedom are 1/2(p + q)(p + q + 1) – t, where p and qare as described previously, and t is the number offree parameters in θ . This χ 2 divided by modeldegrees of freedom has been suggested as a usefulgoodness-of-fit measure. However, in this context,the logic of significance testing is different fromsignificance of coefficient testing in a regressionequation (Bollen 1989). In the classical application,we hope to reject the null hypothesis, whereas in theSEM (for the χ 2test) the null hypothesis assumesthat the implied model is equal to the true modeland we do not wish to reject it. As a result, a largeχ 2and small p value suggests model lack of fit.MITRA, WASHINGTON, DUMBAUGH & MEYER 63

Thus, a relatively large p value and small χ 2issought and corresponds to a good fit of the modelimpliedvariance-covariance with the observed one.Another class of goodness-of-fit measures availablein SEM is based on the population discrepancyfunction as opposed to the sample discrepancyfunction, such as RMSEA. The RMSEA is obtainedby taking the square root of the population-baseddiscrepancy function divided by its degrees of freedom.Practical experience indicates that a value ofRMSEA of about 0.05 or less indicates a good fit ofthe model.The remaining two goodness-of-fit measures arebased on comparisons with a baseline model. TheNFI proposed by Bentler and Bonett (1980) indicatesthe level of improvement in the overall fit ofthe present model compared with the baselinemodel and is given asFNFI = 1 – -----(9)F bwhere F and F b are the discrepancy functions of thefitted and baseline models. The TLI is similar tothis concept, but in addition to the discrepancyfunctions, the degrees of freedom associated withthe fitted model (df), as well as the baseline model(df b ), are considered in calculating the index, thus apenalty can be imposed for larger models similar toan adjusted R 2 in regression. The index is given asFTLI b ⁄ df b – F ⁄ df= ------------------------------------F b ⁄ df b – 1More information on SEM estimation, goodness offit, variable selection, specification, and interpretationcan be found in Bollen (1989), Arminger et al.(1995), Hoyle (1995), Schumacker and Lomax(1995), Kline (1998), and Washington et al. (2003).SEM MODEL STARTER SPECIFICATIONThe hypotheses mentioned previously, and describedin greater detail here, helped to provide the researchteam with an initial SEM specification.Hypothesis 1. The breadth and depth of statewideprograms should in theory influence statewidesafety, albeit with a time lag. It is hypothesized thatstates with relatively poor safety records will havebroad and intensive safety programs, in response toa needed safety improvement. This finding wouldreflect an appropriate allocation of federal funds forimproving safety across states. Because changes instatewide safety typically are not immediate, andbecause program benefits tend to lag programinvestments, it is assumed that depth and breadth ofsafety programming will be negatively associatedwith statewide safety. This anticipated relationshipis aggregate in nature and exceptions may occur.Hypothesis 2. GHSAs that perceive benefits fromparticipating in the transportation planning processwill be more likely to adopt a coordinated approachto safety and will, consequently, be more likely toidentify new opportunities for addressing safety,thereby yielding increased safety performance.Understanding how these agencies develop their perceptionsof planning activities is difficult to assess.For instance, an unfavorable attitude could representan institutional unwillingness to coordinate withother agencies or may be the result of a previouslyunsuccessful attempt at coordinating with otheragencies. Alternatively, a positive perception ofplanning may be the result of successful experiencesin previous coordination attempts or may simplyrepresent an appreciation for the potential benefitsof a coordinated approach. It could also represent alatent agency willingness to adopt new and innovativeapproaches to transportation safety, even ifthe agency has never previously attempted tocoordinate their efforts with planning entities. It ishypothesized that in aggregate, agencies with apositive perception of planning are expected to bewilling to introduce a broad range of programsaddressing safety, as well as yield better than averagesafety records.Although these hypotheses represent a prioribeliefs about the relationships between latent variablesand guided the specification of the structuralrelationships in the SEM models, the latent factorswere identified through an EFA. The surveyresponse—observed endogenous variables (endogenousbecause they are influenced by the underlyinglatent variables)—form the x and y vectors in equation(1) and may be related to one or more latentvariables. The factor loadings give an indication ofhow many distinctly different “dimensions” exist inthe data.The exploratory factor analysis output (table 2)clearly shows significant loadings for some variables64 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 2 Results of the ExploratoryFactor AnalysisObservedvariables Factor 1 Factor 2 Factor 3PEDEDU9 0.584 –0.197 0.348PEDS2 0.893 0.052 0.101SDWLK13 0.518 0.034 0.735CRSWLK13 0.408 0.035 0.643MPO14 –0.037 –0.052 0.883BIKE2 0.708 0.073 0.155BIKEDU10 0.783 –0.086 0.332TOLFTVMT –0.081 0.864 –0.037ALCFTVMT –0.062 0.868 0.035PEDFTPOP 0.048 0.525 –0.052BIKFTPOP 0.102 0.491 0.162on a specific factor compared with others. Forexample, the variable PEDS2 loads significantly onthe first factor but not on the second and thirdfactors. These differences in factor loadings help theanalyst to determine which observed variables areinfluenced by a common underlying factor, howmany latent variables to consider in a SEM, and howto specify the measurement portion of a SEM (e.g.,which observed endogenous variables measure thelatent variables). The EFA in this study producedstrong evidence in support of three latent variables,which are described as:1. Breadth of the programs (PROGRAM infigure 1). This latent variable reflects theextent of programs reported by GHSAsaround the United States. The questions thatloaded heavily (were influenced by breadthof programs) on this factor included Q2a–Q2e, Q9a–Q9c, and Q10a–Q10d, surveyresponses that describe agency goals forpedestrian and bike safety programs, education,and enforcement.2. Attitude of the agencies toward planning(ATTITUDE_PLN in figure 1). This latentvariable influences collectively the responsesto questions Q13a–Q13g, Q14a, Q15a, andQ16a, which represent attitudinal and perception-relatedquestions.3. Risk. This latent variable is strongly associatedwith variables such as total and alcoholrelatedcrash rates and pedestrian and bicyclerelatedcrash rates. Thus, the variable reflectsthe amount of motor vehicle-related riskRESULTSacross the states. It is worthwhile to note thatthe observed crash rates measure the degreethat something is not safe, and thus the latentvariable is labeled RISK.Using Mplus software, we obtained the results ofthe SEM estimated on the survey and statewidecrash data. The relationships among the observedand latent variables are shown in figure 1. For easeof understanding, the observed endogenous variablesare shown as rectangles, while both latentendogenous and exogenous variables appear asellipses. The circles represent the unobserved measurementerror terms. Arrows in the diagram suggestthe direction of influence, thereby identifying theendogenous and exogenous variables. For example,the base of an arrow is attached to an exogenousvariable while the variable to which it points isendogenous. A similar concept is also valid for theerror terms. A 0 next to a variable indicates that itsmean is set to 0 and the 1 near the arrow means theregression weight is given as 1. There must also be atleast two observed endogenous variables pointing toa latent variable for identifiability of the model (anecessary condition for ensuring that sufficient informationexists to estimate the model parameters).Overall Model Goodness-of-FitAs discussed previously, the hypothesized relationshipsbetween variables were used to identifystructural relationships, while survey questions andstate-level crash data were used to formulate themeasurement portion of the model. The latentvariables in the starter specification model wereloaded with all the significant variables obtainedfrom the exploratory factor analysis based on thefactor loadings. A variable with a factor loading ofgreater than 0.5 was considered significant andincluded in the model. However, including all of thesignificant observed variables in the measurementmodel resulted in non-identifiability of the model(too many model parameters relative to the data toestimate).As a result, an iterative process was adoptedwhere the “least” significant variables were removedand an improved SEM model was obtained based onMITRA, WASHINGTON, DUMBAUGH & MEYER 65

FIGURE 1 Final Model Specifications0, 0,e2e3110,ALCFTVMTPEDFTPOPe40,1zeta21BIKFTPOPRISK010,zeta10 10, 0,d5d711SDWLK13MP01410,1PROGRAMATTITUDE_PLNPEDEDU910,d2BIKEDU101 0,d3BIKE210,d4the model fit and convergence criteria. Note thatchanges during this process were made only to themeasurement model and not to the structural modelrelating latent variables. For example, TOLFTVMT,which presents the total number of crashes perVMT, was dropped from the final model, because abetter fitting model was achieved using three otheraccident-related variables explaining the latent variableRISK. Deleting TOLFTVMT from RISK wasnot detrimental to model fit, as it explains the totalcrash including pedestrian, bike, and alcohol-relatedaccidents, and these were already taken into considerationby the other three observed variables.The problem of restricting the measurement modelsto a few select variables was dependent on samplesize and model complexity and is addressed in thesection on further research.Table 3 shows the final SEM specification results.The interpretation of the results in the table isstraightforward and consistent with the arrowsbetween-variablesexplanation of figure 1. Thefirst row in table 3 shows that the latent variablePROGRAM acts as an exogenous variable on thelatent variable RISK with a coefficient estimate of0.026, standard error of 0.021, and t value of1.226. The second part of table 3 presents theestimated intercepts of the observed endogenousvariables.Table 4 shows various goodness-of-fit statisticsused during model selection. The chi-square valuefor the final model is 15.455 with 17 degrees offreedom (p value of 0.5627), which indicates themodel fit cannot be rejected at p = 0.05. Becausethe chi-square goodness-of-fit test is used to test fordifferences between the implied model variancecovariancematrix and the observed one, a modelthat will not reject the null hypothesis is a desiredoutcome. The RMSEA for the final model was0.003, which clearly indicates a close-fitting model.Also, the calculated NFI and TLI are close to 1,indicating considerable improvement over the baselinemodel.General FindingsThe model results suggest a two-way relationshipbetween risk and the program efforts by GHSAs, orthat these two aspects are mutually endogenous.Risk affects programming, and programming alsoaffects risk. States with high safety risk actively implementeda wide variety of safety programs resulting ina breadth of the programs being positively associatedwith safety risk. This finding agreed with66 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 3 Weighted Least Squares Estimate of the ModelSEM regression weightsRegressionweightsStandarderrorCriticalratioRISK

CONCLUSIONSISTEA and the TEA-21 legislation raised the visibilityof safety conscious planning in the UnitedStates. While safety-related planning has historicallybeen reactive, new initiatives and investments areintended to change the status quo and encourage anew approach for considering safety at the transportationplanning level. In particular, the NCHRP8-44 project is oriented toward contributing andunderstanding tools for proactive planning amongDOTs, MPOs, and GHSAs. This paper presents anexploratory analysis aimed at better understandingthe relationships between GHSA-implemented safetyprograms and the actual safety scenario, as well asthe effect of coordination among the various agencieson statewide safety.The study revealed that coordination of transportationsafety across DOTs, MPOs, GHSAs, anddepartments of public safety appears to be generallybeneficial to safety, particularly in the long term. Inaddition, better safety planning coordination ischaracterized by positive attitudes toward incorporatingsafety into planning and also implementing awide range of programs to improve safety. Furthermore,mechanisms for improving cooperation,coordination, and collaboration among the agenciesalso appear to be worthwhile investments.FUTURE WORKThe results presented in this paper are exploratorydue to a lack of a well-articulated theory regardingthe subject matter. Additional information and somecontrolled data-collection would be required todraw more definitive conclusions. For example,panel data over a period of 5 to 10 years would berequired to examine the lag between safety investmentsand risk, as well as attitudes and programsimplemented over time. Additional data from all 50states would sufficiently increase the number ofobservations necessary to improve the WLS estimatesobtained in this analysis, allowing for more“complex” models. The WLS estimator requires atleast 1/2(p + q)(p + q + 1) observations where (p + q)are the number of observed dependent variables.Hence, the explanatory power of the model greatlydepends on the number of observations.This study was restricted to three main latentvariables and a few carefully selected observedendogenous variables in the measurement model,due partly to data limitations. A larger study wouldenable the research team to focus on perhaps otherrelevant variables critical to statewide safety performance,such as the types of programs implemented.As a result, the present model remains speculativeand further data are needed to validate it. Furthermore,the results are time dependent, due to theobserved response from the 2002 to 2003 timeperiods. As mentioned previously, there is everypossibility of a lagged effect of safety improvementprograms on state safety performance, which is notproperly captured in this modeling effort. Regardless,some initial insights into relationships amongagencies were found and are encouraging for thesuccessful implementation of ISTEA and TEA21legislation targeted towards national safetyimprovements.ACKNOWLEDGMENTSThe authors would like to acknowledge theNational Cooperative Highway Research Program(NCHRP 8-44) for providing the funding for thisresearch. This paper represents interim preliminaryfindings that have not been reviewed nor areendorsed by the NCHRP, its staff, or the panel overseeingthis research effort.68 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

REFERENCESAmato, P.R. and B. Alan. 1995. Changes in Gender Role Attitudesand Perceived Marital Quality. American SociologicalReview 60(1):58–66.Arminger, G., C. Clogg, and M. Sobel. 1995. Handbook of StatisticalModeling for the Social and Behavioral Sciences. NewYork, NY: Plenum Press.Ben-Akiva, M., F. Humplick, S. Madanat, and R. Ramaswamy.1991. Latent Performance Approach to Infrastructure Management.Transportation Research Record 1311:188–195.Bentler, P.M. and D.G. Bonett. 1980. Significance Tests andGoodness of Fit in the Analysis of Covariance Structures.Psychological Bulletin 88:588–606.Bollen, K.A. 1989. Structural Equations with Latent Variables.New York, NY: Wiley.Everitt, B.S. 1984. An Introduction to Latent Variables. London,England: Chapman & Hall.Golob, T.F. and A. Regan. 2000. Freight Industry AttitudeTowards Policies to Reduce Congestion. TransportationResearch E 36(1):55–77.Hoyle, R., ed. 1995. Structural Equation Modeling: Concepts,Issues, and Applications. Thousand Oaks, CA: Sage Publications,Inc.Insurance Institute for Highway Safety (IIHS). 2004. Availableat http://www.hwysafety.org/safety_facts/safety.htm.Johnson, R. and D. Wichern. 2002. Applied Multivariate StatisticalAnalysis. Upper Saddle River, NJ: Prentice Hall.Kline, R. 1998. Principles and Practice of Structural EquationModeling. New York, NY: Guilford Press.Loehlin, J.C. 2004. Latent Variable Models: An Introduction toFactor, Path, and Structural Equation Analysis. Mahwah,NJ: Lawrence Erlbaum Associates.Manly, B. 1986. Multivariate Statistical Methods: A Primer.New York, NY: Chapman & Hall.Molenaar, K., S. Washington, and J. Dickmann. 2000. StructuralEquation Model of Construction Contract Dispute Potential.Journal of Construction Engineering and Management, July/August:1–10.Östberg, M. and B. Hagekull. 2000. A Structural ModelingApproach to the Understanding of Parenting Stress. Journalof Clinical Child Psychology 29(4):615–625.Rubio, D.M., M.B. Weger, and S.S. Tebb. 2001. Using StructuralEquation Modeling to Test for Multidimensionality.Structural Equation Modeling: A Multidisciplinary Journal8(4):613–626.Schumacker, R.E. and R.G. Lomax. 1995. A Beginner’s Guideto Structural Equation Modeling. Mahway, NJ: LawrenceErlbaum Associates.U.S. Department of Transportation (USDOT), National HighwayTraffic Safety Administration. 2001. Traffic Safety Facts2001. Washington, DC.Washington, S., M. Karlaftis, and F. Mannering. 2003. Statisticaland Econometric Methods for Transportation Data Analysis.Boca Raton, FL: Chapman & Hall/CRC.APPENDIXSurvey QuestionnaireSurvey Question 1: Is your agency located within, or directly affiliated with, another state agency,such as the Department of Transportation?1a. affil1—Affiliated with another state agency?1 = Yes0 = No1b. agency1—Name of affiliated agency.1c. agcycod—Coding of agency affiliation.0 = No affiliation1 = State DOT2 = State police3 = Department of Public Safety4 = Department of Motor Vehicles5 = Other affiliation(survey questionnaire continues on next page)MITRA, WASHINGTON, DUMBAUGH & MEYER 69

Survey Question 2: Do your agency’s mission statement, goals, or objectives explicitly address any ofthe following issues?2a. peds2—Pedestrian safety.2b. bikes2—Bicycle safety.2c. drived2—Driver education.2d. schooled2—Safety education in school.2e. enforce2—Traffic law enforcement.2f. coopdot2—Cooperation with the state DOT.2g. cooploc2—Cooperation with local officials.2h. coopplan2—Interaction with regional or local transportation planners.2i. safdes2—Incorporating safety into the design of transportation facilities.2j. safops2—Incorporating safety into transportation facility operation.2k. data2—Collecting safety-related data.1 = Yes0 = NoSurvey Question 3: How many professional staff members (i.e., those focused on highway safety, notclerical or support staff) does your agency have?Staff3—Number of agency employees.Survey Question 4: Do any members of your staff have expertise in the following areas?4a. Eng4—Transportation engineering.4b. plan4—Transportation planning.4c. ops4—Traffic operations.4d. enf4—Law enforcement.4e. edu4—Education.4f. mktg4—Marketing/media relations.1 = Yes0 = NoSurvey Question 5: Federal regulations require Governors Highway Safety agencies to developannual plans, as well as performance measures for evaluating program effectiveness. How importantare these performance measures in influencing the types of projects and programs implemented byyour organization?perfms5—Importance of annual performance measures on agency projects.5 = Very important4 = Somewhat important3 = No opinion2 = Not very important1 = Not at all importantSurvey Question 6: Are your agency’s performance measures shared by other agencies responsiblefor the transportation system (e.g., by the state DOT or by regional transportation planning agencies inyour state)?6a. Sharepm6—Other agencies sharing performance measures.1 = Yes0 = No6b. agency6—Names of agencies sharing performance measures, if any.70 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Survey Question 7: Does your agency develop longer term performance targets beyond the federallyrequired 1-year targets?7a. perftgt7—Performance targets beyond federal requirements.1 = Yes0 = No7b. tgtyear7—Furthest target year in future.Survey Question 8: What is the planning time horizon for your agency?Agyhzn8—Agency planning horizon.Survey Question 9: Which of the following pedestrian-related safety programs does your agencyimplement?9a. Pededu9—Education on safe street crossing.9b. pedcrwk9—Crosswalk enforcement.9c. pedschl9—Safe routes to schools program.1 = Yes0 = No9d. other9—Other pedestrian programs, if any.Survey Question 10: Which of the following bicycle-related safety programs does your agencyimplement?10a. Bikedu10—Bicycle education campaigns.10b. bkhelm10—Bicycle helmet programs.10c. bklite10—Lights on bicycles at night.10d. bkbrk10—Bicycle brake requirements.1 = Yes0 = No10e. other10—Other bicycle programs, if any.Survey Question 11: Has your agency undertaken any innovative safety programs using federalflexible funds, such as Section 407 funds that provide flexible incentive grants for programs aimed atincreasing highway safety?11a. Innov11—Innovative programs using flexible funds.1 = Yes0 = No11b. prgrm111—Name of innovative program 1, if any.11c. effct111—Effectiveness of program.5 = Very effective4 = Somewhat effective3 = No opinion2 = Somewhat effective1 = Not effective11d. prgrm211—Name of innovative program 2, if any.11e. effct211—Effectiveness of program 2.5 = Very effective4 = Somewhat effective3 = No opinion2 = Somewhat effective1 = Not effective(survey questionnaire continues on next page)MITRA, WASHINGTON, DUMBAUGH & MEYER 71

Survey Question 11 (continued): Has your agency undertaken any innovative safety programs usingfederal flexible funds, such as Section 407 funds that provide flexible incentive grants for programsaimed at increasing highway safety?11f. prgrm311—Name of innovative program 3, if any11g. effct311—Effectiveness of program 3.5 = Very effective4 = Somewhat effective3 = No opinion2 = Somewhat effective1 = Not effective11h. prgrm411—Name of innovative program 4, if any.11i. effct411—Effectiveness of program 4.5 = Very effective4 = Somewhat effective3 = No opinion2 = Somewhat effective1 = Not effective11j. prgrm511—Name of innovative program 5, if any.11k. effct511—Effectiveness of program 5.5 = Very effective4 = Somewhat effective3 = No opinion2 = Somewhat effective1 = Not effectiveSurvey Question 12: This study seeks to understand how often your agency interacts with otherindividuals, agencies, or groups that may have an influence on highway safety issues. For each of thefollowing, please indicate whether your agency interacts with them monthly, once every three months,once every six months, once per year, or not at all.12a. Dot12—Frequency of interaction with the state DOT.12b. spolce12—Frequency of interaction with the state police.12c. lpolce12—Frequency of interaction with the local police.12d. plan12—Frequency of interaction with MPOs.12e. legs12—Frequency of interaction with state legislators.12f. gov12—Frequency of interaction with the governor’s staff.12g. hwy12—Frequency of interaction with highway contractors.12h. engnr12—Frequency of interaction with engineering consultants.12i. school12—Frequency of interaction with school officials.12j. local12—Frequency of interaction with local officials.4 = At least monthly3 = Once every three months2 = Once every six months1 = Once per year0 = Never72 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Survey Question 13: Has your agency considered integrating state safety programs with any of thefollowing transportation-related activities:13a. Sdwlk13—Considered sidewalk provisions.13b. crswlk13—Considered crosswalk signals.13c. bike13—Considered bike signals.13d. speed13—Considered design strategies to reduce speeding.13e. turn13—Considered design strategies to prevent turning movements.13f. rdside13—Considered eliminating roadside hazards.13g. monitr13—Considered using monitoring systems.1 = Yes0 = NoSurvey Question 14: Every urbanized area in a state must have a comprehensive regionaltransportation planning process. For such areas in your state, has your agency participated in theregional transportation planning process during the last 5 years?14a. mpo14—Participated in regional transportation planning during the last 5 years.1 = Yes0 = NoIf mpo14 = 014b. blrp14—Benefited from participating in MPO long-range planning process (if no 14mpo).1 = Yes0 = No14c. bgopm14—Benefited from developing MPO goals, objectives, and performance measures(if no 14mpo).1 = Yes0 = No14d. bpep14—Benefited from participating in MPO project evaluation and programming (if no14mpo).1 = Yes0 = NoSurvey Question 15: Many states have regional planning agencies that represent rural,non-urbanized portions of a state. Has your agency participated in the transportation planning processfor rural areas during the last 5 years?15a. Rural15—Participated in rural planning process during the last 5 years.1 = Yes0 = NoIf rural15 = 015b. blrp15—Benefited from participating in rural long-range planning process (if no 15rural).15c. bgopm15—Benefited from developing rural goals, objectives, and performance measures (ifno 15rural).15d. bpep15—Benefited from participating in rural project evaluation and programming (if no15rural).1 = Yes0 = No(survey questionnaire continues on next page)MITRA, WASHINGTON, DUMBAUGH & MEYER 73

Survey Question 16: Every state has a statewide transportation planning process that, at a minimum,is responsible for producing a state transportation plan. Has your agency participated in the statewidetransportation planning process during the last 5 years?16a. 16stp—Participated in state transportation planning process during the last 5 years.1 = Yes0 = NoIf stp16 = 016b. blrp16—Benefited from participating in state long-range planning process (if no 16stp).16c. bgopm16—Benefited from developing state goals, objectives and performance measures (ifno 16stp).16d. bpep16—Benefited from participating in state project evaluation and programming (if no16stp).1 = Yes0 = NoSurvey Question 17: To what extent does the transportation planning process in your state influencethe programs or initiatives undertaken by your agency?Influ17—Influence of transportation planning process on highway safety programs.2 = Strongly influences1 = Moderately influences0 = Does not influence9 = Don’t know74 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

Vehicle Breakdown Duration ModelingWENQUN WANG 1,*HAIBO CHEN 2MARGARET C. BELL 21 Atkins Transport SystemsWoodcote Grove Ashley RoadEpsom, England KT18 5BW2 Institute for Transport StudiesUniversity of LeedsLeeds, England LS2 9JTABSTRACTThis paper analyzes the characteristics of vehiclebreakdown duration and the relationship betweenthe duration and vehicle type, time, location, andreporting mechanisms. Two models, one based onfuzzy logic (FL) and the other on artificial neural networks(ANN), were developed to predict the vehiclebreakdown duration. One advantage of these methodsis that few inputs are needed in the modeling.Moreover, the distribution of the duration does notaffect the results of the prediction. Predictions werecompared with the actual breakdown durationsdemonstrating that the ANN model performs betterthan the FL model. In addition, the paper advocatesfor a standard way to collect data to improve theaccuracy of duration prediction.INTRODUCTIONA traffic incident is a nonrecurrent event. It is not aplanned closure of a road nor a special event; therefore,there is no advanced notice. Examples includevehicle breakdowns, accidents, natural disasters,and those caused by humans. An accident is a specifictype of incident that normally involves humaninjury or casualty.Email addresses:* Corresponding author—wenqun.wang@atkinsglobal.comH. Chen—hchen@its.leeds.ac.ukM.C. Bell—mbell@its.leeds.ac.ukKEYWORDS: Traffic incident management, vehicle breakdownduration, fuzzy logic, neural networks.75

Incidents have become one of the main causes oftraffic congestion. Lindley (1987) showed thatbetween 50% and 75% of the total traffic congestionon urban motorways in the United States isincident-induced. Moreover, there is a symbioticrelationship between incidents and congestion. Asincidents cause more congestion, more congestionbrings with it more incidents. Traffic incidents haveother impacts: the risk of secondary crashes for otherroad users and those dealing with the incident; andpossible reductions in air quality due to increasedfuel consumption caused by the congestion.In recent years, investment in developing systemsto manage incidents has increased. The FederalHighway Administration defines incident managementas the systematic, planned, and coordinateduse of human, institutional, mechanical, and technicalresources to reduce the duration and the impactof incidents, and improve the safety of motorists,crash victims, and incident responders (USDOT2000). Therefore, incident duration predictionbecomes an important tool for incident management.Reliable duration prediction can help trafficmanagers apply appropriate management strategies,and it can also be used to evaluate the efficiency ofthe management strategies that are implemented.Furthermore, duration prediction can provide accurateand essential information to road users.Vehicle breakdown is one type of incident thatoften occurs on motorways and represents morethan 80% of all types of incidents. In this paper, weanalyze the characteristics of vehicle breakdownsand develop vehicle breakdown duration modelsbased on fuzzy logic (FL) and artificial neural networks(ANN). We use incident data collected fromthe M4 motorway in the United Kingdom to validateour models.LITERATURE REVIEWIncident duration is the time period between theoccurrence and clearance of an incident. During thisperiod, the following activities occur: incident detection,verification, response, clearance, and recovery.Components of incident management include trafficmanagement and traffic information. To accomplishthis, information is exchanged between the differentparties involved, including the police and the breakdownrecovery service.Golob et al. (1987) analyzed data from over9,000 accidents involving large trucks and combinationvehicles collected over a two-year period onfreeways in the greater Log Angeles area. Theyfound that accident duration fitted a log-normal distribution.The factors used in their accident durationmodel were collision type, accident severity, and laneclosures. Their data were shown to be more statisticallysignificantly similar to the log-normal than thelog-uniform distribution. However, the sample sizeof each group was small (between 21 and 57).Giuliano (1989) extended the research of Golobet al. by applying a log-normal distribution in theincident duration analysis of 512 incidents in LosAngeles. The author found that the factors affectingincident duration were incident type, lanes closed,time of day, accident type, and whether or not atruck was involved. The variance within each categorywas large making it difficult to forecast theincident duration.Jones et al. (1991) made further improvementsby imposing a conditional probability; that is, giventhat the incident has lasted X minutes, it will end inthe Yth minute. The authors analyzed 2,156 incidentsin the metropolitan Seattle area and found thatthe duration of incidents conformed to a log-logisticinstead of log-normal distribution (they applied ahazard duration model to estimate the incident duration).However, some factors used in their model,such as the age of the driver, were found to beimpractical, because this information was often notavailable when the incident occurred. They statedthat more appropriate and accurate data are veryimportant in incident duration analysis.Nam and Mannering (2000) further developedthe hazard duration model in an analysis of incidentduration. They analyzed 681 incidents inWashington state, collected over two years. Theycontinued to use the log-logistic model of Jones etal. (1991) but removed the impractical variablesand applied hazard-based functions to estimate theincident duration. This study provided evidence thathazard-based approaches are suited to incident analysisfor the individual stage of the incident, includingdetection time, response time, and clearance time.76 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

However, one drawback, highlighted by the authors,is that they could not draw definitive conclusionsconcerning the actual duration of the incidentbecause data were insufficient.Sethi et al. (1994) developed a decision tree topredict incident duration. They based their researchon the statistical analysis of 801 incidents from theNorthwest Central Dispatch. This predictionmethod was very easy and practical to use; however,all the unknown incident durations were set to 23minutes, and this oversimplification of the modelwas detrimental to the accuracy of the predictions.Other papers that present complementary statisticalanalyses of incident duration include Wang(1991), Sullivan (1997), Cohen and Nouveliere(1997), Garib et al. (1997), Smith and Smith (2000),and Fu and Hellinga (2002).FL has been used in the transportation field sincethe theory was first developed by Zadeh (1965).The method offers much potential in the traffic andtransport field, because many problems and parametersare characterized by linguistic variables. Moreover,many problems in this field are ill defined,ambiguous, and vague. Such situations are difficultto model using traditional methods. A review byTeodorovic (1999) of state-of-the-art FL systems fortransport engineering clearly showed the potentialfor the application of FL.Choi (1996) was the first researcher to use an FLsystem to predict incident duration. He used incidentdata on vehicle problems, types of assistance, andthe location of disabled vehicles to demonstrate thesuitability of FL for solving problems characterizedby elements of uncertainty and ambiguity. Moreover,the FL system was shown to perform well with fewervariables compared with the statistical models.Kim and Choi (2001) updated the model andimproved the performance by refining the fuzzy sets.However, the authors did not categorize the type ofincidents, and this may have a significant effect onincident duration. Another shortcoming of this workis the limited incident data available to validate themodel.Wang et al. (2002) used FL to model vehiclebreakdown duration by analyzing the characteristicsof the breakdown by vehicle type, time of day,and location. Over 200 incident records from theM4 Motorway in the United Kingdom were used todemonstrate the credibility of the FL approach forestimating incident duration.A number of studies have reported the increasingpopularity of the application of the ANN theory totransportation. A review by Dougherty (1995)reported its wide application in a number of areas(e.g., traffic control, vehicle detection, driver behavioranalysis, traffic pattern analysis, traffic forecasting,and parameter estimation). More recent applicationsinclude incident detection analysis by Teng and Qi(2003) and Yuan and Cheu (2003). The theory ofANN is presented later in this paper.In summary, incident duration research has beendeveloped gradually over the last decade. Variousmethods have been applied, including statisticalanalysis and fuzzy logic. However, comparing previousresearch results is difficult for a number ofreasons: different variables have been used by theresearchers; the data were collected from differentareas in the world; and each dataset had its owncharacteristics. This review has provided us with thefoundation on which we developed an alternativeapproach to model traffic incident duration usingANN. The results are presented here and are comparedwith those of an FL model, building on theearlier work of Wang et al. (2002).DATA DESCRIPTIONFor this research, the incident duration data werecollected from one of the busiest roads in the UnitedKingdom, the M4 between Junction 22 and Junction49. The average traffic flow on this section of theM4 was 65,000 vehicles per day, with a maximumflow of 102,000 vehicles per day in 2001 (Departmentfor Transport 2002).The MANTAIN CYMRU Traffic Managementand Information Centre (TMIC), developed by apublic/private partnership led by the NationalAssembly of Wales, provides a cost efficient methodof improving traffic management. TMIC’s responsibilityincludes 129 kilometers of motorway andparts of other trunk roads, as illustrated by figure 1.TMIC collects information using several mediaincluding: a closed circuit television system, trafficsensors, roadside meteorological systems, probevehicles, police traffic reports, and other sources.WANG, CHEN & BELL 77

FIGURE 1 Map of the M4 MotorwayA40A470A465A48A483MerthyrTydfilA465A40A40M4A465A4060A4042A470A449SwanseaM4M4M48BridgendM4A48MNewportM4M49A4232CARDIFFM5Source: Available at www.traffic-wales.com.FIGURE 2 Distribution of Vehicle BreakdownDuration302520151050Percent0 12 24 36 48 60 72 84 96 108 120Duration (minutes)Weibull distributionThe Road Network Master Database (RNMD)stores all the information, which can be processed,transferred, and published to a third party as well asthe public (James and Wainwright 2002).We obtained 1,080 incidents records fromRNMD for May 2000 to April 2001. The incidentswere divided into three types: crashes, vehicle breakdowns,and other incidents. The majority of incidentswere vehicle breakdowns, 64% of all thetraffic incidents on the motorways. Crashes andother incidents made up the remainder, 20% and16% of all incidents, respectively.This paper reports the results of 695 vehiclebreakdowns. Many of the records were incomplete;that is, the end time of the incidents was often notrecorded. An in-depth look at the data gave us 213complete incident records, which we present in thispaper.Figure 2 shows the distribution of the incidentduration. A Kologorov-Smirnov test shows that itconforms to a Weibull distribution (sig. = 0.432),instead of a log-normal distribution (sig. = 0.043),which is consistent with the research of Nam andMannering (2000).Figure 3 demonstrates that incident duration displaysa relationship to the time of day and showspeaks during the morning and evening rush hour.The figure also shows that vehicle breakdown durationtends to be longer at night. These characteristicsare consistent with the higher traffic flow that causescongestion during the day and the poorer quality ofrecovery service during the late evening and overnightwhen traffic flows are substantially lower.Figure 4 compares the arithmetic and geometricmeans of the vehicle breakdown data according tovehicle type. As expected, the geometric mean isconsistently smaller than the arithmetic mean for allvehicles, because most incidents are of short duration.So the distribution is skewed to the right. The78 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 3 Vehicle Breakdown Duration andTime of DayTABLE 1 Kruskal-Wallis Test ofVehicle Breakdown Duration1008060Duration(minutes)Geometric meanArithmetic meanPoly. (arithmetic mean)Poly. (geometric mean)Variable Chi-square dfSignificancelevelReport16.7 1 0.44*10E–4mechanismVehicle type 17.1 3 0.67*10E–3Location 8.5 2 0.014Time of day 12.8 5 0.025402000 4 8 12 16 20 24Hour of dayFIGURE 4 Vehicle Breakdown Duration andVehicle TypeDuration (minutes)80706050403020100MotorcycleArithmetic meanGeometric meanCarVanHGVTanker truckVehicle typeKey: HGV = heavy goods vehicle (over 3,500 kg or 7,716 lbsdesign, gross vehicle weight).Totalduration of a tanker breakdown is the greatest,which is not surprising. The latter interpretation,however, should be viewed with caution due to thesmall sample size for this type of incident.Based on the available data and discussions withthe operators in the traffic control center, the potentialvariables to be considered in the vehicle breakdownduration model were vehicle type, location,time of day, and report mechanism. We investigatedthe difference between the incident duration categoriesusing the Kruskal-Wallis test, the results ofwhich are shown in table 1. This test indicates thatthe overall differences between the categories are statisticallysignificant, in particular the vehicle typesand report mechanisms categories had a significancelevel of less than 0.001.VEHICLE BREAKDOWN DURATIONMODELINGIn this section, we present two vehicle breakdownduration models. The first is based on FL, while thesecond uses the ANN approach.The Model Based on FLThis research used the Mamdani-type FL system.Mamdani (1974) proposed this method in anattempt to control a steam engine and boiler combinationby synthesizing a set of linguistic controlrules obtained from experienced human operators.The Mamdani-type inference expects the outputmembership functions to be fuzzy sets. After theaggregation process, the fuzzy set for the outputvariable needs defuzzification. The inputs of theincident duration were vehicle type, location, timeof day, and report mechanism. The dependent variablewas the vehicle breakdown duration. These aredetailed in table 2.Figure 5 illustrates the structure of the FL system.The system comprises four elements: the fuzzifierthat maps the crisp value into a fuzzy set; the rulebase that saves the fuzzy rules; the interface that generatesthe fuzzy output from the input based on thefuzzy rules; and finally the defuzzifier that transfersWANG, CHEN & BELL 79

TABLE 2 Variables in the Fuzzy Logic ModelVariableFuzzy setInput Vehicle type SmallMediumBigVery bigLocationAt nodeClose to nodeFar from nodeTimeNightEarly morningMorningAfternoonAfternoon peak timeEveningReport mechanism ETS usedNo ETS usedOutput Duration Very shortShortMediumLongVery longKey: ETS = emergency telephone service.FIGURE 5 Structure of the FL SystemInputRule baseFuzzifier Interface DefuzzifierOutputthe fuzzy output into a crisp value. The detailedexplanation of the FL theory can be found inPedrycz and Gomide (1998).This research was based on the fuzzy sets of eachvariable, the characteristics of the data presentedabove, and the fuzzy rules derived from an understandingof the experience of the operators at theMANTAIN CYMRU TMIC gained in the interviewsurveys. One example of the 112 fuzzy rules used inthis work is the following:If the vehicle is CAR, and location is ATTHE JUNCTION, and the time isMORNING, and the report mechanismis ETS (emergency telephone service),then the vehicle breakdown duration isSHORT.There are many defuzzification methods, includingthe mean of the range of maximal values and thecenter of the area that returns the center of gravityof the area under the curve. The latter is the mostpopular method used in defuzzification and the oneadopted in this study.Matlab was used to generate the model and simulatethe results (Biran and Breiner 1999). Figure 6shows the model surface depending on the vehicletype and time of day and clearly illustrates the nonlinearrelationship between the inputs and outputs.Figure 7 displays the value predicted using FLcompared with the observed value. The modelshows promise as an estimator of breakdown durationand the pattern of results is consistent with theresearch by Cohen and Nouveliere (1997).The Model Based on the ANN SystemAn ANN is a massively parallel distributed processorthat has a natural propensity for storingexperiential knowledge and making it available foruse (Aleksander and Morton 1990). The knowledgeis acquired through a learning process and is storedas synaptic weights. The structure of the ANN isdescribed later in this section.The advantages of the ANN are as follows. First,the ANN is nonlinear, thus it can be applied tomodel a nonlinear physical mechanism easily. Second,the learning process enables the ANN to bemodified, in accordance with an appropriate statisticalcriterion, to minimize the difference betweenthe desired response and the actual response of thenetwork driven by the input. This makes the ANNa suitable candidate to model incident duration.In this research, a multilayer perceptron networkwas used, in which IW{n,1} is the input weightmatrix; LW{n,1} is the layer weight matrix; and b{n}are bias vectors, where n is the layer number. The80 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 6 Surface of the FL SystemDuration (minutes)807060504030202015Time of day1050 01234Vehicle type5choice of the neurons in the ANN is based on thenumber of inputs, outputs, and the sample size. Theneuron number is determined following the guideby NeuralWare (1993). In this research, to maintainsimplicity and avoid redundant architecture theANN model has 17 neurons in one hidden layer(figure 8).The output of each layer, which is the input forthe next layer, is calculated using the following formula:⎛N – 1 ⎞y j = f ⎜∑ w ij x i – θ ⎟⎜j⎟⎝i = 0⎠0 ≤ j ≤ N 1 – 1wherey j = the jth output,θ j = the bias in the nodes,w ij = the weight,N = the number of inputs, andN 1 = the neuron number.In this research, the transfer function of the firsthidden layer was the sigmoid function:fx ( )1= ----------------1 + e – xIn the output layer, a linear function is used as thetransfer function to generate the desired output.The inputs to the ANN system were vehicle type,location, time of day, and report mechanism. Theoutput was vehicle breakdown duration. The ANNmodel was trained with the back-propagationFIGURE 7 Result of the FL ModelModeled value (minutes)1401201008060402000204060100FIGURE 8 Structure of the ANN SystemIW{1,1}b{1}17 17120140training algorithm (Lau 1992), which is a generalizationof the least mean squares algorithm. It uses agradient search technique to minimize the meansquare difference between the desired and the actualoutputs.80Observed value (minutes)LW{2,1}b{2}1WANG, CHEN & BELL 81

FIGURE 9 Result of the ANN ModelModeled value (minutes)1401201008060402000204060100120140Of the 213 vehicle breakdown incidents, 113 incidentswere used to train the model and 50 were usedin validation during the training. The remaining 50incidents were used to test the performance of themodel. Figure 9 compares the ANN prediction withthe observed value with encouraging results. Itdemonstrates that the performance was better thanthat of the FL model, because the predicted valuewas closer to the observed value. However, it alsoshows that the ANN model systematically generatedthe same durations when the observed valueswere different. In general, the ANN in this casefailed to predict the larger values and outliers. Onereason for this was that the number of explanatoryvariables was insufficient. Therefore, the ANNmodel could not be trained to perform well. Thisproblem could be solved by including additionalvariables and is a subject of future research.In order to estimate the influence of the inputvariables on the output of the model, we conducteda sensitivity test. This was achieved by excludingone input variable at a time and quantifying thedeterioration of the performance of the predictioncaused by the missing variable. The performancemeasure used was defined as the percentage changein the root mean square error (RMSE). The RMSEgives a measure of the difference between theobserved and modeled value. It is defined as:RMSE=80Observed value (minutes)N1---- fN ∑ ( n – v n ) 2n = 1wheref n = the modeled value,v n = the observed value, andN = the number of observations.The percentage change of the error P% is given byRMSEP%n – 1 – RMSE= ---------------------------------------------------- n× 100%RMSE nwhereRMSE n = the RMSE of the model with all ninputs.The sensitivity test showed that all four variablesinfluenced the performance of the ANN vehiclebreakdown duration model, as the error consistentlyincreased when each input was removed fromthe model. In particular, the report mechanism wasfound to have the greatest effect, because the errorincreased by 23% when it was removed from themodel. The location had the least effect, with a 12%increase (table 3).TABLE 3 Sensitivity Test of the ANN Input VariablesModelRMSEANN model with all four inputs 19.5ANN model withoutreport mechanismANN model withoutvehicle typeANN model withouttime of dayCOMPARISON OF THE RESULTS OFFL AND ANNErrorincrease24.1 23%23.8 22%22.5 15%ANN model without location 22.0 12%Key: RMSE = root mean square error.We conducted statistical tests to compare the performanceof these two models. In this paper, the R 2 testand the RMSE were applied. These methods arecommonly used to evaluate the relative performanceof traffic models (Clark et al. 2002).The coefficient of variation R 2 is shown in table4. We tested two ANN models, one with 17 neuronsin the hidden layer and one with 10 neuronsin the hidden layer, and found that the number ofneurons affects the performance of the model. Thetable shows that the ANN model with 17 neurons82 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 4 Comparison of the FL and ANN ModelsModel R 2 AdjustedR 2 Sig. RMSEFL model 0.265 0.262 0.000 24.0ANN model 1* 0.414 0.411 0.000 19.5ANN model 2** 0.215 0.211 0.000 24.1* ANN model 1 has 17 neurons in the hidden layer.** ANN model 2 has 10 neurons in the hidden layer.Key: RMSE = root mean square error.performed best, while the performance of the FLmodel fell in the middle of the two ANN models. Atthe time that an incident occurs, the operator in thecontrol center estimates the anticipated duration ofthe resulting congestion, based on engineering judgmentand experience. The RMSE of this estimationis 42 minutes. It shows that both the ANN modelsand the FL model gave better estimates than theoperators judgment.Both ANN and FL methods show promise in predictingthe incident duration. However, given thatthe R 2 value is not very high, and the RMSE value islarge, the performance needs to be improved. Thiscan be addressed by including more variables inthe model. However, this requires more data to becollected and the cooperation of the operators andthose responsible for motorway incident management.Future work will be concentrated in theseareas. Despite the fact that the significance levels ofthe three models are low, the modeled values areconsistently better than the estimated values by theoperators. Therefore, these results are of interest tothe motorway incident management team.CONCLUSIONSThis paper analyzed the characteristics of vehiclebreakdown duration and the main factors that mayaffect the duration. Two models, one based on FLand the other on ANN, were developed and theirperformances compared.The research demonstrated that FL and ANNcan provide reasonable estimates for the breakdownduration with few variables. They consistently outperformthe existing method based solely on theengineering judgment of the operators. Also, for thespecific data used in this research, the ANN modelperformed better than the FL model according tothe characteristics of statistical parameters. However,both models had difficulties in predicting theoutliers. As further data characterizing the outliersbecome available, the relative performance of ANNand FL may change.Finally, the research highlights the need to collectinformation required for incident management in astandard way to improve the accuracy of prediction,enhance the management of incidents, andenable the authorities to share the data. Currentresearch, using a specially designed electronic databasetool, will improve the quantity and quality ofthe data records and thus begin to explain more ofthe variation in the data. In the future, the combinedFL-ANN approach can be used to analyze incidentduration, because this method can combine theexperiences of the experts and the statistical characteristicsof ANN.ACKNOWLEDGMENTThe authors would like to thank W.S. Atkins forsupplying the traffic data used in this study.REFERENCESAleksander, I. and H. Morton. 1990. An Introduction to NeuralComputing. London, England: Chapman & Hall.Biran, A. and M. Breiner. 1999. Matlab 5 for Engineers. Reading,England: Addison-Wesley.Choi, H.-K. 1996. Predicting Freeway Traffic Incident Durationin an Expert System Context Using Fuzzy Logic, Ph.D.dissertation. University of Southern California.Clark, S.D., S.M. Grant-Muller, and H. Chen. 2002. UsingNonparametric Tests to Evaluate Traffic Forecasting Performance.Journal of Transportation and Statistics 5(1):47–56.Cohen, S. and C. Nouveliere. 1997. Modelling Incident Durationon an Urban Expressway. IFAC/IFIP/FORS Symposium.Edited by M. Papageorgiou and A. Pouliezos. Chania,Greece.Department for Transport. 2002. Transport Statistics Bulletin:Road Traffic Statistics: 2001. Compiled by A. Silvester andA. Smith. London, England.Dougherty, M. 1995. A Review of Neural Networks Applied toTransport. Transport Research C 3:247–260.Fu, L. and B. Hellinga. 2002. Real-Time, Adaptive Prediction ofIncident Delay for Advanced Traffic Management Systems.Proceedings of the Annual Conference of the CanadianInstitute of Transportation Engineers, May 12–15, 2002,Waterloo, Ontario, Canada.WANG, CHEN & BELL 83

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Using Generalized Estimating Equations to Account forCorrelation in Route Choice ModelsMOHAMED ABDEL- ATYDepartment of Civil and Environmental EngineeringUniversity of Central FloridaOrlando, FL 32816-2450Email: mabdel@mail.ucf.eduABSTRACTThis paper presents the use of binary and multinomialgeneralized estimating equation techniques(BGEE and MGEE) for modeling route choice. Themodeling results showed significant effects onroute choice for travel time, traffic information,weather, number of roadway links, and driver ageand education level, among other factors. Eachmodel was developed with and without a covariancestructure of the correlated choices. The effect ofcorrelation was found to be statistically significant inboth models, which highlights the importance ofaccounting for correlation in route choice modelsthat may lead to vastly different travel forecasts andpolicy decisions.INTRODUCTIONHow and when travelers make decisions aboutwhat route they will take to their destination is anarea of great interest to researchers and decisionmakersalike. In this paper, binary and multinomialgeneralized estimating equation techniques (BGEEand MGEE) are used to model route choice.Binary and multinomial route choice modelsmay have two different kinds of correlation. First,repeated observations may be correlated. This isKEYWORDS: Route choice, repeated observations, overlappingroutes, BGEE, MGEE, logit.85

usually the case for studies that use surveys/simulationswhere each respondent/subject providesrepeated responses. Second, the overlapping distancebetween alternative routes may be correlated in multinomialroute choice models. In a multinomial routechoice model, the case is further complicated whenthe data structure includes both types of correlation.In the 1980s, most discrete choice models werecalibrated using binary logit (BL) and multinomiallogit (MNL) models (Yai et al. 1997). BL and MNLmodels characterize the choice of dichotomous orpolytomous alternatives, made by a decisionmaker(in our study, the driver) as a function of attributesassociated with each alternative as well as the characteristicsof the individual making the choice.An advantage of both BL and MNL models istheir analytical tractability and ease of estimation.However, a major restriction of MNL models is theIndependence from Irrelevant Alternatives (IIA)property, which arises because all observations areassumed to have the same error distribution in theutility term based on a Gumbel distribution (IIAarises because the assumption of being Independentand Identically Distributed is made for the Gumbel).Therefore, BL and MNL models assume independencebetween observations, which is not true ifeach subject/driver has more than one observation.Also, MNL models assume independence betweenalternatives, which is not true when routes overlap.A major statistical problem with clustercorrelateddata, for which BL/MNL models do notaccount, arises from intracluster correlation or thepotential for cluster mates to respond similarly. Thisphenomenon is often referred to as overdispersionor extra variation in an estimated statistic beyondwhat would be expected under independence. Analysesthat assume independence of the observationswill generally underestimate the true variance andlead to test statistics with inflated Type I errors(Louviere and Woodworth 1983).Gopinath (1995) demonstrated that differentmodel forecasts result when the heterogeneity oftravelers is not considered. Delvert (1997) arguedthat models of travel behavior in response toAdvanced Traveler Information Systems mustaddress heterogeneity in behavior. When we cannotconsider the observations to be random draws froma large population, it is often reasonable to think ofthe unobserved effects as parameters to estimate, inwhich case we use fixed-effects methods. Even if wedecide to treat the unobserved effects as randomvariables, we must also decide whether the unobservedeffects are uncorrelated with the explanatoryvariables, which is the case in many situations. Todraw accurate conclusions from correlated data, anappropriate model of within-cluster correlationmust be used. If correlation is ignored by using amodel that is too simple, the model would underestimatethe standard errors of modeling effects(Stokes et al. 2000).This paper reviews the existing methodologies forroute choice modeling that account for one or bothtypes of correlation mentioned above. The advantagesand drawbacks of each methodology arestated. The main objective of this paper is to suggesta methodology (used in other fields) that accountsfor correlation in binary and multinomial routechoice modeling. BGEE and MGEE techniques areintroduced with a binomial logit link function forBGEE and polytomous logistic link function forMGEE. The advantage of these techniques is thatthey account for correlation using a simple logisticlink function instead of the probit function, whichneeds tremendous computational effort and cannotbe used for relatively high numbers of alternatives orwith large networks in multinomial models.METHODOLOGIES THAT ACCOUNT FORCORRELATIONRepeated ObservationsStatisticians and transportation researchers havedeveloped several methodological techniques toaccount for correlation between repeated observationsmade by the same traveler in binary andmultinomial route choice models. Louviere andWoodworth (1983) and Mannering (1987) correctedthe standard errors produced in a repeatedresponses regression model by multiplying the standarderrors by the square root of the number ofrepeated observations. Kitamura and Bunch (1990)used a dynamic ordered-response probit model ofcar ownership with error components. Manneringet al. (1994) used an ordered logit probability86 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

model and a duration model with a heterogeneitycorrelation term. Morikawa (1994) used logitmodels with error components to treat serial correlation.Abdel-Aty et al. (1997) and Jou (2001)addressed this issue using individual-specific randomerror components in binary models with a normalmixing distribution. The standard deviation of theerror components were found significant in bothstudies, which clearly showed the need for someformal statistical corrections to account for theunobserved heterogeneity. Jou and Mahmassani(1998) used a general probit model form for thedynamic switching model, allowing the introductionof state dependence and serial correlation in themodel specification.At the multinomial level, Mahmassani and Liu(1999) used a multinomial probit model frameworkto capture the serial correlation arising fromrepeated decisions made by the same respondent.Garrido and Mahmassani (2000) used a multinomialprobit model with spatial and temporally correlatederror structure.Overlapping AlternativesThe correlation between alternative routes due primarilyto overlapping distances has attracted manyresearchers to overcome the limitations of MNLmodels. The nested logit (NL) model (proposed byBen-Akiva 1973) is an extension of the MNL modeldesigned to capture correlation among alternatives.It is based on the partitioning of the choice set intodifferent nests. The NL model partitions some or allnests into subnests, which can in turn be dividedinto subnests. This model is valid at every layer ofthe nesting, and the whole model is generated recursively.The structure is usually represented as a tree.Clearly, the number of potential structuresreflecting the correlation among alternatives can bevery large. No technique has been proposed thusfar to identify the most appropriate correlationstructure directly from the data (apart from using aheteroskedastic extreme value choice model as asearch engine for specification of NL structures). TheNL model is designed to capture choice problemswhere alternatives within each nest are correlated.No correlation across nests can be captured by theNL model. When alternatives cannot be partitionedinto well separated nests to reflect their correlation,the NL model is not appropriate.Cascetta et al. (1996) introduced the C-logitmodel as a MNL model that captures the correlationamong alternatives in a deterministic way. Theauthors use a term called “commonality factor,”which they add to the deterministic part of the utilityfunction to capture the degree of similarity betweenthe alternative and all other alternatives in the choiceset. The lack of theory or guidance on which form ofcommonality factor should be used is a drawback ofthe C-logit method.McFadden (1978) presented the cross-nestedlogit (CNL) model as a direct extension of the NLmodel, where each alternative may belong to morethan one nest. Similar to the NL model, the choiceset is partitioned into nests. Moreover, for eachalternative i and each nest m, parameters α im , representingthe degree of membership or the inclusiveweight of alternative i in nest m, have to be defined.A CNL model is not appropriate for high numbersof alternatives.Vovsha and Bekhor (1998) proposed and used alink-nested logit model as an application of theCNL model. The largest network they used contained1 origin-destination pair, 8 nodes, 11 links,and 5 routes. Papola (2000) estimated a CNL modelfor intercity route choice with a limited number ofalternative routes. Swait (2001) proposed the choiceset generation logit model, in which choice sets formthe nests of a CNL structure. The author acknowledgedthe computational difficulties of estimatingthis model when the choice set is large. It was concludedthat, for a realistic size network and a realisticnumber of links per path, the CNL model and itsapplications become quite complex and thereforecomputationally onerous.NL, C-logit, and CNL models are all extensionsof the MNL models that use a logit utility function.An alternative technique is the multinomial probit(MP) model, which is derived from the assumptionthat the error terms of the utility functions are normallydistributed. It uses a probit link functioninstead of a logit function. The MP model capturesexplicitly the correlation among all alternatives.Therefore, an arbitrary covariance structure can bespecified. Mostly, this covariance structure wasABDEL- ATY 87

proportional to overlap length. Routes were alsoassumed to have heteroskedastic error terms wherevariance was proportional to route length orimpedance. Yai et al. (1997) introduced a functionthat represents an overlapping relation betweenpairs of alternatives. The difficulty in implementingthe probit model is that no closed form exists forthe Gaussian cumulative distribution function, sonumerical techniques must be used. Estimating anMP model is difficult even for a relatively lownumber of alternatives. Moreover, the number ofunknown parameters in the variance-covariancematrix grows with the square of the number ofalternatives (McFadden 1989).Ben-Akiva and Bolduc (1996) introduced a multinomialprobit model with a logit kernel (or hybridlogit) model, which combines the advantages oflogit and probit models. It is based on a utility functionthat has two error matrices. The elements of thefirst matrix are normally distributed and capturecorrelation between alternatives. The elements ofthe second matrix are independent and identicallydistributed. These combined models have the samecomputational difficulties as pure MP. In general,any application of hybrid logit or probit to largescaleroute choice is questionable in terms of thecomputational effort needed for estimating theparameter coefficients and their marginal effects,especially for large networks.Based on the above review, a clear need exists fora methodology that accounts for the two kinds ofcorrelation in binary and multinomial route choicemodels with a computationally easy and statisticallyefficient technique, both for small and large networks.This paper applies BGEE and MGEE withlogit functions (binary and polytomous) to accountfor correlation between repeated observations inbinary models and correlation between repeatedobservations and overlapping routes in multinomialmodels.ApplicationsRoute Choice and SwitchingPre-trip and en-route route switching is a directresponse to Advanced Traveler Information Systems(ATIS). Network conditions, travel time, travel timevariability, delays associated with congestion andincidents, and traveler attributes are significantdeterminants of route choice (Spyridakis et al. 1991;Adler et al. 1993; Mannering et al. 1994; Abdel-Atyet al. 1995a, b, 1997). Some studies proved thatproviding information induces greater switching inroute choice behavior (Mahmassani 1990; Conquestet al. 1993; Abdel-Aty et al. 1994b). For example,Conquest et al. (1993) reported that 75% of commuterschange either departure time or route inresponse to information. Liu and Mahmassani(1998) concluded that travelers were more likely tochange their route when their current choice wouldcause them to arrive late. They also concluded thatdrivers exhibited some inertia in route choice,requiring travel time savings of at least one minuteon the alternative route.Benefits of ATISMany studies have examined the potential benefitsof providing pre-trip and en route real-time informationto travelers. Much research focuses on theeffects of ATIS on all types of travel decisions. Anumber of studies show that ATIS results inreduced travel time, congestion delays, and incidentclearance time (Wunderlich 1996; Abdel-Aty et al.1997; Sengupta and Hongola 1998). Empirical evidencesupports the hypothesis that travelers altertheir behavior in response to ATIS (Bonsall andParry 1991; Zhao et al. 1996; Mahmassani andHu 1997). Reiss et al. (1991) reported travel timesavings ranging from 3% to 30% and reduction inincident and congestion delays of up to 80% forimpacted vehicles.Drivers’ Familiarity with the Networkand DiversionPolydoropoulou et al. (1996) and Khattak et al.(1996) concluded that drivers exhibit some inertiaand tend to follow the same route, especially forhome-to-work trips. Polydoropoulou et al. foundthat drivers are more likely to divert to anotherroute when they learn of a delay before a trip. Driversare less likely to divert during bad weather, as alternativeroutes may be equally slow. Prescriptiveinformation greatly increases travelers’ diversionprobabilities, although similar diversion rates areattainable by providing real-time quantitative or predictiveinformation about travel times on usual and88 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

alternative routes. The authors suggest that driverswould prefer to receive travel time information andmake their own decisions. Abdel-Aty et al. (1994a)showed that ATIS has great potential to influencecommuters' route choice even when advising a routedifferent from the usual one.Studies also indicate that traffic informationshould be provided along with alternative routeinformation. Streff and Wallace (1993) reporteddifferences in information requirements betweencommuting, noncommuting trips, and trips in anunfamiliar area. Khattak et al. (1996) found thattravelers who were unfamiliar with alternative routesor modes were particularly unwilling to divert. Thisconfirms the work of Kim and Vandebona (2002),which concluded that drivers who were familiarwith an area had a high propensity to change theirpreselected routes. Further, accurate quantitativeinformation might be able to overcome behavioralinertia if commuters are willing to follow advicefrom a prescriptive ATIS (Khattak et al. 1996;Lotan 1997). Adler and McNally (1994) found thattravelers who were familiar with the network wereless likely to consult information. Bonsall and Parry(1991) found that user acceptance declined withdecreasing quality of advice in an unfamiliar network,and in a familiar network, drivers were lesslikely to accept advice from the system. However,Allen et al. (1991) found that familiarity does notaffect route choice behavior.GENERALIZED ESTIMATING EQUATIONSThe generalized estimating equations (GEE) techniqueanalyzes discrete and correlated data withreasonable statistical efficiency. Liang and Zeger(1986) introduced GEE for binary models (BGEE)as an extension of generalized linear models (GLM).Lipsitz et al. (1994) extended the BGEE methodologyto model correlation between repeated multinomialcategorical responses (MGEE).The GEE methodology models a known functionof the marginal expectation of the dependent variableas a linear function of the explanatory variables.With GEE, the analyst describes the random componentof the model for each marginal response witha common link and variance function, similar towhat happens with a GLM model. However, unlikeGLM, the GEE technique accounts for the covariancestructure of the repeated measures. Thiscovariance structure across repeated observations ismanaged as a nuisance parameter. The GEE methodologyprovides consistent estimators of the regressioncoefficient and their variances under weak assumptionsabout the actual correlation among a subject’schoices.In the following section, we provide a briefexplanation of the BGEE models. The MGEEmethodology is included in the appendix at the endof this paper.Binary Generalized Estimating EquationsSuppose a number of n i choices are made by subjecti, where the total number of subjects is K, and y ijdenotes the jth response from subject i. There areK∑n i total choices (measurements). Let the vectori = 1of choices made by the ith subject beY i = ⎛y i1 ,...,y ⎞′⎝ ini ⎠and let V i be an estimate of the covariance matrix ofy i . Let the vector of explanatory variables for the jthchoice on the ith subject be X ij1 = ( x ij1 ,...,x ijp )′.The GEEs for estimating the ( 1 × p)vector ofregression parameters β is an extension of the independenceestimating equation to correlated dataand is given byK∂µ′ i – 1∑---------V (1)∂ β i ( Y i – µ ( i β )) = 0i = 1where p is the number of regression parameters,Since g ( µ ij ) = x ij , β, the p × n i matrix of partialderivatives of the mean with respect to the regressionparameters for the ith subject is given by∂µ′--------- i∂ β=x i11---------------- .....g′ ( µ i1 ):·x i1p---------------- .....g′ ( µ i1 )x ini 1-------------------g′ ⎛ µ in⎞⎝ i ⎠:·x ini p-------------------g′ ⎛µ ini⎞⎝ ⎠(2)whereg is the logit link function g ( µ ) = log( p( 1 – p )),which is the inverse of the cumulative logistic distributionfunction, which is:ABDEL- ATY 89

Fx ( )Working Correlation Matrix in BGEE(3)Let R i ( α) be an n i × n i “working” correlationmatrix that is fully specified by the vector of parametersα (the correlation between any two choices).The (j, k) element of R i ( α)is the known, hypothesized,or estimated correlation between y ij and y ik .The covariance matrix of Y i is modeled as(4)whereA i is an n i × n i diagonal matrix with v ( µ ij ) as thejth diagonal element.φ is a dispersion parameter and is estimated by1φˆ (5)N------------- Kn iK– pe 2= ∑ ∑ , N =ij ∑ n ii = 1 j = 1i = 1R is the working correlation matrix. It is the samefor all subjects, is not usually known, and must beestimated. The estimation occurs during the iterativefitting process using the current value of theparameter matrix β to compute appropriate functionsof the Pearson residualye ij – µij = ----------------- ij.v ( µ ij )If R i ( α)is the true correlation matrix of Y i , thenV i is the true covariance matrix of Y i . If the workingcorrelation is specified as R = I, which is the identitymatrix, the GEE reduces to the independence estimatingequation. The exchangeable correlationstructure introduced by Liang and Zeger (1986)assumes constant correlation between any twochoices within a subject/cluster. This exchangeablecorrelation structure can be used in the BGEE wherethe correlation matrix of each subject/cluster isdefined as:⎧Corr( y ij , y ik )1, j = k ⎫= ⎨ ⎬⎩ α, j ≠ k ⎭where1= ----------------1 + e – x1--1--2 2V i = φA i R( α)A ie.g., →1αˆ = -------------------------- e( N∗ ij e ik– p )φ∑ ∑N∗ =K∑i = 1Kn i ( n i – 1 )i = 1 j ≠ kR 3x3=1 ααα 1 ααα1and(6)(7)DATA COLLECTION AND EXPERIMENTDESCRIPTIONWe used the travel simulator, Orlando TransportationExperimental Simulation Program (OTESP), tocollect dynamic pre-trip and en-route route choicedata. OTESP is an interactive windows-based computersimulation tool. It simulates a commuterhome-to-work morning trip. OTESP provides fivescenarios (levels) of traffic information to the subjects.In scenario #1, subjects receive no trafficinformation. Pre-trip information without and withadvice are presented in scenarios #2 and #3, respectively.En route information, keeping the pre-tripinformation, without and with advice is presentedin scenarios #4 and #5, respectively. The subject isrequired to choose his/her link-by-link route from aspecified origin to a specified destination. The subjecthas the ability to move the vehicle on differentsegments of the network using the computer’smouse. Driving and riding one of two available busroutes are the travel modes used in OTESP. However,this study focuses only on the drive option.In this study, we used a real network with historicalcongestion levels and weather conditions (figure1). Intersections, recurring congestion, nonrecurringcongestion (incidents), toll plazas, and weather conditiondelays are considered. The Moore’s shortestpath algorithm (Pallottino and Grazia 1998) wasemployed in the OTESP code to determine thetravel-time-based shortest path, which is introducedas advice to the subjects in some scenarios.The simulation starts and ends with a short surveyto collect the subjects’ sociodemographic characteristics,preferences, perceptions, and feedback. Afour-table database was created to capture all theinformation/advice provided and the traveler decisions.The program presents 10 simulated days (2days for each scenario) after familiarizing the subjectswith the system by introducing a training dayfor each scenario. Figure 1 shows a spot view ofOTESP in its third scenario as an example.NetworkFigure 1 presents a portion of the city of Orlandonetwork captured from a geographic informationsystem database. The network has a unique origindestinationpair, where the assumed origin is the90 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

FIGURE 1 Sample View of a Screen from the Orlando TransportationExperimental Simulation Program (Scenario #3)SimulationNow, you are going toyour work near the UCFarea coming from yourhome near the intersectionbetween road 436 and thestate HWY 408.Time in minutes 0.0Valid intersectionsAccidentFree flow linksModerate flowCongested flowShortest path408Home2.5 4.40.8 20.82.43.4 4.6 3.3 3.85.24363.82.22.1 3.12.12.67.33.82.7 2.3 2.31.91.9 2.91.61.50.73.04.9 0.23.6 2.8Work1.29.66.93.63.12.70.8NBusNo informationNo adviceStartPre-trip informationNo advice AdviceStart StartEn-route informationNo advice AdviceStart StartValid IntersectionsGo to trainingday #4subject’s home and the assumed destination is thesubject’s work place. The network consists of 25nodes and 40 links. This network portion wascarefully chosen from the entirety of the Orlandonetwork. It comprises different types of highways,including six-lane principle arterials, four-lane principlearterials, six-lane minor arterials, two-laneminor arterials, and local collectors. The networkalso includes two expressways.SubjectsSubjects were recruited based on an experiment toguarantee the inclusion of groups of drivers thatrepresent different incomes (two levels), ages (threelevels), gender, familiarity with the network (twolevels), and education (two levels). Because the subjectsdrove for their morning home-to-work trips,they were instructed that their main task was tominimize the overall trip travel time by decidingwhen and when not to follow the information and/or advice provided. Subjects were asked not to gothrough the simulation unless they had at least 30minutes to devote to it (the average simulation took23.77 minutes) and felt they could concentrate on it.Moreover, during the simulation, the subjects’response times were measured without notifyingthem, to ensure that they were paying attention. Atotal of 65 subjects participated in the simulationfor 10 trial days each. Twenty-two subjects wereunder the age of 25 while 24 subjects were between25 and 40 years of age, and 19 subjects were over40 years old. Of the subjects, 24 were female and 41were male. Two of the 65 subjects were excludedfrom this study, because their response times wereoutliers in the normal distribution (Z = 3.21 and3.78, Z cr = 2.57).BGEE APPLICATIONSubjects viewed the level of congestion of everylink in quantitative (travel time) and qualitative(green, yellow, and red links for free flow, moderate,and congested links, respectively) forms. Thesimulator also provided the shortest path from thesubject’s current position to the destination asadvice. The information/advice level the subjectreceived depended on the scenario, as mentionedabove. At each node, the subject had to decide andchoose between the two upcoming links. We consideredthis choice positive if the subject picked the linkABDEL- ATY 91

that had a lower level of congestion than the others(the delay on a link was equal to the differencebetween actual travel time at a specific movement—when a decision is made—and free flow traveltime). A choice was considered negative if the subjectpicked the link with a higher level of congestion.We focused on the delay on a link when a particularmovement occurred instead of travel time, becausethe links are different in length and speed limit.Sixty-three subjects completed 10 trial dayseach, for a total of 539 trial days in the drive mode(the remainder of the trial days were in the transitmode). During the trial days, 4,753 movements(decisions) were made on the 40 network links. Outof the 4,753 movements, 1,667 were excluded fromthe analysis, because the driver had no choice butto proceed onto a unique coming link. The remaining3,086 link choices make up the data used forthe BGEE model with binomial logistic function.The model was correlated because each subject hadmultiple choices in the data structure. The responsevariable was binary with the value of one for positivechoices and zero for negative choices. Theexplanatory variables follow:1. Information familiarity: one if the subject, inreal life, uses pre-trip and/or en route informationusually or everyday, zero otherwise.2. Information provision: one for trial dayswhere en route information was provided,zero otherwise.3. Same color: one if the two coming links hadthe same color (qualitative congestion level),zero otherwise. This variable tests the effect ofqualitative vs. quantitative information.4. System learning: one for the second five trialdays of the simulations, zero for the first five.This is based on the assumption that the subjectin the last five simulation runs is morefamiliar with the information system and canuse and benefit from it more effectively.5. Heavy rain: one for heavy rain conditions;zero for light rain or clear sky conditions.Weather conditions were provided as part ofthe information.6. Number of movements from the origin: representingthe closeness to the destination.Table 1 presents the results of the BGEE modelfor the independent case (no correlation is considered)and for the proposed exchangeable correlation.The differences in the results are due to the effectof correlation. By comparing the overall F statisticvalues for the two models, the exchangeable modelwas favored over the independent model. This indicatesthat the model has correlation that should beaccounted for.The modeling results showed that, in general, theprovision of en route information increases the likelihoodof making a positive link choice. This meansthat the en route short-term information has a goodchance of being used. When the two coming linkshad the same qualitative level of congestion, driverswere less likely to make a positive choice. Thus, thequalitative information is more likely to be used thanthe quantitative information. Therefore, it is notenough to provide the driver with the expected traveltime or that there is congestion, but providing thedriver with information on the level of congestion isalso necessary.The following effects/interactions increase thelikelihood of following the en route short-terminformation:1. Being familiar with traffic information;2. Learning and being familiar with the systemthat provides the information;3. Heavy rain conditions;4. Being away from the origin, that is, close tothe destination (presented by the number ofmovements since the origin);5. Providing qualitative information in heavyrain conditions; and6. Being away from the origin and being familiarwith the device that provides the information.MGEE APPLICATIONThe long-term route choices of the subjects in theexperiment were used as the database for estimatingthis model. The 539 routes that were chosen duringthe 539 trial days (each subject chooses one routeeach trial day) were identified and categorized bythe sequence of links that were traversed on a giventrial day. The network used consists of four westeastexpressway/arterials that connect the origin to92 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 1 Modeling Results for the BGEE Model with and without CorrelationWithout correlationWith correlationParameter Coefficient t statistic Coefficient t statisticIntercept –3.682 –20.29 –3.699 –20.11Information familiarity: 1 if subject usespre-trip and/or en route trafficinformation usually or everyday, 0otherwise0.406 10.12 0.421 9.94Information provision: 1 for scenario 4where en route information is providedwithout long-term advice, 0 otherwiseSame color: 1 if the two coming linkshad the same color (qualitativecongestion level), 0 otherwiseSystem learning: 1 for the second 5 trialdays of the experiment, 0 for the first 5trial daysHeavy rain: 1 for heavy rain condition, 0for light rain or clear sky0.236 2.07 0.243 2.11–0.467 –4.20 –0.476 –4.283.469 15.75 3.598 15.700.415 3.24 0.402 3.17Number of movements since the origin 0.610 9.78 0.634 9.61Interaction termsHeavy rain × Same color 0.453 2.25 0.536 2.16Number of movements since theorigin × System learning0.406 6.14 0.511 6.06Summary statistics df F statistic df F statisticOverall model 9 6,742.27 10 8,543.12the destination: named here MR1, MR2, MR3, andMR4.MR1 represents the expressway alternative onthe network. MR2 is a six-lane arterial while MR3is mainly a four-lane arterial with a relatively highnumber of traffic lights. MR4 is primarily a rural,two-lane, two-way arterial with a speed limitapproximately equal to that of MR2 and MR3.MR1 has the highest speed limit among the fouralternatives with few traffic lights, because it consistsmainly of expressway links. The network has alsofive local collectors that allow the subject to divertfrom one main route to another.In order to come up with a reasonable number ofalternatives, in the analysis phase, the route choicesmade during the trial days were aggregated into theabove four main routes. We considered that eachchosen route belonged to a main route if most of thechosen route’s links belong to this main route. Thatis, a chosen route was assigned to a certain mainarterial if, and only if, the chosen route overlapswith this main arterial for a longer distance than itdoes with any of the other three main arterials. As aresult, the four main routes MR1, 2, 3, and 4 werechosen 374, 99, 37, and 29 times, respectively.The proposed MGEE method with a generalizedpolytomous logit function was employed to modelcorrelated route choices. The categorical dependentvariable has four alternatives, MR1, MR2, MR3,and MR4. These four alternatives form the fixedchoice set available for all subjects at all trial days.The reference alternative for which all attributes inthe analysis are set equal to zero is MR4. Thisroute was chosen because it was picked with lesserfrequency over the other three main routes. TheABDEL- ATY 93

dependent variable takes on a value of one to four.The independent variables include:1. Age: one if the subject’s age is over 30, zerootherwise;2. Income: one if household income is greaterthan $65,000, zero otherwise;3. Education: one if the subject has a graduateleveldegree or higher, zero otherwise;4. Shortest 1: one if MR1 was the shortest path,zero otherwise;5. Shortest 2: one if MR2 was the shortest path,zero otherwise;6. Shortest 3: one if MR3 was the shortest path,zero otherwise;7. Advised 2: one if MR2 was the shortest pathand the trial day was under scenario #3 or #5(i.e., MR2 was the suggested route), zero otherwise;8. Advised 3: one if MR3 was the shortest pathand the trial day was under scenario #3 or#5 (i.e., MR3 was the suggested route), zerootherwise;9. Travel time 1: travel time on MR1;10. Travel time 2: travel time on MR2;11. Travel time 3: travel time on MR3;12. Travel time 4: travel time on MR4.Tables 2 and 3 show the modeling results usingthe MGEE model for the independent case (nocorrelation is considered) and for the proposedexchangeable correlation, respectively. The differencesin the results are due to the effect of correlation.By comparing the overall F statistic values forthe two models, the exchangeable model wasfavored over the independent model (83,417.09 vs.11,464.98). Also, as expected, the independentMGEE model underestimated the standard errors ofthe modeling effects that lead to inflated t statisticvalues (table 2).In table 3, the t statistics were lower when comparedwith the corresponding values in table 2 (formost of the effects), indicating that the proposedmethodology has also adjusted this error. Thismeans that the proposed methodology overcomesthe disadvantage of underestimating the standarderrors for models that do not account for correlation.A number of studies reported this disadvantage(Louviere et al. 1983; Mannering 1987; Gopinath1995; Abdel-Aty et al. 1997; and Stokes et al. 2000).The model produced three logistic equations for thefour alternatives (MR1 vs. MR4; MR2 vs. MR4,MR3 vs. MR4). These equations are:πˆ MR1⎛ ⎞log⎜------------⎟ = – 65.12 + 3.42Age + 2.36Income⎝πˆ MR4 ⎠+ 5.00Education + 22.15S1+ 11.65S2 + 13.23S3 + 29.60A1– 4.70A2 – 4.87A3–6.00TT1– 2.35TT2– 0.67TT3 + 9.56TT4πˆ MR2⎛ ⎞log⎜------------⎟ = – 35.39 + 2.41Age + 1.01Income⎝πˆ MR4 ⎠+ 1.99Education + 21.62S1+ 12.17S2 – 7.01S3 + 5.56A1+ 11.34A2 – 25.95A3–4.28TT1– 2.18TT2– 0.36TT3 + 7.36TT4πˆ MR3⎛ ⎞log⎜------------⎟ = – 3.63 + 9.38Age + 2.49Income⎝πˆ MR4 ⎠+ 12.37Education– 10.49S1– 48.61S2 + 22.67S3 + 3.69A1– 44.56A2 + 1.41A3–0.79TT1– 0.10TT2– 1.00TT3 + 1.89TT4where the symbols Sx, Ax, and TTx refer to theeffects “Shortest x,” “Advised x,” and “Travel timex,” respectively, where x is the main route number.Using the above equations, the probability ofchoosing an alternative given a set of values for theindependent variables is simple compared withusing any probit link function (probit models).Moreover, computing a certain marginal effect ofany variable on choosing an alternative is straightforwardand simple regardless of the number ofalternatives used in the model, which is not the casefor the corresponding multinomial probit models.In the above equations, exponentiating the estimatedregression coefficient yields the odds ofchoosing the corresponding alternative vs. choosingthe base alternative MR4 for each one-unit increasein the corresponding explanatory variable. Forexample, the ratio of odds for a one-unit change inthe travel time on MR2 is equal to e –2.18 = 0.11.This shows the ease of this model compared withthe corresponding probit models.Tables 2 and 3 also show the parameter coefficientsfor each equation with the corresponding t94 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 2 Modeling Results for the MGEE Model without CorrelationEquation 1 Equation 2 Equation 3MR1 vs. MR4 MR2 vs. MR4 MR3 vs. MR4Parameter Coefficient t statistic Coefficient t statistic Coefficient t statisticIntercept –41.31 –12.17 –24.93 –8.14 6.02 1.64Age 0.04 1.15 0.42 0.55 6.70 5.50Income 2.27 3.42 3.85 4.50 2.44 2.98Education level 0.22 0.21 –2.36 –1.26 8.73 7.01Shortest 1 12.71 9.92 13.37 10.64 –18.65 –17.52Shortest 2 11.65 9.84 13.07 10.23 –23.48 –12.32Shortest 3 1.65 1.83 –7.66 –5.63 22.67 16.71Advised 1 7.93 9.24 21.79 16.86 3.69 3.67Advised 2 7.26 5.12 12.95 8.22 –6.38 –2.98Advised 3 –6.81 –7.04 –18.10 –11.33 1.41 1.35Travel time 1 –6.07 –24.52 –4.35 –11.27 –0.89 –10.73Travel time 2 –2.34 –19.66 –2.23 –20.18 –0.17 –2.82Travel time 3 –0.67 –19.72 –0.36 –5.89 –0.96 –18.87Travel time 4 9.44 26.15 7.36 13.34 1.89 22.90Overall Summary Statisticsdf F statisticOverall model 42 11,464.98Intercept 3 80.11Age 3 12.10Income 3 7.96Education level 3 20.44Shortest 1 3 197.39Shortest 2 3 117.23Shortest 3 3 167.53Advised 1 3 96.60Advised 2 3 44.95Advised 3 3 57.78Travel time 1 3 202.42Travel time 2 3 151.75Travel time 3 3 400.09Travel time 4 3 478.48statistic of each effect. Furthermore, tables 2 and 3present the F statistic for each effect in the overallMGEE model. These values indicate the individualsignificance of every effect in the overall model anddetermine if changing the value of this effect statisticallychanges the probability of choosing a certainalternative. A certain effect may appear significantin one equation but be insignificant in another. All13 effects included were found significant.The parameter coefficients in table 3 show thatolder drivers (>30), those with larger householdincomes, and those with a high level of educationare, in general, more likely to choose MR1, MR2,or MR3 than MR4; that is, they are more likelyto choose the expressways and/or the multilanearterials. Recall, MR4 is a two-lane, two-way ruralarterial. However, the increase in this likelihood insome cases is not statistically significant. For example,these three socioeconomic factors above do notaffect the probability of choosing MR2 vs. MR4 (tstatistics = 1.07, 0.45, 0.74 < 1.96).“Shortest 1,” “Shortest 2,” and “Shortest 3”measure the effect of providing information withoutadvice to the subjects. The significance of “Shortest1” in the first equation, with a positive coefficientparameter (22.15), shows that the probability ofchoosing the first alternative, MR1, increases if thisroute is the travel-time-based shortest route on thenetwork, even with providing advice-free information.This means that the subjects were able to useand benefit from the qualitative and quantitativeinformation provided to them. Moreover, theymight be able to identify and then take the shortestroute themselves using the travel times given toABDEL- ATY 95

TABLE 3 Modeling Results for the MGEE Model with CorrelationEquation 1 Equation 2 Equation 3MR1 vs. MR4 MR2 vs. MR4 MR3 vs. MR4Parameter Coefficient t statistic Coefficient t statistic Coefficient t statisticIntercept –65.12 –3.80 –35.39 –1.89 –3.63 –0.29Age 3.42 2.56 2.41 1.07 9.38 3.87Income 2.36 1.12 1.01 0.45 2.49 1.69Education level 5.00 2.43 1.99 0.74 12.37 4.48Shortest 1 22.15 2.74 21.62 3.51 –10.49 –1.62Shortest 2 11.65 2.12 12.17 3.56 –48.61 –12.12Shortest 3 13.23 5.04 –7.01 –3.13 22.67 6.57Advised 1 29.60 3.85 5.56 0.76 3.69 0.67Advised 2 –4.70 –1.22 11.34 3.79 –44.56 –10.03Advised 3 –4.87 –0.64 –25.95 –2.98 1.41 0.24Travel time 1 –6.00 –8.80 –4.28 –4.04 –0.79 –3.33Travel time 2 –2.35 –5.61 –2.18 –6.03 –0.10 –0.67Travel time 3 –0.67 –3.58 –0.36 –2.31 –1.00 –5.14Travel time 4 9.56 7.03 7.36 3.99 1.89 3.24Overall Summary Statisticsdf F statisticOverall model 43 83,417.09Intercept 3 22.05Age 3 10.31Income 3 2.21Education level 3 10.93Shortest 1 3 79.65Shortest 2 3 703.45Shortest 3 3 57.34Advised 1 3 21.51Advised 2 3 48.55Advised 3 3 19.91Travel time 1 3 100.18Travel time 2 3 36.34Travel time 3 3 15.80Travel time 4 3 81.22them by the information system. The same interpretationapplies to the coefficient parameters of theeffects “Shortest 2” and “Shortest 3” in equations 2and 3, respectively. By comparing these three coefficients(22.15, 12.17, 22.67), differences can be seen.This indicates that the marginal effects of these variablesare not the same. However, they measure thesame independent variable for different alternatives.Thus, it can be concluded that providing trafficinformation to drivers increases the likelihood thatthey will choose the shortest path (identified by themor given to them by an information system), but theodds differ between the shortest path and another,depending on the characteristics of each route.To measure the effect of advising drivers to take aparticular route, in addition to providing trafficinformation on all links of the network, the threeeffects, “Advised 1,” “Advised 2,” and “Advised 3”were employed. Advising MR1 or MR2 to the subjectsincreased the likelihood of their being theirchosen (coefficients of 29.60 and 11.34, respectively).However, advising MR3 as the shortest pathfor a certain trial day does not affect its probabilityof being chosen (t statistic = 0.24). This result wasnot surprising, because MR3 is well known for itsregular congestion due to its high accessibility andmany traffic lights (most of the subjects were familiarwith the network).Similar to the effect of information withoutadvice, the coefficient parameters “Advised 1” inequation 1, “Advised 2” in equation 2, and“Advised 3” in equation 3 (29.60, 11.34, 1.41,respectively) show that it is unclear that advisingdrivers to take a certain route increases the likeli-96 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

hood they will chose to do so. The characteristics ofthe route itself seem to be a factor in the decision. Inthis analysis, advising drivers to use an expresswayor six-lane arterial increased the likelihood of itbeing chosen (MR1 and MR2). When drivers wereadvised to use a four-lane arterial with high densityand traffic lights it did not affect the likelihood ofthat route being chosen. From these data, we canconclude that the characteristics of a certain routeaffect whether it is chosen even if the informationadvises drivers to use it.The effect of travel time was represented in ourmodel by the variables TT1, TT2, TT3, and TT4.The first three variables have negative coefficients inthe three equations, with significant effects for TT1in equation 1, TT2 in equation 2, and TT3 in equation3. This clearly shows that the probability ofchoosing a certain route decreases as travel timeincreases. The effect TT4, the travel time of the baseroute MR4, showed up as a positive significant variablein the three equations. Therefore, the probabilityof choosing the other route (not choosing thisbase route) increases as travel time rises for the basealternative.CONCLUSIONSThe proposed BGEE and MGEE techniques addnew and useful methodology to the family of modelsthat account for correlation in discrete choicemodels, especially for route choice applications. Theliterature review illustrated that a methodology wasneeded to account for correlation between repeatedchoices and/or between overlapping alternativeswith simple computational effort and that can beapplied to large networks. The proposed modelproved to account for both types of correlation withsimple computational effort and reasonable statisticalefficiency for small and large networks. Thismakes BGEE and MGEE superior to the existingmethodologies.As a BGEE application, this paper presents amodel of short-term route choice in compliancewith ATIS. The paper also presents a multinomialroute choice model (as an MGEE application). Bothapplications were developed with and withoutaccounting for correlation. In both applications, theeffect of correlation was tested statistically andfound significant, which shows the importance ofaccounting for correlation in route choice modelsthat may lead to different travel forecasts and policydecisions. This also shows the importance of ourproposed methodology for large networks wherethe efficiency of the existing methodologies is questionable,as discussed in the literature review.In this paper, we interpreted the modeling outputof the BGEE and MGEE applications. The shorttermroute choice (BGEE) modeling results showthat the provision of en route information increasesthe likelihood of making a positive link choice. Thequalitative short-term information is more likely tobe used than the quantitative information. Othereffects were found to increase the usage of en routeshort-term traffic information: being familiar withthe system that provides the information, heavy rainconditions, and proximity to the destination.The multinomial route choice (MGEE) modelingresults show that the subjects were able to use andbenefit from the qualitative and quantitative informationprovided to them. Moreover, they might beable to identify the shortest route themselves usingthe travel times given to them. Finally, the odds ofchoosing a certain shortest route (advised or recognizedby drivers using the advice-free traffic informationprovided) varied from one route to anotherand depended on the characteristics of the routeitself. For example, the analysis in this papershowed that advising the use of the expressway orthe six-lane arterial increase the likelihood of theroute being chosen (MR1 and MR2). While advisingthe use of a four-lane arterial with a large number oftraffic lights does not affect its likelihood of beingchosen.ACKNOWLEDGMENTThe author thanks Dr. M. Fathy Abdalla for his significantcontribution to this paper. The results inthis paper are based on a research project funded bythe Center for Advanced Transportation SimulationSystems (CATSS) at the University of Central Florida(UCF) and the Florida Department of Transportation,and were included in Dr. Abdalla's Ph.D.dissertation at UCF, for which the author was theacademic advisor (Abdalla 2003).ABDEL- ATY 97

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the relevant covariates including the intercept,between- and within-subject covariates. Therefore,each subject has a matrix of covariatesX i = x i1 ,...,x iTi′of dimension T i × p , where p is the total number ofcovariates excluding the intercept.The distribution of y it is multinomial with theprobability functionfy ( it x it , β) = π ikt(8)where π ikt = Ey ( ikt x it , β) = pr{ y ikt = 1 x it , β } isthe probability that subject i had choice k at time t,and β is a p × 1 vector of parameters. When y it isbinary, π ikt is usually modeled with a logistic orprobit link function (Zeger et al. 1988). When k > 2with non-ordered response, the generalized polytomouslogit link is appropriate (Lipsitz et al. 1994).The matrix of coefficient parameters β is associatedwith the [( K – 1) × 1]marginal probabilityvector(9)These marginal probability vectors can be groupedtogether to form the [ T i ( K – 1) × 1]vector′EY ( i X i ) = π i ( β) = π′ i1 ,...,π′ iTiwhereK∏k = 1y iktEY ( it X i ) = π it ( β) = π it1 ,...,π i K′Y i = Y′ i1 ,...,Y′ iTi′, ( – 1 ),t(10)The GEEs of the following form can be used to estimateβ (Liang and Zeger 1986; Lipsitz et al. 1994)Nu⎛ βˆ ⎞d[ π i ( β)]′ –1= (11)⎝ ⎠ ∑-----------------------Vˆ i Yi – πˆdβi = 0i = 1where V i is the covariance matrix of Y i . This covariancematrix, V i , is a function of β and other nuisanceparameters α , which is a function of thecorrelation between repeated choices made by thesame subject i. Also, V i depends on the correlationbetween overlapped (or correlated) alternativeroutes. This covariance matrix, V i , has [ T i × T i ]blocks. Each block has [( K – 1) × ( K – 1)] elements.Estimating the Covariance MatrixTo get a general form of V i , the correlation matrixof the elements of Y i must be developed or estimatedfirst. Therefore, the pairwise correlation betweenthe (K – 1) elements of Y is and Y it , which accountsfor correlation between observations s and t of subjecti, must be determined. A typical element of thecorrelation matrix of the elements of Y i is, for anypair of responsive levels j and k and pair of times sand t,Corr( Y ijs , Y ikt ) = Ee [ ijs e ikt ],Ywhere e ikt – π iktikt = ---------------------------------------------(12)1 ⁄ 2π ikt ( 1 – π ikt )The element e ikt is the residual for Y ikt . This residuale ikt is a typical element of the residual vector– 1 ⁄ 2e it = A it –where A it is a function of β and is equal to:A it = Diag π i1t ( 1 – π i1t ),...,or– 1 ⁄ 2A itY itπ it...,π i K, – 1,t 1whereê i = ê i1 ,...,ê iTi , andA i = Diag A i1 ,...,A iTi( – π i,K–1,t )= Diag ( π i1t ( 1–π i1t ) ) 1 ⁄ 2,...,...,( π i, K–1,t ( 1–π iK , – 1,t )) 1 ⁄ 2The correlation matrix of Y i = R i ( α)a typical element can be written asCorr( Y i ) = R i ( α) = var( e i )– 1 ⁄ 21= A i var( Y i )A i– ⁄ 21 ⁄ 21 ⁄ 2var( Y i ) = V i = A i Corr( Y i )A i(13)(14)with e ikt as(15)(16)Then, var(Y i ) depends on β and R i ( α)where thelatter takes the effect of correlation in computingthe covariance matrix var(Y i ). The matrix R i ( α)isa T i by T i block diagonal matrix. Each block is a[( K – 1) × ( K – 1)] matrix. The tth diagonal block100 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

– 1⁄2 – 1 ⁄ 2of R i ( α) is A it V it A it , also the sth-row and tthcolumnoff-diagonal block ρ ist ( α)is– 1 ⁄ 2ρ ist ( α) = A is E ⎛⎝Y is – π ⎞is ⎠⎛ – π ⎞′⎝ it ⎠• Y it– 1⁄2Ait(17)whereV it = var( Y it ) = Diag[ π it ] – π it π′ itand Diag[ π it ] denotes a diagonal matrix with elementsof π it on the main diagonal and zero offdiagonalelements. The diagonal blocks of R i ( α)depend only on π i ( β). In these diagonal blocks, thediagonal elements are:Corr⎛Y ikt , Y ⎞⎝ ikt = 1⎠and the off-diagonal elements are(18)cov⎛Y ijt , Y ⎞Corr⎛Y ijt , Y ⎞⎝ ikt⎠⎝ ikt = ------------------------------------------------------------------------------⎠{ π ijt ( 1 – π ijt )π ikt ( 1 – π ijt )} – 1 ⁄ 2–π ijt π= -------------------------------------------------------------------------------ikt{ π ijt ( 1 – π ijt )π ikt ( 1 – π ikt )} – 1 ⁄ 2 (19)Recall that these off-diagonal elements of the diagonalblocks of R i ( α)depend only on the tth choiceof subject i from the K alternatives available. Thisclearly takes care of any correlation among thedifferent alternatives of the multidimensional routechoice model, usually due to overlapping distancesbetween different routes. Thus, the unknownelements of R i ( α)are the elements of its offdiagonalblocks ρ ist ( α). This must be estimated.If ρ ist ( α) is known, then R i ( α)is known. Theonly unknown term in equation 11 then is β . Theestimated βˆcan be obtained by a Fisher scoringalgorithm until convergence,βˆ m + 1= βˆ m+N∑i = 1d π ⎛i βˆ m ⎞⎝ ⎠-------------------------- ⎛βˆ m ⎞′dβ ⎝ ⎠• Y i– π ⎛i βˆ m ⎞⎝ ⎠(20)where m is the iteration number. A starting β canbe obtained by applying the regular MNL model.Iteration should continue until βˆ m + 1= βˆ mandαˆ m + 1= αˆ m, where αˆ mis the estimated ρ ist ( α)inthe mth step.Estimating the Off-Diagonal Blocksof the Correlation MatrixLipsitz et al. (1994) extended the exchangeablecorrelation structure, introduced by Liang andZeger (1986), used in BGEE for multidimensionalmodels. They used the same assumption that anytwo observations on the same subject/cluster i andcategory k are equally correlated. Under thisassumption, ρ ist ( α)can be estimated as′∑ ∑ ê is ê itαˆ = ρ ist ( αˆ ) =i = 1 t > s-------------------------------------------------------N∑i = 1N0.5T i ( T i – 1)– p(21)where p is the total number of independent variables,including any interactions. The residual vector– 1 ⁄ 2ê it =  it Y it – πˆ it ,which is estimated by plugging βˆfrom a previousstep of iteration into A it and π it . It is worthmentioning that the elements of the sth-row andtth-column off-diagonal block ρ ist ( α)do notdepend on the times s and t, but they do dependon the levels j and k.V ⎛i βˆ m , αˆ m ⎞•⎝ ⎠–1d π ⎛i βˆ m ⎞⎝ ⎠-------------------------- βˆ mdβ–1N•∑i = 1d π ⎛i βˆ m ⎞⎝ ⎠-------------------------- ⎛βˆ m ⎞′dβ ⎝ ⎠ Vi⎛βˆ m , αˆ m ⎞⎝ ⎠–1ABDEL- ATY 101

BOOK REVIEWSEconomic Impacts of Intelligent TransportationSystems: Innovations and Case StudiesE. Bekiaris and Y.J. Nakanishi, editorsElsevierJuly 2004, 655 pagesISBN 0762309784$95 €150 £100This new addition to the series, Research in TransportationEconomics, is dedicated to the economicvaluation of intelligent transportation systems (ITS)and telematics. The editors include the papers ofclose to 50 authors, thus ensuring comprehensivecoverage of the topic. ITS technologies typicallyhave short life cycles; they are rapidly evolving andhave minimal historical data associated with them.Recognizing that ITS life cycles and cost structuresdiffer greatly from that of regular infrastructure,techniques to address these issues are presented. Thebook covers a wide range of ITS technologies,including freeway management, electronic toll collection,advanced driver assistance systems, andtraveler information systems.The introductory chapter of this book recapsthe goals and objectives of ITS as envisioned inlandmark legislation. The chapter presents aMitretek (2003) compilation of recent cost-benefitanalysis that draws on experiences up to 2003.Also provided are definitions for acronymsdirectly downloaded from an ITS architecturewebsite. Distinctly absent, however, is a critiqueof ITS implementations over the past twodecades. This type of discussion would have giventhe readers some perspective on the topic.The section on “Relevant Technologies andMarket” identifies the marketplace for various ITStechnologies. Two articles are included: the first, byPanou and Bekiaris, puts forth a taxonomy of technologiesinto clusters in the United States and overseas;the second, by Kauber, assesses the emergingmarkets through 2010.The centerpiece of the volume is really the sectionon “Evaluation Technologies/Methodologies,”commanding no less than 120 pages. Aside fromtraditional techniques such as cost-benefit analysis, Iam pleased to see contributions on “AnalyticalAlternatives” (Haynes and Li), and I am equallydelighted to see microsimulation being used in evaluating“Variable-Message-Signs Route Guidance”(Ozbay and Bartin).While the methodologies section is cut and dried,the articles in the “Case Studies” sections makethem come to life. They include: Incident Freeway Management, Electronic Toll Collection and CommercialVehicle Operation, Public Transport, and Advanced Driver Assistance Systems (ADAS) andDriver/Traveler Information.Aside from the “Evaluation Technologies/Methodologies”section, I view these 300 pages among themost useful parts of the book, covering the keycomponents of ITS.In the section on “Assessing the Impact of ITSon the Overall Economy,” Kawakami et al. putforth a compact general equilibrium model tomeasure the implications of ITS. Gillen et al. evaluatethe productivity gains from using AutomaticVehicle Location. I would have liked to have seenmore contributors in this section, because itaddresses a key objective of this volume; in fact itis the basic premise of the book.Among the finishing touches, the book includespolicy recommendations. Again, I rank this sectionof the book very highly. I am particularly partial tothe guidelines laid down for implementations. Forexample, recommendations are made by Bekiariset al. for two ADAS technology clusters: advancedcruise control and intelligent speed adaptation.I am a bit disappointed, however, with the brevityof the conclusions chapter, which says nothingnew or important. Considering the richness of thecontributions of so many authors, surely the editorscould have summarized them better and in moredetail.I am also disappointed in the lack of a subjectindex, which discounts the usefulness of the book.More importantly, it reinforces the impression thatthere is only a limited amount of editorial oversight.Overall, this is a welcome addition to theResearch in Transportation Economics series. ManyBOOK REVIEWS 103

This is a statistical book. This is a statistical book.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical b ok. This is astatistical book. This is a statistical book. Alpha is awesome.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical book. This is a statisticalbook. This is a statistical book. This is a statistical book.This is a statistical book.This is a statistical book. This is a statistical book.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical b ok. This is astatistical book. This is a statistical book. Alpha is awesome.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical book. This is a statisticalbook. This is a statistical book. This is a statistical book.This is a statistical book.This is a statistical book. This is a statistical book.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical b ok. This is astatistical book. This is a statistical book. Alpha is awesome.This is a statistical book. This is a statistical book. This is astatistical book. This is a statistical book. This is a statisticalbook. This is a statistical book. This is a statistical book.This is a statistical book.of the 50 authors included in the volume arerespected figures in this field, and the separate papersprovide much useful information. Integrating thechapters into a book entitled Economic Impacts ofITS, however, falls a bit short of my expectations.ReferenceMitretek Systems. 2003. ITS Benefits and Costs: 2003 Update,prepared for the Federal Highway Administration, U.S.Department of Transportation.Reviewer address: Yupo Chan, Professor and FoundingChair, Department of Systems Engineering, University ofArkansas at Little Rock, 2801 South University, LittleRock, AR 72204-1099. Email: yxchan@ualr.edu.Principles of Transport EconomicsEmile Quinet and Roger VickermanEdward Elgar Publishing Company2004, 385 pagesISBN 1-84064-865-1$120 hardback ($60 paperback)£75 hardback (£35 paperback)Instructors of upper-level undergraduate transportationeconomics courses have typically been frustratedsearching for a suitable textbook. Thetraditional transportation books are long on institutionaldescription and short on analytical method.A recent pair of books attempted to remedy this.Kenneth Boyer’s Principles of Transportation Economics(Addison Wesley, 1998, $124.40) is wellwritten but pitched at too low a level for studentswho have completed intermediate microeconomics.Patrick McCarthy’s Transportation Economics(Blackwell, 2001, $108.95) is the opposite. There istoo much detail for a typical undergraduate who isnot specializing in transportation, and it is a toughread in places. In my class, I have been using JoséGómez-Ibáñez, William Tye, and Clifford Winston’sedited volume Essays in Transportation Economicsand Policy: A Handbook in Honor of John R.Meyer (Brookings Institution, 1999, at the attractiveprice of $22.95 in paperback), which is a mixedbag and really does not function as a textbook.To this mix is added a new text by Quinet andVickerman. Actually, it is an updated Englishlanguageversion of an earlier book in French byQuinet. The addition of Vickerman from Englandhas given the book a more pan-European feel. Thelimitation of nearly all applied economics texts isthat their examples are parochial. European studentshave limited interest in the detailed economics of theMackinac Straits bridge in Michigan or the Lindenwoldtransit line in Philadelphia, and converselythe Channel Tunnel and the externality costs oftruck traffic in Switzerland do not stir the imaginationof American students. Therefore, Quinet andVickerman face a tough task in breaking into theNorth American market.The book is divided into three sections. The firstfifth (in terms of pages) deals with putting transportationin its wider context in relation to economicactivity, location theory, and urban economics. Thenext quarter deals with the basics of demand andcost. The remaining pages cover market equilibrium,market failure, and public policy intervention.Overall, I consider the book to be a pedagogicalfailure. For example, within the first 40 pages thereis a quick gallop through price elasticities (page 17),cost functions and the envelope theorem (page 27),and the throw away parenthetical comment on page37 while discussing a model of interregional tradethat “there is no trade initially (infinite transportcosts).” All of this while the reader has yet to beintroduced to basics of transportation demand andsupply.With my students, I consider it to be a majorsuccess if they can interpret and use elasticities,understand how a cost function is derived and estimated,and fully understand the role of transportationin trade equilibria and how a demand functionfor freight transportation can be derived. This bookis not supportive of the crucial material that I feel isessential for my students to understand. While thefirst section contains important concepts, I felt thatthe material could have been better organized, andperhaps combined with topics covered later in thebook, to produce a more logical and instructivenarrative.104 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

I found the second section dealing with demandand costs to be the strongest part of the book. Thechapter on demand contains a particularly gooddescription of the underpinning of traditional fourstagedemand models. However, it deals with puretheory. There is no discussion of the practical econometricsof estimation or any empirical results. Thisis in contrast to McCarthy’s text that has extensivepractical discussion of this topic. However, the mostamazing thing is that after 45 pages of discussingpassenger demand models, freight traffic models areconsidered in under a page. Of course, this is notentirely the authors’ fault. The profession has notlavished the attention on freight demand models theway that it has for passenger movement. This is asad state of affairs in the North American contextgiven the importance of freight railroads and competitionwith trucks, barges, and pipelines.The chapter on costs is also quite good and discussessocial costs as well as production costs. Tomy tastes, I felt there should have been a moreextensive industrial organization-style analysis ofproduction costs. After all, production costs drivefirm behavior and market equilibrium. For example,on page 147 there is only passing reference to thedifference between economies of firm size, economiesof density, and economies of scope. And thediscussion is based on ill-defined equations and notsupported by any intuition. Yet, with my students, Ifind that driving home these distinctions producesgreater appreciation of the differences betweentransportation modes and the debate concerningregulatory reform.The final section of the book is a random walkthrough market equilibria and public policy. Againthe book fails pedagogically by giving short shrift toimportant tools in transportation economics. Conceptssuch as Ramsey pricing (in the cost chapter,page 153), an undefined “Mohring effect” (also inthe cost chapter, page 158), cost-benefit analysis(page 239), and reaction functions and the conductparameter (page 266) are all mentioned in passingbut not given the full treatment that undergraduatesrequire. Overall, the chapters in the final section ofthe book are adequate and cover most of the importantissues. However, I felt they lacked a structurethat students could use to guide their studies.Overall, one can say that the book touches on allof the topics usually found in an upper level transportationeconomics course, however, the orderingof material detracts from the learning experience.One can always quibble about the organization ofthe material, and I would accept that this is partly amatter of taste, and there will be deficiencies inalmost any ordering. However, I would suggest thatMcCarthy and (especially) Boyer have got it right byusing the structure of a typical intermediate microeconomicstextbook as a guide to a logical sequenceof topics.The other failure of this book is in explainingand illustrating the principal tools of transportationeconomics in a way that undergraduates would finduseful. One might consider that there are threemain types of academic writing that do not reportoriginal research results. One is a handbook chapterpresenting core reference material for a knowledgeablenew researcher in a field. The second is a“handbook chapter on steroids” prepared forknowledgeable insiders and published in places suchas the Journal of Economic Literature. The third istextbook writing designed for newcomers to thefield who only have basic economic training. Theauthors of this book have failed; they have pitchedthe book somewhere in the middle and thereby satisfiednone of the three markets.How did this happen? The basic problem is thatthe market for a post-intermediate microeconomicstext on transportation is very small. Publishers are,therefore, unwilling to invest resources in extensiveuse of referees, prepublication testing in a classroomsetting, copy editors, graphic designers, andthe preparation of end-of-chapter exercises. EdwardElgar, the publisher of this book, is not a majorplayer in the mass-market textbook publishingbusiness. Consequently the authors did not get thefeedback they should have received at an earlystage that would have allowed them to make this amore pedagogically useful tool.Reviewer address: Ian Savage, Department of Economics,Northwestern University, 2001 Sheridan Road, EvanstonIL 60208, USA. Email: ipsavage@northwestern.edu.BOOK REVIEWS 105

Data ReviewEmployment in the Airline Industry1 This includes all carriers that operate at least 1 aircraftwith a carrying capacity of 18,000 pounds (passengers,cargo, and fuel). Regional carriers were excluded fromreporting until 2003.2 Available at www.bts.gov/programs/airline_information/number_of_employees/.3 Available at www.bts.gov/press-releases.Airlines report employment levels to the federal governmenton a monthly basis. 1 The release of theemployment numbers on the Bureau of TransportationStatistics (BTS) website and through monthlypress releases allows tracking of employment trendsin the industry resulting from the financial crisesexperienced by many airlines after the terrorist andrecession events of 2001. The employment numbersreflect the resultant reduction in the networkcarriers’ operations and the subsequent growth oflow-cost and regional carriers.BTS makes year-end (December) airline employmentdata available online. 2 These data are supplementedby the monthly press releases, which BTSbegan reporting in March 2005. 3 Using these BTSdata, analyses of the changes in the number of airlineemployees can be performed by business model,revenue size, or individual carrier.The best representation of the current airlineindustry structure is a business model definition,which contains three carrier groupings: network,low cost, and regional. Network carriers use a traditionalhub-and-spoke system for scheduling flights.Low-cost carriers operate under a generally recognizedlow-cost business model, which may includea single passenger class of service, standardized aircraftutilization, limited in-flight services, use ofsmaller and less expensive airports, and loweremployee wages and benefits. Regional carriersprovide service from small cities and primarily usesmaller jets. Regional carriers are also used to supportlarger network carrier traffic into and out ofsmaller airports to the network carriers’ hub airports.The BTS online database uses an operating revenueclassification system with three major categories:majors, nationals, and regionals. 4 Majorcarriers have annual operating revenues above $1billion, national carriers have operating revenuesbetween $100 million and $1 billion, and regionalcarriers have operating revenues less than $100million. The regional category may not include thesame carriers under the revenue size definition andthe business model definition.Using the business model classification, there areseven network carriers (Alaska Airlines, AmericanAirlines, Continental, Delta, Northwest, United,and US Airways) and eight low-cost carriers (AirTran, America West, ATA, Frontier, Independence,JetBlue, Southwest, and Spirit). December 2004employment data provided by the airlines showsthat American Airlines was the largest employer(71,232 full-time personnel) in the industry (table1). American became the largest employer in 2001,the year it acquired the assets of Trans World Airlines.United was the second largest networkemployer in December 2004 with 54,460 full-timeemployees, followed by Delta (53,394). Theremaining network carriers all employed less than40,000 full-time personnel each.4 This system of classification emerged during the industry’spre-deregulation era.Review by: Jennifer Brady, Analyst, Bureau of TransportationStatistics, Research and Innovative TechnologyAdministration, U.S. Department of Transportation, 4004Seventh This system St. SW, of classification Room 3430, is Washington, based the pre-deregulationEmail state address: of the jennifer.brady@dot.gov.DC 20590.industry.107

TABLE 1 Airline Employees by Business Model andSize Classification: 2004CarrierAllemployeesFull-timeemployeesBusiness modelclassificationSizeclassificationAmerican 82,222 71,232 Network MajorUnited 61,092 54,460 Network MajorDelta 59,972 53,394 Network MajorNorthwest 39,784 37,572 Network MajorContinental 35,395 28,227 Network MajorUS Airways 26,169 23,180 Network MajorAlaska Airline 9,857 8,747 Network MajorSouthwest 31,274 30,749 Low cost MajorAmerica West 12,654 10,129 Low cost MajorJetBlue 7,399 5,956 Low cost NationalAirTran 6,072 5,754 Low cost NationalATA 6,268 5,625 Low cost MajorFrontier 4,492 3,620 Low cost NationalIndependence 4,301 4,014 Low cost NationalSpirit 2,627 2,339 Low cost NationalSource: U.S. Department of Transportation, Research and Innovative TechnologyAdministration, Bureau of Transportation Statistics, Certified Carriers (Full-time and Part-time),available at www.bts.gov/programs/airline_information/number_of_employees.All network carriers experienced employmentgrowth throughout the 1980s. After a slowdownduring the early 1990s, precipitated by the 1991recession and the Gulf War, the number of networkcarrier employees began to increase again in 1995.However, immediately following the 2001 terroristevents and the simultaneous mild U.S. recession,employment decreased for the network carriergroup.Between December 2000 and 2004, all the networkcarriers reduced their numbers of full-timeemployees; however, certain carriers were particularlyhard hit. The total number of US Airways fulltimepersonnel decreased by 44% from December2000 to 2004, and United experienced a 40%reduction in their full-time work force. The otherfive major carriers reduced their total number offull-time employees by approximately 20%, exceptAlaska Airlines, which sustained a 4% loss.Southwest Airlines employs the most personnelamong the low-cost carriers. Its December 2004employment rolls indicate more than twice the numberof full-time employees (30,749) worked forSouthwest than the next largest employer, AmericaWest (10,129). The remaining low-cost carriersemployed less than 10,000 full-time personnel each.As a demonstration of the growing strength oflow-cost carriers, Southwest, America West, andATA generate sufficient revenues to qualify as majorcarriers. Furthermore, Southwest employs morepeople than two of the network carriers (US Airwaysand Alaska Airlines).It is difficult to analyze historic trends for theairline industry because of an evolving carrier populationand the financial demise of previouslyqualifying airlines. Among the network airlinesoperating in 1970, most had their highest employmentlevels before 2001. From December 2000 to2004, the number of full-time personnel employedby network carriers decreased 31% 5 (table 2).During the same time period, employment amongseven low-cost carriers reporting to BTS throughoutthe entire period (excluding Independence Air)increased 17%.5 December 2000 and 2001 data include statistics forTWA, which was purchased by American Airlines in2001.108 JOURNAL OF TRANSPORTATION AND STATISTICS V8, N1 2005

TABLE 2 Airline Employees: 2000–2004(all data are from December of a given year)Type ofcarrier 2000 2001 2002 2003 2004Percentagechange 1Network 399,971 348,882 334,444 286,940 276,812 –31%Low cost 54,746 53,258 59,803 64,048 64,172 17%1 Among those airlines reporting in 2000 and 2004.Source: U.S. Department of Transportation, Research and Innovative Technology Administration,Bureau of Transportation Statistics, Certified Carriers (Full-time and Part-time), available atwww.bts.gov/programs/airline_information/number_of_employees.New BTS monthly employment statistics showthat the reduction in the number of network carrieremployees has slowed, as has growth among lowcostcarriers. In December 2004, January 2005,February 2005, and March 2005, full-time employmentamong network carriers showed decreasesranging from 3.5% to 5.3% (table 3). (The datacomparisons presented here are for the samemonths in 2003 and 2004 or 2004 and 2005, not afull year of data.) Even low-cost carrier full-timeemployment experienced negative growth in themost recent period (March) at –0.3%.Regional carrier data are also available in BTSpress releases and online. However, not all of thecurrently reporting carriers were required to reportuntil 2003, thus only 8 reported in 2000 and 13reported in 2004, making comparisons over timeproblematic.Raw data on airline employment are availableon the BTS website (see footnote 2). CertificatedCarriers (Full-time and Part-time) provides employmentdata beginning in 1970, and P10—AnnualEmployee Statistics by Labor Category, covering1998 through 2003, provides detailed informationfor each airline by labor category and geographicgroupings. Among the 15 labor categories detailedin the P10 database are pilots and co-pilots, maintenancestaff, and cargo handling and other flightpersonnel. The four geographic groupings in theP10 database are domestic, Atlantic, Latin America,and Pacific. Low-cost carriers are almost exclusivelydomestic operators.BTS will continue to issue monthly press releaseswith the most current data and employment trends.Using these press releases, it is possible to supplementthe online databases with monthly data.Finally, the press releases provide documentation ofbusiness model changes by carriers, resulting in newgroupings.For further information on this topic, send emailto answers@bts.gov or call 1-800-853-1351.TABLE 3 Percentage Change in Airline EmploymentType ofcarrierDecember2003 and 2004January2004 and 2005February2004 and 2005March2004 and 2005Network –3.5 –4.5 –5.0 –5.3Low cost 6.5 0.3 0.3 –0.3Source: U.S. Department of Transportation, Research and Innovative Technology Administration, Bureauof Transportation Statistics, Table 1: Passenger Airline Employment, monthly press releases, 2005,available at www.bts.gov/press-releases.DATA REVIEW 109

JOURNAL OF TRANSPORTATION AND STATISTICSGuidelines for Manuscript SubmissionPlease note: Submission of a paper indicates theauthor’s intention to publish in the Journal of Transportationand Statistics (JTS). Submission of a manuscriptto other journals is unacceptable. Previouslypublished manuscripts, whether in an exact or approximateform, cannot be accepted. Check with the ManagingEditor if in doubt.Scope of JTS: JTS publishes original research usingplanning, engineering, statistical, and economic analysisto improve public and private mobility and safety inall modes of transportation. For more detailed information,see the Call for Papers on page 112.Manuscripts must be double spaced, including quotations,abstract, reference section, and any notes. Allfigures and tables should appear at the end of themanuscript with each one on a separate page. Do notembed them in your manuscript.Because the JTS audience works in diverse fields,please define terms that are specific to your area ofexpertise.Electronic submissions via email to the ManagingEditor are strongly encouraged. We accept PDF, Word,Excel, and Adobe Illustrator files. If you cannot sendyour submission via email, you may send a CD byovernight delivery service or send a hardcopy by theU.S. Postal Service (regular mail; see below). Do notsend CDs through regular mail.Hardcopy submissions delivered to BTS by the U.S.Postal service are irradiated. Do not include a disk inyour envelope; the high heat will damage it.The cover page of your manuscript must include thetitle, author name(s) and affiliations, and the telephonenumber and surface and email addresses of all authors.Put the Abstract on the second page. It should beabout 100 words and briefly describe the contents ofthe paper including the mode or modes of transportation,the research method, and the key results and/orconclusions. Please include a list of Keywords todescribe your article.Graphic elements (figures and tables) must be calledout in the text. Graphic elements must be in black ink.We will accept graphics in color only in rare circumstances.References follow the style outlined in the ChicagoManual of Style. All non-original material must besourced.International papers are encouraged, but please besure to have your paper edited by someone whose firstlanguage is English and who knows your researcharea.Accepted papers must be submitted electronically inaddition to a hardcopy (see above for information onelectronic submissions). Make sure the hardcopy correspondsto the electronic version.Page proofs: As the publication date nears, authorswill be required to proofread and return article pageproofs to the Managing Editor within 48 hours ofreceipt.Acceptable software for text and equations is limitedto Word and LaTeX. Data behind all figures, maps,and charts must be provided in Excel, Word, or Delta-Graph (unless it is proprietary). American StandardCode for Information Interchange (ASCII) text will beaccepted but is less desirable. Acceptable software forgraphic elements is limited to Excel, DeltaGraph, orAdobe Illustrator. If other software is used, the file suppliedmust have an .eps or .pdf extension. We do notaccept PowerPoint.Maps are accepted in a variety of Geographic InformationSystem (GIS) programs. Files using .eps or.pdf extensions are preferred. If this is not possible,please contact the Managing Editor. Send your filesvia email or on a CD via overnight delivery service.Send all submission materials to:Marsha Fenn, Managing EditorJournal of Transportation and StatisticsBTS/RITA/USDOT400 7th Street, SW, Room 4117Washington, DC 20590Email: marsha.fenn@dot.gov111

Journal of Transportationand Statisticscall for papersJTSis broadening its scope and will nowinclude original research using planning,engineering, statistical, and economic analysis toimprove public and private mobility and safetyin transportation. We are soliciting contributionsthat broadly support this objective.Examples of the type of material sought includeAnalyses of transportation planning andoperational activities and the performance oftransportation systemsAdvancement of the sciences of acquiring,validating, managing, and disseminatingtransportation informationAnalyses of the interaction of transportationand the economyAnalyses of the environmental impacts oftransportationSee our website at www.bts.dot.gov/jts forfurther details and Guidelines for Submission.If you would like to receive a free subscriptionsend an email to the Managing Editor:marsha.fenn@dot.gov

U.S. Department of TransportationResearch and Innovative Technology AdministrationBureau of Transportation StatisticsJOURNAL OF TRANSPORTATIONAND STATISTICSVolume 8 Number 1, 2005ISSN 1094-8848CONTENTSLEONARD MACLEAN, ALEX RICHMAN, STIG LARSSON +VINCENT RICHMAN The Dynamics of Aircraft Degradation andMechanical FailureMIRIAM SCAGLIONE + ANDREW MUNGALL Air Traffic at ThreeSwiss Airports: Application of Stamp in Forecasting Future TrendsSCOTT DENNIS Improved Estimates of Ton-MilesADRIAN V COTRUS, JOSEPH N PRASHKER + YORAM SHIFTANSpatial and Temporal Transferability of Trip Generation Demand Modelsin IsraelSUDESHNA MITRA, SIMON WASHINGTON, ERIC DUMBAUGH +MICHAEL D MEYER Governors Highway Safety Associations andTransportation Planning: Exploratory Factor Analysis and StructuralEquation ModelingWENQUN WANG, HAIBO CHEN + MARGARET C BELL VehicleBreakdown Duration ModelingMOHAMED ABDEL-ATY Using Generalized Estimating Equations toAccount for Correlation in Route Choice ModelsBook ReviewsData ReviewEmployment in the Airline Industry, a review of Bureau ofTransportation Statistics data by Jennifer Brady