Multilevel modelling and time series analysis in ... - ERSO - Swov

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Chapter 2of the functions present in MLwiN but without its easily accessible userinterface.The standard statistical software packages allow multilevel modelling to someextent. Most notably SAS, allows the estimation of all models presented in thisdocument (Littell, Milliken, Stroup, and Wolfinger, 1996). However, it does notenable the detailed diagnostics tailored to these models. SPSS only allows theestimation of linear multilevel models. An excellent collection of reviews how toimplement multilevel models in a wide variety of statistical software can befound on the MLwiN website (www.mlwin.com/softrev/index.html).Within the present chapter on multilevel modelling, there is a build-up ofinformation about the use of MLwiN. The chapters on linear models form anintroduction to MLwiN and some of its possibilities as well. They contain verydetailed information how to address the functions and how to interpret theoutput. In later chapters this information is more compressed. This all said, thefocus of this document is not to learn to deal with MLwiN (for all details thereader is referred to the MLwiN manual by Rasbash, Steel, Brown, & Prosser,2004) but to get a practical introduction to the multilevel analysis of road safetydata.
2.2 Multilevel linear regression modelsHeike Martensen and Emmanuelle Dupont (IBSR)2.2.1 Basic two level random intercept and random slopemodelsThe example data used in this and the following section are based on a nationalspeed survey conducted in Belgium. The speed of 4994 cars was “measured” at131 randomly selected road sites. Additionally, the length of each car wasrecorded. The question pursued here, is whether there is a relation between thespeed and the length of the car (considered here as rough indicator of itsengine power). The data contain the following variables:IDlocation Identifies the road site (i.e. the location)IDsubject Identifies the subjects, i.e. the individual cars within eachlocationSpeed Indicates the speed of that carLength Indicates the length of that carLengthCentred Indicates the length of that car minus the average lengthLengthCat Indicates whether a car is shorter (0) or longer (1) than 4.3mTrafficCount Indicates the number of cars passing a road site duringmeasurementTrafficCountCat Indicates whether fewer (0) or more (1) than 100 cars passedProvince The Belgian Province in which measurement has taken placeData loadTo begin with, we will import the data from Excel.• Open MLwiN• Open the data file (SPEED.xls) in Excel• Select all columns (ctrl A) and copy them (ctrl C) in Excel• Go to MLwiN, press Ctrl VThe following window appears:
Page 1 and 2: Deliverable D7.5Multilevel modellin
Page 3 and 4: 3.6 State space models.............
Page 5 and 6: Chapter 1 - IntroductionHeike Marte
Page 7 and 8: IntroductionFigure 1.2: Structure o
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Page 15 and 16: 2.2 Linear multilevel modelsResults
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Page 28 and 29: Chapter 2intercept between location
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Page 32 and 33: 2.3 Discrete response models2.3.1 I
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Page 40 and 41: 2.3.3 Multinomial responsesHeike Ma
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Chapter 2We will now add a random s
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Chapter 2All fixed and random effec
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Chapter 2We can see that the level-
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Chapter 2In this case, all fixed ef
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Chapter 2Another issue that needs t
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Chapter 2In the bottom line of the
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2.4 Longitudinal dataHeike Martense
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Chapter 2Than open the “Names”
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Chapter 2• Click “Calc” to ca
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Chapter 2Results and Interpretation
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Chapter 2Results and Interpretation
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Chapter 2Now a variable that contai
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Chapter 2 Click “Done”• Estim
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Chapter 2As described in the multiv
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Chapter 2▪ Click on resp1 or resp
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Chapter 2Before we proceed in fitti
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Chapter 2▪ Click on the Estimates
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Chapter 2We will now proceed in bui
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Chapter 2A significant regional var
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Chapter 2▪ Click More to run the
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Chapter 2The fixed effect of enforc
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Chapter 3 - Time series analysis3.1
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Chapter 3manual's objective: "even
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Chapter 3The option “Variable Vie
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Chapter 3The figure displayed below
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Chapter 3
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Chapter 3Then mark and click the va
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Chapter 3The residual analysis in t
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Chapter 3A new window “Linear Reg
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Chapter 3The result stated above sh
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Chapter 3The same result is obtaine
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Chapter 3In this new opened window
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Chapter 3To compute the last variab
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Chapter 3
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Chapter 3time series on “Squared
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Chapter 33.2.2 Generalized linear m
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Chapter 3SPSS (Version 14.0) was us
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Chapter 33.4.2 ARIMA models for sta
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Chapter 3• Click on Graphs..Seque
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Chapter 3The ACF plot indicates the
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Chapter 3The ACF plot of the filter
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Chapter 3• Click on Statistics th
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Chapter 3Model Description ARIMA(0,
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Chapter 3In addition to the precedi
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Chapter 3Note that it is very diffi
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Chapter 3In the case the Residuals
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Chapter 3The normal Q-Q plot compar
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Chapter 33.4.4 ARIMA models for sea
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Chapter 33.4.4.2. Model identificat
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Chapter 3The ACF plot indicates obv
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Chapter 33.4.4.3. Model estimation
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Chapter 3• Click on Plots tab and
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Chapter 3Model Description ARIMA (2
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Chapter 33.4.4.4. Graphical results
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Chapter 3Kolmogorov-Smirnov TestIn
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Chapter 3Here are the SPSS results
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Chapter 3of the residuals, up to or
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Chapter 3HistogramQQ-plot
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Chapter 3As the intervention variab
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Chapter 3The addition of the two ex
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Chapter 3Histogram
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Chapter 3Kolmogorov-Smirnov TestIn
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Chapter 33.5 DRAG modelsThe DRAG mo
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Chapter 3a summary of results and s
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Chapter 3This data file consists of
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Chapter 3 Then click on the Finish
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Chapter 3Independence Q(6,6) 28.8 1
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Chapter 3Step 4: Graphics of model
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Chapter 3 Shortly examine the figur
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Chapter 3The STAMP graphics window
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Chapter 334, we better use the Door
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Chapter 3The auxiliary residuals ar
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Chapter 33.6.2.2 Stochastic level m
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Chapter 3convergence criteria used
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Chapter 36.25Log_NO_fatTrend_Log_NO
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Chapter 3 Go to the STAMP window ag
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Chapter 3 Click OK.
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Chapter 3The list of forecast resul
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Chapter 33.6.3 Local linear trend m
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Chapter 3Irr 0.021360 ( 1.0000) Che
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Chapter 3 In the Residual graphics
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Chapter 33.6.3.2. Stochastic linear
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Chapter 3Estimation sample is 1970.
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Chapter 37.0 Log_FI_fat Trend_Log_F
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Chapter 3The goodness-of-fit is cle
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Chapter 3The STAMP graphics window
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Chapter 33.6.4 Local linear trend p
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Chapter 3Prediction error variance
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Chapter 3Parameter estimation sampl
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Chapter 38.007.757.507.257.000.2Log
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Chapter 3Goodness-of-fit results fo
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Chapter 3interpretation of the test
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Chapter 3The text "Lvl 1983.2" appe
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Chapter 3Normality N 2.40 5.99 +Tab
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Chapter 32Residual Log_UKdriversKSI
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Chapter 32IrrRes Log_UKdriversKSI0.
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Chapter 33.6.6 Explanatory variable
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Chapter 3function has increased fro
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Chapter 3Figure 3.6.18: Observed lo
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Chapter 3 Use the menu or to save
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Chapter 32IrrRes Log_UKdriversKSI0.
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Chapter 3for this period. The actua
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Chapter 3the top figure and the ori
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Chapter 4 - ConclusionThe present d
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Chapter 4researchers conduct valid
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ReferencesLISREL for Windows. Scien
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