Mplus Users Guide v6.. - Muthén & Muthén

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CHAPTER 18model with one less class than the estimated model. The Lo-Mendell-Rubin approach has been criticized (Jeffries, 2003) although it is unclearto which extent the critique affects its use in practice. The p-valueobtained represents the probability that the data have been generated bythe model with one less class. A low p-value indicates that the modelwith one less class is rejected in favor of the estimated model. Anadjustment to the test according to Lo-Mendell-Rubin is also given. Themodel with one less class is obtained by deleting the first class in theestimated model. Because of this, it is recommended when usingstarting values that they be chosen so that the last class is the largestclass. In addition, it is recommended that model identifying restrictionsnot be included in the first class. TECH11 is available only forESTIMATOR=MLR. The TECH11 option is not available for theMODEL CONSTRAINT command, the BOOTSTRAP option of theANALYSIS command, training data, and for models with more than onecategorical latent variable.TECH12The TECH12 option is used in conjunction with TYPE=MIXTURE torequest residuals for observed versus model estimated means, variances,covariances, univariate skewness, and univariate kurtosis. The observedvalues come from the total sample. The estimated values are computedas a mixture across the latent classes. The TECH12 option is notavailable for TYPE=RANDOM, the MONTECARLO command, theCONSTRAINT option of the VARIABLE command, and when there areno continuous dependent variables.TECH13The TECH13 option is used in conjunction with TYPE=MIXTURE torequest two-sided tests of model fit for univariate, bivariate, andmultivariate skew and kurtosis (Mardia’s measure of multivariatekurtosis). Observed sample values are compared to model estimatedvalues generated over 200 replications. Each p-value obtainedrepresents the probability that the estimated model has generated thedata. A high p-value indicates that the estimated model fits the data.TECH13 is available only when the LISTWISE option of the DATAcommand is set to ON. TECH13 is not available forTYPE=TWOLEVEL MIXTURE, ALGORITHM=INTEGRATION, theBOOTSTRAP option of the ANALYSIS command, the CONSTRAINT658
OUTPUT, SAVEDATA, And PLOT Commandsoption of the VARIABLE command, and when there are no continuousdependent variables.TECH14The TECH14 option is used in conjunction with TYPE=MIXTURE torequest a parametric bootstrapped likelihood ratio test (McLachlan &Peel, 2000) that compares the estimated model to a model with one lessclass than the estimated model. The p-value obtained represents anapproximation to the probability that the data have been generated by themodel with one less class. A low p-value indicates that the model withone less class is rejected in favor of the estimated model. The modelwith one less class is obtained by deleting the first class in the estimatedmodel. Because of this, it is recommended that model identifyingrestrictions not be included in the first class. In addition, it isrecommended when using starting values that they be chosen so that thelast class is the largest class. TECH14 is not available forTYPE=RANDOM unless ALGORITHM=INTEGRATION is used, theBOOTSTRAP option of the ANALYSIS command, training data, theCONSTRAINT option of the VARIABLE command, with samplingweights, and for models with more than one categorical latent variable.Following is a description of the bootstrap method that is used inTECH14. Models are estimated for both the number of classes in theanalysis model (k) and the number of classes in the analysis modelminus one (k–1). The loglikelihood values from the k and k-1 classanalyses are used to compute a likelihood ratio test statistic (-2 times theloglikelihood difference). Several data sets, referred to as bootstrapdraws, are then generated using the parameter estimates from the k-1class model. These data are analyzed for both the k and k-1 class modelsto obtain loglikelihood values which are used to compute a likelihoodratio test statistic for each bootstrap draw. The likelihood ratio teststatistic from the initial analysis is compared to the distribution oflikelihood ratio test statistics obtained from the bootstrap draws tocompute a p-value which is used to decide if the k-1 class model fits thedata as well as the k class model.The parametric bootstrapped likelihood ratio test can be obtained in twoways. The default method is a sequential method that savescomputational time by using a minimum number of bootstrap draws todecide whether the p-value is less than or greater than 0.05. The number659
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Statistical Analysis With Latent Va
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TABLE OF CONTENTSChapter 1: Introdu
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IntroductionCHAPTER 1INTRODUCTIONMp
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CHAPTER 1• Regression analysis•
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CHAPTER 1When there are no covariat
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CHAPTER 1model. For example, variab
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CHAPTER 112
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CHAPTER 2details of the analysis. T
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CHAPTER 2TITLE: this is an example
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CHAPTER 2The Mplus Base and Multile
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CHAPTER 3• Wald chi-square test o
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CHAPTER 3EXAMPLE 3.1: LINEAR REGRES
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CHAPTER 3EXAMPLE 3.3: CENSORED-INFL
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CHAPTER 3example above, u1 is a bin
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CHAPTER 3EXAMPLE 3.8: ZERO-INFLATED
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CHAPTER 3x1yx2sIn this example a re
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CHAPTER 3When two parameters are re
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CHAPTER 3logistic regressions. An e
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CHAPTER 3EXAMPLE 3.15: PATH ANALYSI
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CHAPTER 3The difference between thi
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CHAPTER 3The TECH8 option is used t
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CHAPTER 4CLUSTER, and WEIGHT option
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CHAPTER 4ANALYSIS: TYPE = EFA 1 4;T
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CHAPTER 4EXAMPLE 4.3: EXPLORATORY F
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CHAPTER 4ANALYSIS command is used t
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CHAPTER 4indicators. Rotated soluti
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CHAPTER 5and a set of Poisson or ze
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CHAPTER 5Following is the set of CF
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CHAPTER 5y1f1y2y3y4f2y5y6In this ex
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CHAPTER 5above, all six factor indi
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CHAPTER 5computationally demanding
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CHAPTER 5y1 y2 y3 y4y5 y6 y7 y8y9 y
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CHAPTER 5EXAMPLE 5.8: CFA WITH COVA
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CHAPTER 5y1af1y1by1cy2af2y2by2cIn t
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CHAPTER 5that the three test forms
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CHAPTER 5EXAMPLE 5.12: SEM WITH CON
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CHAPTER 5interaction is shown in th
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CHAPTER 5In multiple group analysis
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CHAPTER 5square brackets. When a mo
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CHAPTER 5EXAMPLE 5.18: TWO-GROUP TW
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CHAPTER 5EXAMPLE 5.20: CFA WITH PAR
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CHAPTER 5unit variance of the laten
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CHAPTER 5EXAMPLE 5.24: EFA WITH COV
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CHAPTER 5y7 y8 y9 y10 y11 y12y1y2f1
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CHAPTER 5y1 y2 y3 y4y5 y6 y7 y8y9 y
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CHAPTER 5In this example, the multi
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CHAPTER 5MODEL: f1-f2 by y1-y10 (*1
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CHAPTER 6slopes are also used to re
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CHAPTER 6for each graphical display
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CHAPTER 6In this example, the linea
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CHAPTER 6be different across time a
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CHAPTER 6name of the censored varia
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CHAPTER 6outcomes with a numerical
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CHAPTER 6EXAMPLE 6.7: LINEAR GROWTH
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CHAPTER 6EXAMPLE 6.8: GROWTH MODEL
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CHAPTER 6EXAMPLE 6.10: LINEAR GROWT
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Examples: Growth Modeling And Survi
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CHAPTER 6EXAMPLE 6.17: LINEAR GROWT
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CHAPTER 6y1 y2 y3 y4isx a21 a22 a23
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CHAPTER 6The GROUPING option is use
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CHAPTER 6occurred, and a missing va
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CHAPTER 6In this example, the conti
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CHAPTER 6intervals plus one. These
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CHAPTER 6140
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CHAPTER 7zero-inflated Poisson regr
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CHAPTER 7Graphical displays of obse
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CHAPTER 7EXAMPLE 7.1: MIXTURE REGRE
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CHAPTER 7is to be performed. By sel
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CHAPTER 7EXAMPLE 7.2: MIXTURE REGRE
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CHAPTER 7u1u2cu3u4In this example,
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CHAPTER 7In the MODEL command, user
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CHAPTER 7EXAMPLE 7.9: LCA WITH CONT
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CHAPTER 7indicators, the default co
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CHAPTER 7EXAMPLE 7.12: LCA WITH BIN
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CHAPTER 7The first hypothesis is sp
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CHAPTER 7The CLASSES option is used
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CHAPTER 7between the first two vari
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CHAPTER 7EXAMPLE 7.17: CFA MIXTURE
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CHAPTER 7u11 u12 u13u21 u22 u23c1c2
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CHAPTER 7In this example, the model
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CHAPTER 7EXAMPLE 7.21: MIXTURE MODE
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CHAPTER 7y1y2cy3y4In this example,
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CHAPTER 7ycx1x2In this example, the
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CHAPTER 7MODEL:%OVERALL%y ON x1 x2;
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CHAPTER 7In this example, the zero-
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CHAPTER 7EXAMPLE 7.27: FACTOR MIXTU
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CHAPTER 7algorithm will be used. No
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CHAPTER 7u11 u12 u13 u14u21 u22 u23
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CHAPTER 7MODEL:OUTPUT:PLOT:%OVERALL
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CHAPTER 7196
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CHAPTER 8All longitudinal mixture m
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CHAPTER 8• 8.8: GMM with known cl
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CHAPTER 8to the growth factors i an
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CHAPTER 8estimated as the default,
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CHAPTER 8EXAMPLE 8.3: GMM FOR A CEN
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CHAPTER 8algorithm will be used. No
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CHAPTER 8by adding to the name of t
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CHAPTER 8y1 y2 y3 y4isx c uThe diff
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CHAPTER 8y1 y2 y3 y4 y5 y6 y7 y8i1
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CHAPTER 8where c2#1 refers to the f
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CHAPTER 8parts of the model, starti
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CHAPTER 8MODEL c1:MODEL c2:MODEL c3
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CHAPTER 8MODEL c.c1:%c#1.c1#1%[u11$
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CHAPTER 8used to select a different
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CHAPTER 8ALGORITHM=INTEGRATION as i
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CHAPTER 8ON statement describes the
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CHAPTER 9VARIABLE command. Observed
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CHAPTER 9for individual data or the
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CHAPTER 9• 9.16: Linear growth mo
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CHAPTER 9TITLE:this is an example o
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CHAPTER 9Following is the second pa
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CHAPTER 9xsyWithinwyBetweenxmsThe d
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CHAPTER 9EXAMPLE 9.3: TWO-LEVEL PAT
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CHAPTER 9integration are used with
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CHAPTER 9EXAMPLE 9.5: TWO-LEVEL PAT
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CHAPTER 9using the ON option. In th
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CHAPTER 9constrained to be equal ac
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CHAPTER 9does not require numerical
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CHAPTER 9In the within part of the
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CHAPTER 9u1x1fw1u2u3u4x2fw2u5u6With
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CHAPTER 9In the between part of the
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CHAPTER 9y1y2fwsy5y3y4Withiny1Betwe
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CHAPTER 9the factor fb and the clus
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CHAPTER 9and individuals with g equ
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CHAPTER 9y1y2y3y4iwswxWithinBetween
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CHAPTER 9residual variances of the
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CHAPTER 9EXAMPLE 9.14: TWO-LEVEL GR
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CHAPTER 9as y1, y2, y3, and y4 in t
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CHAPTER 9u11u21u31u12 u22 u32 u13 u
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CHAPTER 9statements are fixed at ze
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CHAPTER 9timesya3Withinx1yBetweenx2
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CHAPTER 9EXAMPLE 9.17: TWO-LEVEL GR
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CHAPTER 9model, the variances of th
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CHAPTER 9288
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CHAPTER 10• Complex survey data
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CHAPTER 10• 10.13: Two-level LTA
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CHAPTER 10across clusters. The rand
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CHAPTER 10refers to the part of the
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CHAPTER 10EXAMPLE 10.2: TWO-LEVEL M
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CHAPTER 10the end of the arrow poin
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CHAPTER 10EXAMPLE 10.3: TWO-LEVEL M
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CHAPTER 10random intercept y is sho
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CHAPTER 10y1 y2 y3 y4y5cfwWithinBet
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CHAPTER 10EXAMPLE 10.5: TWO-LEVEL I
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CHAPTER 10latent variable c. The fi
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CHAPTER 10u1 u2 u3 u4u5u6cxWithinBe
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CHAPTER 10EXAMPLE 10.7: TWO-LEVEL L
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CHAPTER 10In the overall part of th
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CHAPTER 10y1 y2 y3 y4iwsswxWithinBe
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CHAPTER 10Following is an alternati
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CHAPTER 10y1 y2 y3 y4iwswcxWithinBe
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CHAPTER 10coefficients of the inter
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CHAPTER 10y1 y2 y3 y4iwswcxWithinBe
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CHAPTER 10EXAMPLE 10.11: TWO-LEVEL
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CHAPTER 10In the overall part of th
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CHAPTER 10In this example, the two-
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CHAPTER 10336
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CHAPTER 11With Bayesian analysis, m
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CHAPTER 11number of parameters and
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CHAPTER 11EXAMPLE 11.2: DESCRIPTIVE
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CHAPTER 11MODEL:OUTPUT:i s | y0@0 y
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CHAPTER 11y0 y1 y2 y3 y4 y5i s qd1
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CHAPTER 11analysis. In the second p
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CHAPTER 11DATA IMPUTATION:NDATASETS
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CHAPTER 11MODEL: %WITHIN%f1w BY u11
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CHAPTER 11TITLE:DATA:this is an exa
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CHAPTER 11The ANALYSIS command is u
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CHAPTER 12saved in an external file
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CHAPTER 12• 12.11: Monte Carlo si
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CHAPTER 12MONTE CARLO OUTPUTChi-Squ
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CHAPTER 12The column labeled Popula
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CHAPTER 12In this example, data are
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CHAPTER 12covariances of the indepe
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CHAPTER 12slope factor s. The binar
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CHAPTER 12ANALYSIS: TYPE = MIXTURE;
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CHAPTER 12MODEL MISSING:[y1-y4@-1];
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CHAPTER 12The default estimator for
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CHAPTER 12EXAMPLE 12.6 STEP 2: EXTE
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CHAPTER 12EXAMPLE 12.7 STEP 2: MONT
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CHAPTER 12MODEL MISSING command spe
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CHAPTER 12MODEL:OUTPUT:iu su | u1@0
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CHAPTER 12continuous-time survival
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CHAPTER 12MODEL:%WITHIN%c | y ON x;
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CHAPTER 12invariance across groups
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CHAPTER 13EXAMPLE 13.1: A COVARIANC
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CHAPTER 13EXAMPLE 13.4: NON-NUMERIC
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CHAPTER 13EXAMPLE 13.7: TRANSFORMIN
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CHAPTER 13EXAMPLE 13.10: EQUALITIES
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CHAPTER 13TITLE: this is an example
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CHAPTER 13EXAMPLE 13.14: SAVING DAT
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CHAPTER 13EXAMPLE 13.17: MERGING DA
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CHAPTER 13EXAMPLE 13.19: GENERATING
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CHAPTER 14• User-specified starti
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CHAPTER 14conjunction with the | sy
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CHAPTER 14Loadings for indicators o
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CHAPTER 14possible that a local sol
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CHAPTER 14GENERAL CONVERGENCE PROBL
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CHAPTER 14Model identification can
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CHAPTER 14computations will become
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CHAPTER 14covariances and regressio
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CHAPTER 14MODEL COMMAND IN MULTIPLE
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CHAPTER 14in the other two groups.
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CHAPTER 14MODEL g2: y1-y5 (2);MODEL
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CHAPTER 14variances in a model with
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CHAPTER 1432 32 2 32 2 2 3where the
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CHAPTER 14WEIGHTED LEAST SQUARES ES
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CHAPTER 14Multiple data sets genera
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CHAPTER 14Observation Cohort HD82 H
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CHAPTER 14CALCULATING PROBABILITIES
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CHAPTER 14log odds (x 0 +1) = a + b
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CHAPTER 14values are exponentiated
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CHAPTER 14available for these model
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CHAPTER 14The joint probabilities f
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CHAPTER 15THE DATA COMMANDThe DATA
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CHAPTER 15DATA LONGTOWIDE:LONG =WID
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CHAPTER 15to the number of variable
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CHAPTER 15TYPEThe TYPE option is us
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CHAPTER 15and saved using another c
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CHAPTER 15LISTWISE = ON;SWMATRIXThe
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CHAPTER 15parentheses following its
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CHAPTER 15uses a model of unrestric
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CHAPTER 15WIDEThe WIDE option is us
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CHAPTER 15LONG = y | x;where y and
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CHAPTER 15categorical using the CAT
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CHAPTER 15THE DATA MISSING COMMANDT
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CHAPTER 153. The value zero is assi
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CHAPTER 15NAMESThe NAMES option ide
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CHAPTER 15cohort. In the example ab
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CHAPTER 15THE VARIABLE COMMANDVARIA
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CHAPTER 15ASSIGNING NAMES TO VARIAB
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CHAPTER 15The USEVARIABLES option i
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CHAPTER 15MISSING ARE ethnic (9 99)
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CHAPTER 15CATEGORICALThe CATEGORICA
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CHAPTER 15where the set of variable
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CHAPTER 15COUNT = u1-u4 (p);The COU
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CHAPTER 15GROUPINGThe GROUPING opti
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CHAPTER 15TSCORESThe TSCORES option
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CHAPTER 15parentheses is placed beh
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CHAPTER 15the VARIABLE command and
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CHAPTER 15WTSCALEThe WTSCALE option
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CHAPTER 15ANALYSIS command. The sam
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CHAPTER 15MIXTURE MODELSThere are t
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CHAPTER 15Fractional values can be
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CHAPTER 15CONTINUOUS-TIME SURVIVAL
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CHAPTER 15THE DEFINE COMMANDDEFINE:
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CHAPTER 15The _MISSING keyword can
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CHAPTER 15where the variable ymean
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CHAPTER 15518
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CHAPTER 16WLS;WLSM;WLSMV;ULS;ULSMV;
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CHAPTER 16STSCALE = random start sc
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CHAPTER 16The ANALYSIS command is n
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CHAPTER 16TYPE = GENERAL RANDOM;or
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CHAPTER 16• COMPLEX computes stan
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CHAPTER 16where the first two numbe
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CHAPTER 16TWOLEVELMUML***ML**MLR**M
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CHAPTER 16BAYESIAN ESTIMATIONBayesi
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CHAPTER 16LOGIT REGRESSION VERSUS L
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CHAPTER 16where .5 is the value of
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CHAPTER 16ROTATION = TARGET (ORTHOG
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CHAPTER 16For the FAY resampling me
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CHAPTER 16OPTIONS RELATED TO NUMERI
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CHAPTER 16For other outcome types a
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CHAPTER 16BOOTSTRAPThe BOOTSTRAP op
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CHAPTER 16values produced by the pr
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CHAPTER 16OPTSEEDThe OPTSEED option
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CHAPTER 16DIFFTEST = deriv.dat;wher
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CHAPTER 16RITERATIONSThe RITERATION
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CHAPTER 16MIXUThe MIXU option is us
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CHAPTER 16With multiple chains, par
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CHAPTER 16such that convergence is
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CHAPTER 16skipped. A setting of 1 s
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CHAPTER 16566
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CHAPTER 17DEPENDENT OR INDEPENDENT
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CHAPTER 17| names and defines rando
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CHAPTER 17short for measured by. ON
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CHAPTER 17because BY statements are
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CHAPTER 17allowed with TYPE=GENERAL
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CHAPTER 172001). The target factor
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CHAPTER 17specifies that regression
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CHAPTER 17PON, the number of variab
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CHAPTER 17impliesy1 WITH y4;y1 WITH
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CHAPTER 17refers to the means of va
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CHAPTER 17f1 ON x1 x2 x3;f2 ON x1 x
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CHAPTER 17By placing an asterisk (*
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CHAPTER 17possible thresholds, thre
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CHAPTER 17A list of equality constr
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CHAPTER 17parameters. Following is
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CHAPTER 17Although y5 is assigned a
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CHAPTER 17LABELING CLASSES OF A CAT
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CHAPTER 17[y1-y4@0 i s q];If the |
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CHAPTER 17Linear for acount outcome
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CHAPTER 17MultilevelMultipleindicat
Page 614 and 615: CHAPTER 17In mixture models for con
Page 616 and 617: CHAPTER 17ATThe AT option is used w
Page 618 and 619: CHAPTER 17Numerical integration bec
Page 620 and 621: CHAPTER 17INDThe variable on the le
Page 622 and 623: CHAPTER 17PARAMETERS LABELLED IN TH
Page 624 and 625: CHAPTER 17right-hand side of one or
Page 626 and 627: CHAPTER 17Type of Parameter Distrib
Page 628 and 629: CHAPTER 17number gives the number o
Page 630 and 631: CHAPTER 17These are used to specify
Page 632 and 633: CHAPTER 17so on. In mixture modelin
Page 634 and 635: CHAPTER 17In mixture modeling, the
Page 636 and 637: CHAPTER 17A dependent variable that
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Page 640 and 641: CHAPTER 18CINTERVAL;CINTERVAL (SYMM
Page 642 and 643: CHAPTER 18Following is the summary
Page 644 and 645: CHAPTER 18and thresholds are found
Page 646 and 647: CHAPTER 18printed is too large to f
Page 648 and 649: CHAPTER 18where b is the unstandard
Page 650 and 651: CHAPTER 18the third column. When st
Page 652 and 653: CHAPTER 18When model modification i
Page 654 and 655: CHAPTER 18CONFIDENCE INTERVALS OF M
Page 656 and 657: CHAPTER 18NOSERROR;This option is n
Page 658 and 659: CHAPTER 18FACTOR DETERMINACIESTECHN
Page 660 and 661: CHAPTER 18THETAY1 Y2 Y3 Y4 X_______
Page 662 and 663: CHAPTER 18TECHNICAL 4 OUTPUTTECH4Th
Page 666 and 667: CHAPTER 18of draws varies from 2 to
Page 668 and 669: CHAPTER 18GAMMAThe gamma matrix con
Page 670 and 671: CHAPTER 18• Analysis data• Samp
Page 672 and 673: CHAPTER 18by the program, the recod
Page 674 and 675: CHAPTER 18SIGBETWEENThe SIGBETWEEN
Page 676 and 677: CHAPTER 18using the POPULATION and/
Page 678 and 679: CHAPTER 18SURVIVAL option. Followin
Page 680 and 681: CHAPTER 18FSCORESWhen SAVE=FSCORES
Page 682 and 683: CHAPTER 18COOKSWhen SAVE=COOKS is u
Page 684 and 685: CHAPTER 18For data in fixed format,
Page 686 and 687: CHAPTER 18• Sample proportions•
Page 688 and 689: CHAPTER 18Following is an example o
Page 690 and 691: CHAPTER 18VIEWING GRAPHICAL OUTPUTS
Page 692 and 693: CHAPTER 18Following is the window t
Page 694 and 695: CHAPTER 18The plots can be exported
Page 696 and 697: CHAPTER 19CLASSES =SURVIVAL =TSCORE
Page 698 and 699: CHAPTER 19For Monte Carlo studies,
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Page 704 and 705: CHAPTER 19together to generate miss
Page 706 and 707: CHAPTER 19between dependent and ind
Page 708 and 709: CHAPTER 19categories are referred t
Page 710 and 711: CHAPTER 19Following is the specific
Page 712 and 713: CHAPTER 19TSCORESThe TSCORES option
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CHAPTER 19where estimates.dat is a
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CHAPTER 19710
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CHAPTER 20DATA IMPUTATION:IMPUTE =N
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CHAPTER 20TSCORES AREnames of obser
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CHAPTER 20ESTIMATOR = ML; depends o
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CHAPTER 20STCONVERGENCE = initial s
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CHAPTER 20INTERACTIVE =PROCESSORS =
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CHAPTER 20MODEL COVERAGE:%WITHIN%%B
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CHAPTER 20TYPE IS COVARIANCE; varie
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CHAPTER 20COVERAGE =STARTING =REPSA
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Asparouhov, T. & Muthén, B. (2009a
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Hagenaars, J.A. & McCutcheon, A.L.
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Larsen, K. (2005). The Cox proporti
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Muthén, B. (2002). Beyond SEM: Gen
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Qu, Y., Tan, M., & Kutner, M.H. (19
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738
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CATEGORICALMonte Carlo, 701real dat
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SEM with EFA and CFA factors, 89-91
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inary outcome, 218-19three-category
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two-level growth mixture model (GMM
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PRIORS, 507-8PROBABILITIES, 507-8pr
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TIMEMEASURES, 478-79time-to-event v
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