Mplus Users Guide v6.. - Muthén & Muthén

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Muthén, B. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117.Muthén, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques forlongitudinal data. In D. Kaplan (ed.), Handbook of quantitative methodology for the socialsciences (pp. 345-368). Newbury Park, CA: Sage Publications.Muthén, B. (2006). Should substance use disorders be considered as categorical or dimensional?Addiction, 101 (Suppl. 1), 6-16.Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G.R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 1-24. Charlotte,NC: Information Age Publishing, Inc.Muthén, B. and Asparouhov, T. (2002). Latent variable analysis with categorical outcomes:Multiple-group and growth modeling in Mplus. Mplus Web Notes: No. 4. www.statmodel.com.Muthén, B. & Asparouhov, T. (2006). Item response mixture modeling: Application to tobaccodependence criteria. Addictive Behaviors, 31, 1050-1066.Muthén, B. & Asparouhov, T. (2007). Non-parametric hierarchical regressions. In preparation.Muthén, B. & Asparouhov, T. (2009). Growth mixture modeling: Analysis with non-Gaussianrandom effects. In Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G. (eds.),Longitudinal Data Analysis, pp. 143-165. Boca Raton: Chapman & Hall/CRC Press.Muthén, B. & Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variablesin several groups. Psychometrika, 46, 407-419.Muthén, B. & Masyn, K. (2005). Discrete-time survival mixture analysis. Journal of Educationaland Behavioral Statistics, 30, 27-28.Muthén, L.K. & Muthén, B. (2002). How to use a Monte Carlo study to decide on sample sizeand determine power. Structural Equation Modeling, 4, 599-620.Muthén, B. & Satorra, A. (1995). Complex sample data in structural equation modeling. In P.Marsden (ed.), Sociological Methodology 1995, 216-316.Muthén, B. & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EMalgorithm. Biometrics, 55, 463-469.734
Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squaresand quadratic estimating equations in latent variable modeling with categorical and continuousoutcomes. Unpublished manuscript.Muthén, B., Jo., B., & Brown, H. (2003). Comment on the Barnard, Frangakis, Hill, & Rubinarticle, Principal stratification approach to broken randomized experiments: A case study ofschool choice vouchers in New York City. Journal of the American Statistical Association, 98,311-314.Muthén, B., Asparouhov, T. & Rebollo, I. (2006). Advances in behavioral genetics modelingusing Mplus: Applications of factor mixture modeling to twin data. Twin Research and HumanGenetics, 9, 313-324.Muthén, B., Asparouhov, T., Boye, M.E., Hackshaw, M.D., & Naegeli, A.N. (2009).Applications of continuous-time survival in latent variable models for the analysis of oncologyrandomized clinical trial data using Mplus. Technical Report. www.statmodel.com.Muthén, B., Asparouhov, T., Hunter, A., & Leuchter, A. (2010). Growth modeling with nonignorabledropout: Alternative analyses of the STAR*D antidepressant trial. Submitted forpublication.Muthén, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S.,Carlin, J., & Liao, J. (2002). General growth mixture modeling for randomized preventiveinterventions. Biostatistics, 3, 459-475.Nagin, D.S. (1999). Analyzing developmental trajectories: A semi-parametric, group-basedapproach. Psychological Methods, 4, 139-157.Neale, M.C. & Cardon, L.R. (1992). Methodology for genetic studies of twins and families. TheNetherlands: Kluwer Academic Publishers.Nylund, K. (2007). Latent transition analysis: Modeling extensions and an application to peervictimization. Doctoral dissertation, University of California, Los Angeles.www.statmodel.com.Nylund, K.L., Asparouhov, T., & Muthén, B.O. (2007). Deciding on the number of classes inlatent class analysis and growth mixture modeling: A Monte Carlo simulation study. StructuralEquation Modeling, 14, 535-569.Olsen, M.K. & Schafer, J.L. (2001). A two-part random-effects model for semicontinuouslongitudinal data. Journal of the American Statistical Association, 96, 730-745.735
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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
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CHAPTER 17In mixture models for con
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CHAPTER 17ATThe AT option is used w
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CHAPTER 17Numerical integration bec
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CHAPTER 17INDThe variable on the le
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CHAPTER 17PARAMETERS LABELLED IN TH
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CHAPTER 17right-hand side of one or
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CHAPTER 17Type of Parameter Distrib
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CHAPTER 17number gives the number o
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CHAPTER 17These are used to specify
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CHAPTER 17so on. In mixture modelin
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CHAPTER 17In mixture modeling, the
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CHAPTER 17A dependent variable that
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CHAPTER 17632
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CHAPTER 18CINTERVAL;CINTERVAL (SYMM
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CHAPTER 18Following is the summary
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CHAPTER 18and thresholds are found
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CHAPTER 18printed is too large to f
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CHAPTER 18where b is the unstandard
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CHAPTER 18the third column. When st
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CHAPTER 18When model modification i
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CHAPTER 18CONFIDENCE INTERVALS OF M
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CHAPTER 18NOSERROR;This option is n
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CHAPTER 18FACTOR DETERMINACIESTECHN
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CHAPTER 18THETAY1 Y2 Y3 Y4 X_______
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CHAPTER 18TECHNICAL 4 OUTPUTTECH4Th
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CHAPTER 18model with one less class
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CHAPTER 18of draws varies from 2 to
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CHAPTER 18GAMMAThe gamma matrix con
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CHAPTER 18• Analysis data• Samp
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CHAPTER 18by the program, the recod
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CHAPTER 18SIGBETWEENThe SIGBETWEEN
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CHAPTER 18using the POPULATION and/
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CHAPTER 18SURVIVAL option. Followin
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CHAPTER 18FSCORESWhen SAVE=FSCORES
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CHAPTER 18COOKSWhen SAVE=COOKS is u
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CHAPTER 18For data in fixed format,
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CHAPTER 18• Sample proportions•
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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 702 and 703: CHAPTER 19where c1, c2, and c3 are
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
Page 714 and 715: CHAPTER 19where estimates.dat is a
Page 716 and 717: CHAPTER 19710
Page 718 and 719: CHAPTER 20DATA IMPUTATION:IMPUTE =N
Page 720 and 721: CHAPTER 20TSCORES AREnames of obser
Page 722 and 723: CHAPTER 20ESTIMATOR = ML; depends o
Page 724 and 725: CHAPTER 20STCONVERGENCE = initial s
Page 726 and 727: CHAPTER 20INTERACTIVE =PROCESSORS =
Page 728 and 729: CHAPTER 20MODEL COVERAGE:%WITHIN%%B
Page 730 and 731: CHAPTER 20TYPE IS COVARIANCE; varie
Page 732 and 733: CHAPTER 20COVERAGE =STARTING =REPSA
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Page 736 and 737: Hagenaars, J.A. & McCutcheon, A.L.
Page 738 and 739: Larsen, K. (2005). The Cox proporti
Page 742 and 743: Qu, Y., Tan, M., & Kutner, M.H. (19
Page 744 and 745: 738
Page 746 and 747: CATEGORICALMonte Carlo, 701real dat
Page 748 and 749: SEM with EFA and CFA factors, 89-91
Page 750 and 751: inary outcome, 218-19three-category
Page 752 and 753: two-level growth mixture model (GMM
Page 754 and 755: PRIORS, 507-8PROBABILITIES, 507-8pr
Page 756 and 757: TIMEMEASURES, 478-79time-to-event v
Page 758: MUTHÉN & MUTHÉNMplus SINGLE-USER
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Mplus Users Guide v6.. - Muthén & Muthén

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