Mplus培训手册(2).pdf

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1、Latent Variable Modeling Using Mplus:Day 1Bengt Muth en&Linda Muth enMOctober,2012Bengt Muth en&Linda Muth enMplus Modeling1/186Table of Contents I11.Mplus Background22.Mediation Path Analysis2.1 Example:Mediation Of Fetal Alcohol Syndrome2.2 Example:Moderated Mediation Of Aggressive Behavior2.3 Cau

2、sally-Defined Effects In Mediation Analysis2.4 Two-Level Path Analysis With A Binary Outcome:HighSchool Dropout33.Bayesian Analysis3.1 Bayesian Mediation Modeling With Non-Informative Priors:The MacKinnon ATLAS Example44.Factor Analysis4.1 EFA Of Holzinger-Swineford Mental Abilities Data4.2 Bi-Facto

3、r Modeling Overview4.2.1 Bi-Factor Modeling Of The 24-VariableHolzinger-Swineford DataBengt Muth en&Linda Muth enMplus Modeling2/186Table of Contents II4.3 The ESEM Factor Analysis Approach:Multiple-Group EFAOf Aggressive Behavior Of Males And Females4.4 The BSEM Factor Analysis Approach4.4.1 BSEM F

4、or Holzinger-Swineford 19 Variables4.5.1 Other Factor Models:Second-Order Factor Model4.5.2 Other Factor Models:Multi-Trait,Multi-Method(MTMM)Model4.5.3 Other Factor Models:Longitudinal Factor Analysis Model4.5.4 Other Factor Models:Classic ACE Twin Model55.Measurement Invariance And Population Hete

5、rogeneity5.1 CFA With Covariates(MIMIC):NELS Data5.2 Multiple-Group Analysis66.Structural Equation Modeling(SEM):Classic Wheaton Et Al.SEM6.1 Modeling Issues In SEM77.Growth Modeling:Typical ExamplesBengt Muth en&Linda Muth enMplus Modeling3/186Table of Contents III7.1 Modeling Ideas:Individual Deve

6、lopment Over Time7.2 LSAY Growth Modeling With Time-Invariant Covariates7.3 LSAY Growth Modeling With Random Slopes7.4 Six Ways To Model Non-Linear Growth7.5 Piecewise Growth Modeling7.6 Growth Modeling With Multiple Processes7.7 Two-Part Growth Modeling7.8 Advances In Multiple Indicator Growth Mode

7、ling7.8.1 BSEM for Aggressive-Disruptive Behavior in theClassroom7.9 Advantages Of Growth Modeling In A Latent VariableFrameworkBengt Muth en&Linda Muth enMplus Modeling4/186The Map Of The Mplus Team Bengt Muth en&Linda Muth enMplus Modeling5/186The Other Members Of The Mplus Team ThuyMichelleSarahB

8、engt Muth en&Linda Muth enMplus Modeling6/1861.Mplus BackgroundInefficient dissemination of statistical methods:Many good methods contributions from biostatistics,psychometrics,etc are underutilized in practiceFragmented presentation of methods:Technical descriptions in many different journalsMany d

9、ifferent pieces of limited softwareMplus:Integration of methods in one frameworkEasy to use:Simple,non-technical language,graphicsPowerful:General modeling capabilitiesBengt Muth en&Linda Muth enMplus Modeling7/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent Varia

10、blesExploratory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hidden Markov modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisC

11、ausal inferenceBengt Muth en&Linda Muth enMplus Modeling8/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent VariablesExploratory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hi

12、dden Markov modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisCausal inferenceBengt Muth en&Linda Muth enMplus Modeling8/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent VariablesEx

13、ploratory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hidden Markov modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisCausal

14、inferenceBengt Muth en&Linda Muth enMplus Modeling8/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent VariablesExploratory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hidden M

15、arkov modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisCausal inferenceBengt Muth en&Linda Muth enMplus Modeling8/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent VariablesExplorat

16、ory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hidden Markov modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisCausal infere

17、nceBengt Muth en&Linda Muth enMplus Modeling8/186Mplus Integrates A Multitude Of Analysis TypesUsing The Unifying Theme Of Latent VariablesExploratory factor analysisStructural equation modelingItem response theory analysisGrowth modelingLatent class analysisLatent transition analysis(Hidden Markov

18、modeling)Growth mixture modelingSurvival analysisMissing data modelingMultilevel analysisComplex survey data analysisBayesian analysisCausal inferenceBengt Muth en&Linda Muth enMplus Modeling8/186The Mplus General Latent Variable Modeling Framework Observed variablesx background variables(nomodel st

19、ructure)y continuous and censoredoutcome variablesu categorical(dichotomous,ordinal,nominal)and countoutcome variablesLatent variablesf continuous variablesinteractions among fsc categorical variablesmultiple csBengt Muth en&Linda Muth enMplus Modeling9/186Topics For Day 1 And Day 2 By Latent Variab

20、le TypeLatent Variable TypeAnalysisContinuous CategoricalPath analysisTwo-level path analysisXFactor analysisXTwo-level factor analysisXStructural equation modelingXGrowth modelingXCount regressionXComplier average causal effectsXLatent class analysisXFactor mixture modelingXXLatent transition analy

21、sisXLatent class growth analysisXGrowth mixture modelingXXMissing data modelingXXSurvival modelingXXBengt Muth en&Linda Muth enMplus Modeling10/186Overview Of Day 3More advanced day,focusing on the cutting-edge features in Version7 related to multilevel analysis of complex survey data and itemrespon

22、se theory(IRT)extensions.Topics:IRT analysis,categorical factor analysisBasic IRTIntermediate IRTMultilevel analysisTwo-level analysis with random loadings(discriminations)Three-level analysisCross-classified analysisAdvanced IRT analysisGroup comparisons such as cross-national studiesRandom items,G

23、-theoryRandom contextsLongitudinal studiesBengt Muth en&Linda Muth enMplus Modeling11/1862.Mediation Path Analysis2.1 A simple mediation example:Fetal alcohol syndrome2.2 Moderated mediation example:Aggressive classroombehaviorVersion 7 LOOP plot of moderated mediation2.3 Causally-defined effects in

24、 mediation analysis2.4 Two-level path analysis with a binary outcome:High schooldropoutBengt Muth en&Linda Muth enMplus Modeling12/1862.1 Example:Mediation Of Fetal Alcohol SyndromeThe data are taken from the Maternal Health Project(Nancy Day).The subjects were a sample of mothers who drank at least

25、 three drinksa week during their first trimester plus a random sample of motherswho used alcohol less often.Mothers were measured at the fourth and seventh month of pregnancy,at delivery,and at 8,18,and 36 months postpartum.Offspring weremeasured at 0,8,18 and 36 months.Data for the analysis include

26、 mothers alcohol and cigarette use in thethird trimester and the childs gender,ethnicity,and headcircumference both at birth and at 36 months.Bengt Muth en&Linda Muth enMplus Modeling13/186Fetal Alcohol Syndrome Example:Mediation Model Bengt Muth en&Linda Muth enMplus Modeling14/186Input For Fetal A

27、lcohol Syndrome Mediation ModelTITLE:Fetal Alcohol Syndrome Mediation ModelDATA:FILE=headalln.dat;FORMAT=1f8.2 47f7.2;VARIABLE:NAMES=id weight0 weight8 weight18 weigh36 height0height8 height18 height36 hcirc0 hcirc8 hcirc18 hcirc36 mo-malc1 momalc2 momalc3 momalc8 momalc18 momalc36momcig1 momcig2 mo

28、mcig3 momcig8 momcig18 momcig36gender eth momht gestage age8 age18 age36 esteem8 es-teem18 esteem36 faminc0 faminc8 faminc18 faminc36 mom-drg36 gravid sick8 sick18 sick36 advp advm1 advm2 advm3;MISSING=ALL(999);USEVARIABLES=momalc3 momcig3 hcirc0 hcirc36 gendereth;USEOBSERVATIONS=id NE 1121 AND NOT(

29、momalc1 EQ999 AND momalc2 EQ 999 AND momalc3 EQ 999);Bengt Muth en&Linda Muth enMplus Modeling15/186Input For Fetal Alcohol Syndrome Mediation Model,ContinuedDEFINE:hcirc0=hcirc1/10;hcirc36=hcirc36/10;momalc3=log(momalc3+1);MODEL:hcirc36 ON hcirc0 gender eth;hcirc0 ON momalc3 momcig3 gender eth;MODE

30、L INDIRECT:hcirc36 IND hcirc0 momalc3;hcirc36 IND hcirc0 momcig3;OUTPUT:SAMPSTAT STANDARDIZED;Bengt Muth en&Linda Muth enMplus Modeling16/186Output For Fetal Alcohol Syndrome Mediation ModelTest of Model FitChi-Square Test of Model FitValue1.781Degrees of Freedom2P-Value.4068RMSEA(Root Mean Square E

31、rror Of Approximation)Estimate.00090 Percent C.I.0000.079Probability RMSEA m2.Rotation is avoidedBengt Muth en&Linda Muth enMplus Modeling53/186Factor Analysis:ApplicationsFactor analysis is applied to a variety of measurement instruments:Personality and cognition in psychologyChild Behavior Checkli

32、st(CBCL)MMPIAttitudes in sociology,political science,etc.Achievement in educationDiagnostic criteria in mental healthBengt Muth en&Linda Muth enMplus Modeling54/1864.1 EFA Of Holzinger-Swineford Mental Abilities DataClassic 1939 factor analysis study by Holzinger and Swineford(1939)in Illinois schoo

33、lsTwenty-six tests intended to measure a general factor and fivespecific factorsAdministered to seventh and eighth grade students in twoschoolsGrant-White school(n=145).Students came from homes wherethe parents were mostly American-bornPasteur school(n=156).Students came largely fromworking-class pa

34、rents of whom many were foreign-born andwhere their native language was used at homeSource:Holzinger,K.J.&Swineford,F.(1939).A study in factoranalysis:The stability of a bi-factor solution.SupplementaryEducational Monographs.Chicago,Ill.:The University ofChicagoBengt Muth en&Linda Muth enMplus Model

35、ing55/186Holzinger-Swineford Data,ContinuedCurrent analyses:19 variables using tests hypothesized to measure four mentalabilities:Spatial,verbal,speed,and memory24 variables,adding 5 tests measuring a general ability(deduction,test taking ability)Bengt Muth en&Linda Muth enMplus Modeling56/186 19 Va

36、riables:Expected Factor Loading PatternSpatialVerbalSpeedMemoryvisualx000cubesx000paperx000flagsx000general0 x00paragrap0 x00sentence0 x00wordc0 x00wordm0 x00addition00 x0code00 x0counting00 x0straight00 x0wordr000 xnumberr000 xfigurer000 xobject000 xnumberf000 xfigurew000 xBengt Muth en&Linda Muth

37、enMplus Modeling57/186Holzinger-Swineford,19 Variables:Input Excerpts For EFAVARIABLE:USEVARIABLES=visual-figurew;USEOBSERVATIONS=school EQ 0;ANALYSIS:TYPE=EFA 1 6;ROTATION=GEOMIN;!defaultESTIMATOR=ML;!defaultPARALLEL=50;OUTPUT:SAMPSTAT MODINDICES;PLOT:TYPE=PLOT3;Bengt Muth en&Linda Muth enMplus Mod

38、eling58/186Parallel Analysis Of The Eigenvalues For 19-VariableHolzinger-Swineford,Grant-White EFA 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Sample EigenvaluesParallel Analysis EigenvaluesParallel Analysis 95th Percentile Bengt Muth en&Linda Mut

39、h enMplus Modeling59/186EFA ML 2Tests Of Model Fit For 19-VariableHolzinger-Swineford Data,Grant-White SchoolFactorsChi-SquareBICCFIRMSEASRMR2dfp1469.81152.00018637.68.120.1022276.44134.00018534.86.086.0683188.75117.00018531.93.065.0534110.34101.24818532.99.025.030582.6986.581185791.00.000.0256no co

40、nvergenceBengt Muth en&Linda Muth enMplus Modeling60/186EFA ML Model Test ResultsFor 4-Factor,19-Variable Holzinger-Swineford DataFor The Grant-White(n=145)And Pasteur(n=156)SchoolsModel2dfP-valueRMSEACFIGrant-WhiteEFA1101010.2480.0250.991PasteurEFA1281010.0360.0410.972Estimated EFA factor pattern u

41、sing oblique rotation with Geomin:Grant-White has 6 and Pasteur has 9 significant cross-loadings.Bengt Muth en&Linda Muth enMplus Modeling61/186Grant-White Factor Loading Patterns For EFAPasteur Factor Loading Pattern For EFASpatialVerbalSpeedMemorySpatialVerbalSpeedMemoryvisual0.628*0.0650.0910.085

42、0.580*0.307*-0.0010.053cubes0.485*0.0500.007-0.0030.521*0.027-0.078-0.059paper0.406*0.1070.0840.0830.484*0.101-0.016-0.229*flags0.579*0.1600.0130.0260.687*-0.0510.0670.101general0.0420.752*0.126-0.051-0.0430.838*0.042-0.118paragrap0.0210.804*-0.0560.0980.0260.800*-0.0060.069sentence-0.0390.844*0.085

43、-0.057-0.0450.911*-0.054-0.029wordc0.0940.556*0.197*0.0190.0980.695*0.0080.083wordm0.0040.852*-0.0740.0690.143*0.793*0.029-0.023addition-0.302*0.0290.824*0.078-0.247*0.0670.664*0.026code0.0120.0500.479*0.279*0.0040.262*0.552*0.082counting0.045-0.1590.826*-0.0140.073-0.0340.656*-0.166straight0.346*0.

44、0430.570*-0.0550.266*-0.0340.526*-0.056wordr-0.0240.117-0.0200.523*-0.0050.020-0.0390.726*numberr0.0690.021-0.0260.515*-0.026-0.057-0.0570.604*figurer0.354*-0.033-0.0770.515*0.329*0.0420.1680.403*object-0.1950.0450.1540.685*-0.123-0.0050.333*0.469*numberf0.225-0.1270.246*0.450*-0.0140.0920.0920.427*

45、figurew0.0690.0990.0580.365*0.1390.0130.237*0.291*Bengt Muth en&Linda Muth enMplus Modeling62/186Factor Correlations For Grant-White And Pasteur SchoolsUsing Oblique Geomin RotationGrant-White Factor CorrelationsPasteur Factor CorrelationsSpatialVerbalSpeedMemorySpatialVerbalSpeedMemorySpatial1.0001

46、.000Verbal0.378*1.0000.186*1.000Speed0.372*0.386*1.0000.214*0.326*1.000Memory0.307*0.380*0.375*1.0000.190*0.100*0.242*1.000Bengt Muth en&Linda Muth enMplus Modeling63/186Interpreting Cross-LoadingsThe item figurer is intended to measure the Memory abilityfactor but has a significant cross-loading on

47、 the Spatial abilityfactor for both the Grant-White and Pasteur schoolsRequires remembering a set of figures:Put a check mark()in the space after each figure that was onthe study sheet.Do not put a check after any figure that you havenot studied.Bengt Muth en&Linda Muth enMplus Modeling64/1864.2 Bi-

48、Factor Modeling OverviewGeneral factor influencing all items(deductive,test-takingability);Holzinger-Swineford(1939)24-variable modelTestlet modeling,e.g.for PISA test itemsLongitudinal modeling with across-time correlation for residualsBi-factor modeling is as popular today as in 1939.New developme

49、ntsfor faster maximum-likelihood estimation with categorical items,reducing the number of dimensions for numerical integration:Gibbons,&Hedeker(1992).Full-information item bi-factoranalysis.PsychometrikaReise,Morizot,&Hays(2007).The role of the bifactor model inresolving dimensionality issues in hea

50、lth outcomes measures.Quality of Life ResearchCai(2010).A two-tier full-information item factor analysismodel with applications.PsychometrikaCai,Yang,Hansen(2011).Generalized full-information itembifactor analysis.Psychological MethodsBengt Muth en&Linda Muth enMplus Modeling65/186Bi-Factor Model Fo