Mplus Users Guide v6.. - Muthén & Muthén

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CHAPTER 17PON, the number of variables on the left-hand side of the PON statementmust equal the number of variables on the right-hand side of the PONstatement. For example,y2 y3 y4 PON y1 y2 y3;impliesy2 ON y1;y3 ON y2;y4 ON y3;The PON option cannot be used with the simplified language forcategorical latent variables or unordered categorical (nominal) observedvariables.WITHThe WITH option is used to describe correlational relationships in amodel and is short for correlated with. Correlational relationshipsinclude covariances among continuous observed variables andcontinuous latent variables and among categorical latent variables. Withthe weighted least squares estimator, correlational relationships are alsoallowed for binary, ordered categorical, and censored observedvariables. For all other variable types, the WITH option cannot be usedto specify correlational relationships. Special modeling needs to be usedin these situations, for example, using a latent variable that influencesboth variables.The NOCOVARIANCES setting of the MODEL option of theANALYSIS command specifies that the covariances and residualcovariances among all latent and observed variables in the analysismodel are fixed at zero. The WITH option can be used to free selectedcovariances and residual covariances.Following is an example of how to specify the WITH option:f1 WITH f2;This statement frees the covariance parameter for the continuous latentvariables f1 and f2.582
MODEL CommandSeveral variables can be included on both sides of the WITH statement.In this situation, the variables on the left-hand side of the WITHstatement are crossed with the variables on the right-hand side of theWITH statement resulting in all possible combinations of left- and righthandside variables.The association between two categorical latent variables c1 and c2where c1 has three classes and c2 has four classes is specified asfollows:c1#1 c1#2 WITH c2#1 c2#2 c2#3;The statement above can be simplified to:c1 WITH c2;The association coefficient for the last class of each categorical latentvariable is fixed at zero as the default as in loglinear modeling.PWITHA second form of the WITH option is PWITH. PWITH pairs thevariables on the left-hand side of the PWITH statement with those on theright-hand side of the PWITH statement. For PWITH, the number ofvariables on the left-hand side of the PWITH statement must equal thenumber of variables on the right-hand side of the PWITH statement. Forexample,y1 y2 y3 PWITH y4 y5 y6;impliesy1 WITH y4;y2 WITH y5;y3 WITH y6;whereas,y1 y2 y3 WITH y4 y5 y6;583
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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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Page 540 and 541: CHAPTER 16BAYESIAN ESTIMATIONBayesi
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Page 544 and 545: CHAPTER 16where .5 is the value of
Page 546 and 547: CHAPTER 16ROTATION = TARGET (ORTHOG
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Page 550 and 551: CHAPTER 16OPTIONS RELATED TO NUMERI
Page 552 and 553: CHAPTER 16For other outcome types a
Page 554 and 555: CHAPTER 16BOOTSTRAPThe BOOTSTRAP op
Page 556 and 557: CHAPTER 16values produced by the pr
Page 558 and 559: CHAPTER 16OPTSEEDThe OPTSEED option
Page 560 and 561: CHAPTER 16DIFFTEST = deriv.dat;wher
Page 562 and 563: CHAPTER 16RITERATIONSThe RITERATION
Page 564 and 565: CHAPTER 16MIXUThe MIXU option is us
Page 566 and 567: CHAPTER 16With multiple chains, par
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Page 574 and 575: CHAPTER 17DEPENDENT OR INDEPENDENT
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Page 584 and 585: CHAPTER 172001). The target factor
Page 586 and 587: CHAPTER 17specifies that regression
Page 590 and 591: CHAPTER 17impliesy1 WITH y4;y1 WITH
Page 592 and 593: CHAPTER 17refers to the means of va
Page 594 and 595: CHAPTER 17f1 ON x1 x2 x3;f2 ON x1 x
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Page 600 and 601: CHAPTER 17A list of equality constr
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Page 604 and 605: CHAPTER 17Although y5 is assigned a
Page 606 and 607: CHAPTER 17LABELING CLASSES OF A CAT
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Page 610 and 611: CHAPTER 17Linear for acount outcome
Page 612 and 613: 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
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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
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CHAPTER 18VIEWING GRAPHICAL OUTPUTS
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CHAPTER 18Following is the window t
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CHAPTER 18The plots can be exported
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CHAPTER 19CLASSES =SURVIVAL =TSCORE
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CHAPTER 19For Monte Carlo studies,
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CHAPTER 19binomial model. The lette
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CHAPTER 19where c1, c2, and c3 are
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CHAPTER 19together to generate miss
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CHAPTER 19between dependent and ind
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CHAPTER 19categories are referred t
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CHAPTER 19Following is the specific
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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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