Mplus Users Guide v6.. - Muthén & Muthén

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CHAPTER 7EXAMPLE 7.27: FACTOR MIXTURE (IRT) ANALYSIS WITHBINARY LATENT CLASS AND FACTOR INDICATORSTITLE: this is an example of a factor mixture(IRT) analysis with binary latent classand factor indicatorsDATA: FILE = ex7.27.dat;VARIABLE: NAMES = u1-u8;CATEGORICAL = u1-u8;CLASSES = c (2);ANALYSIS: TYPE = MIXTURE;ALGORITHM = INTEGRATION;STARTS = 50 5;MODEL: %OVERALL%f BY u1-u8;[f@0];%c#1%f BY u1@1 u2-u8;f;[u1$1-u8$1];%c#2%f BY u1@1 u2-u8;f;[u1$1-u8$1];OUTPUT: TECH1 TECH8;u1 u2 u3 u4 u5 u6 u7 u8cf186
Examples: Mixture Modeling With Cross-Sectional DataIn this example, the model shown in the picture above is estimated. Themodel is a generalization of the latent class model where the latent classmodel assumption of conditional independence between the latent classindicators within class is relaxed using a factor that influences the itemswithin each class (Muthén, 2006; Muthén & Asparouhov, 2006; Muthén,Asparouhov, & Rebollo, 2006). The factor represents individualvariation in response probabilities within class. Alternatively, thismodel may be seen as an Item Response Theory (IRT) mixture model.The broken arrows from the categorical latent variable c to the arrowsfrom the factor f to the latent class indicators u1 to u8 indicate that thefactor loadings vary across classes.By specifying ALGORITHM=INTEGRATION, a maximum likelihoodestimator with robust standard errors using a numerical integrationalgorithm will be used. Note that numerical integration becomesincreasingly more computationally demanding as the number of factorsand the sample size increase. In this example, one dimension ofintegration is used with 15 integration points. The ESTIMATOR optioncan be used to select a different estimator. The STARTS option is usedto specify the number of initial stage random sets of starting values togenerate and the number of final stage optimizations to use. The defaultis 10 random sets of starting values for the initial stage and twooptimizations for the final stage. In the example above, the STARTSoption specifies that 50 random sets of starting values for the initialstage and 5 final stage optimizations will be used.In the overall model, the BY statement specifies that the factor f ismeasured by u1, u2, u3, u4, u5, u6, u7, and u8. The mean of the factor isfixed at zero which implies that the mean is zero in both classes. Thefactor variance is held equal across classes as the default. Thestatements in the class-specific parts of the model relax the equalityconstraints across classes for the factor loadings, factor variance, and thethresholds of the indicators. An explanation of the other commands canbe found in Examples 7.1 and 7.3.187
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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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Page 148 and 149: CHAPTER 7zero-inflated Poisson regr
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Page 152 and 153: CHAPTER 7EXAMPLE 7.1: MIXTURE REGRE
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Page 156 and 157: CHAPTER 7EXAMPLE 7.2: MIXTURE REGRE
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Page 160 and 161: CHAPTER 7In the MODEL command, user
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Page 164 and 165: CHAPTER 7EXAMPLE 7.9: LCA WITH CONT
Page 166 and 167: CHAPTER 7indicators, the default co
Page 168 and 169: CHAPTER 7EXAMPLE 7.12: LCA WITH BIN
Page 170 and 171: CHAPTER 7The first hypothesis is sp
Page 172 and 173: CHAPTER 7The CLASSES option is used
Page 174 and 175: CHAPTER 7between the first two vari
Page 176 and 177: CHAPTER 7EXAMPLE 7.17: CFA MIXTURE
Page 178 and 179: CHAPTER 7u11 u12 u13u21 u22 u23c1c2
Page 180 and 181: CHAPTER 7In this example, the model
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Page 190 and 191: CHAPTER 7In this example, the zero-
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Page 204 and 205: CHAPTER 8All longitudinal mixture m
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Page 216 and 217: CHAPTER 8by adding to the name of t
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Page 228 and 229: CHAPTER 8MODEL c1:MODEL c2:MODEL c3
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Page 232 and 233: CHAPTER 8MODEL c.c1:%c#1.c1#1%[u11$
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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 10u11 u12 u13 u14u21 u22 u2
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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
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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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