[SEM] Structural Equation Modeling

1 STATASTRUCTURAL Equation MODELINGREFERENCE MANUALRELEASE 13 A Stata Press PublicationStataCorp LPCollege Station, Texas Copyrightc 1985 2013 StataCorp LPAll rights reservedVersion 13 Published by Stata Press, 4905 Lakeway Drive, College Station, Texas 77845 Typeset in TEXISBN-10: 1-59718-124-2 ISBN-13: 978-1-59718-124-2 This manual is protected by copyright. All rights are reserved. No part of this manual may be reproduced, storedin a retrieval system, or transcribed, in any form or by any means electronic, mechanical, photocopy, recording, orotherwise without the prior written permission of StataCorp LP unless permitted subject to the terms and conditionsof a license granted to you by StataCorp LP to use the software and documentation.

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4 Typehelp copyrightwithin suggested citation for this software isStataCorp. : Release 13. Statistical Software. College Station, TX: StataCorp ..1intro 1 .. Introduction2intro 2 .. Learning the language: Path diagrams and command language7intro 3 .. Learning the language: Factor-variable notation (gsem only)35intro 4 .. Substantive concepts42intro 5 .. Tour of models61intro 6 .. Comparing groups (sem only)82intro 7 .. Postestimation tests and predictions89intro 8 .. Robust and clustered standard errors96intro 9.

5 Standard errors, the full story98intro 10 .. Fitting models with survey data (sem only) 102intro 11 .. Fitting models with summary statistics data (sem only) 104intro 12 .. Convergence problems and how to solve them 112 Builder .. SEM Builder 122 Builder, generalized .. SEM Builder for generalized models 125estat eform .. Display exponentiated coefficients 128estat eqgof .. Equation -level goodness-of-fit statistics 130estat eqtest .. Equation -level test that all coefficients are zero 132estat framework.

6 Display estimation results in Modeling framework 134estat ggof .. Group-level goodness-of-fit statistics 136estat ginvariant .. Tests for invariance of parameters across groups 138estat gof .. Goodness-of-fit statistics 140estat mindices .. Modification indices 143estat residuals .. Display mean and covariance residuals 145estat scoretests .. Score tests 148estat stable .. Check stability of nonrecursive system 150estat stdize .. Test standardized parameters 152estat summarize .. Report summary statistics for estimation sample 154estat teffects.

7 Decomposition of effects into total, direct, and indirect 155example 1 .. Single-factor measurement model 158example 2 .. Creating a dataset from published covariances 164example 3 .. Two-factor measurement model 169example 4 .. Goodness-of-fit statistics 177example 5 .. Modification indices 180example 6 .. Linear regression 183example 7 .. Nonrecursive Structural model 187example 8 .. Testing that coefficients are equal, and constraining them 195example 9 .. Structural model with measurement component 199example 10.

8 MIMIC model 208example 11 .. estat framework 215example 12 .. Seemingly unrelated regression 218example 13 .. Equation -level Wald test 222example 14 .. Predicted values 223example 15 .. Higher-order CFA 225iii Contentsexample 16 .. Correlation 232example 17 .. Correlated uniqueness model 237example 18 .. Latent growth model 244example 19 .. Creating multiple-group summary statistics data 251example 20 .. Two-factor measurement model by group 256example 21 .. Group-level goodness of fit 265example 22.

9 Testing parameter equality across groups 266example 23 .. Specifying parameter constraints across groups 269example 24 .. Reliability 275example 25 .. Creating summary statistics data from raw data 279example 26 .. Fitting a model with data missing at random 287example 27g .. Single-factor measurement model (generalized response) 291example 28g .. One-parameter logistic IRT (Rasch) model 297example 29g .. Two-parameter logistic IRT model 306example 30g .. Two-level measurement model (multilevel, generalized response) 314example 31g.

10 Two-factor measurement model (generalized response) 323example 32g .. Full Structural Equation model (generalized response) 330example 33g .. Logistic regression 336example 34g .. Combined models (generalized responses) 341example 35g .. Ordered probit and ordered logit 347example 36g .. MIMIC model (generalized response) 354example 37g .. Multinomial logistic regression 359example 38g .. Random-intercept and random-slope models (multilevel) 368example 39g .. Three-level model (multilevel, generalized response) 384example 40g.