A Researcher's Guide Using Mplus for Structural Equation Modeling Second Edition For Debra, for her unending patience as I run "just one more analysis" Using Mplus for Structural Equation Modeling A Researcher's Guide Second Edition E Kevin Kelloway Saint Mary's University Los Angeles | London | New Delhi ; Singapore | Washington DC : Copyright © 2015 by SAGE Publications, Inc FOR INFORMATION: All rights reserved No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher i SAGE Publications, Inc ! 2455 Teller Road ' "housand Oaks, California 91320 ; E-mail: order@sagepub.com • SAGE Publications Ltd Printed in the United States of America i i Oliver's Yard j 55 City Road Library of Congress Cataloging-in-Publication Data London EC1Y1SP United Kingdom Kelloway, E Kevin, author ; SAGE Publications India Pvt Ltd ; 1/11 Mohan Cooperative Industrial Area Using Mplus for structural equation modeling : a researcher's guide / E Kevin Kelloway, Saint Mary's University — Second edition , l/lathura Road, New Delhi 110 044 pages cm ihdia ; SAGE Publications Asia-Pacific Pte Ltd Revision of: Using LISREL for structural equation modeling 1998 Includes bibliographical references and indexes i Church Street 1*10-04 Samsung Hub ISBN 978-1-4522-9147-5 (pbk.: alk paper) Mplus LISREL (Computer file) Structural equation modeling—Data processing Social sciences—Statistical methods I Title QA278.3.K45 2015 519.5'3—dc23 i Acquisitions Editor: H e l e n Salmon i A s s i s t a n t Editor: Katie Guarino :Editorial A s s i s t a n t : A n n a Villarruel : B e n n i e Clark Allen Project Editor: Production Editor: : C o p y Editor: Typesetter: Proofreader: Stephanie Palermini C&M Digitals ( P ) Ltd Sally J a s k o l d Jeanne Busemeyer :Cover Candice Harman Designer: This book is printed on acid-free paper J i m Kelly ilndexer: Marketing Manager: 2014008154 N i c o l e Elliott 14 15 16 17 18 Brief Contents Acknowledgments About the Author viii ix Chapter 1: Introduction Chapter 2: Structural Equation Models: Theory and Development Chapter 3: Assessing Model Fit 21 Chapter 4: Using Mplus 37 Chapter 5: C o n f i r m a t o r y Factor Analysis 52 Chapter 6: Observed Variable Path Analysis 94 Chapter 7: Latent Variable Path Analysis 129 Chapter 8: Longitudinal Analysis 151 Chapter 9: Multilevel Modeling 185 References 225 Index 231 Detailed Contents Acknowledgments About the Author Chapter 1: Introduction viii ix Why Structural Equation Modeling? The Remainder of This Book Chapter 2: Structural Equation Models: Theory and Development The Process of Structural Equation Modeling Model Specification Identification Estimation and Fit Choice of Estimators 13 15 16 Sample Size Model Modification 16 17 Chapter 3: Assessing Model Fit 21 Absolute Fit 22 Comparative Fit 26 Parsimonious Fit 29 Nested Model Comparisons Model Respecification Toward a Strategy for Assessing Model Fit Chapter 4: Using Mplus 30 34 35 37 The Data File 37 The Command File 39 Specify the Data 39 Specify the Analysis 41 Specify the Output 42 Putting It All Together: Some Basic Analyses Regression Analysis 42 42 The Standardized Solution in Mplus 47 Logistic Regression 47 C h a p t e r 5: C o n f i r m a t o r y Factor Analysis Model Specification 52 52 From Pictures to Mplus 54 In the Background 55 Identification 56 Estimation 57 Assessment of Fit 69 Model Modification 70 Item Parceling Exploratory Structural Equation Models Sample Results Section 70 71 89 Results 90 Exploratory Analysis 90 C h a p t e r 6: Observed Variable Path Analysis Model Specification 94 94 From Pictures to Mplus 95 Alternative Models 96 Identification 97 Estimation 97 Fit and Model Modification Mediation 97 106 Using Equality Constraints 115 Multisample Analysis 120 C h a p t e r 7: Latent Variable P a t h Analysis Model Specification 129 129 Alternative Model Specifications 130 Model Testing Strategy 130 Sample Results 148 C h a p t e r 8: L o n g i t u d i n a l Analysis 151 Measurement Equivalence Across Time 151 Latent Growth Curves 170 Cross-Lagged Models 176 C h a p t e r 9: Multilevel M o d e l i n g 185 Multilevel Models in Mplus 187 Conditional Models 195 Random-Slope Models 211 Multilevel Modeling and Mediation 217 References 225 Index 231 Acknowledgments SAGE and the author gratefully acknowledge feedback from the following reviewers: • • • • • Alan C Acock, Oregon State University Kevin J Grimm, University of California, Davis George Marcoulides, University of California, Santa Barbara David McDowall, University at Albany—SUNY Rens van de Schoot, Universiteit Utrecht Data files and code used in this book are available on an accompanying website at www.sagepub com/kellowaydata viii About the Author E Kevin Kelloway is the Canada Research Chair in Occupational Health Psychology at Saint Mary's University He received his PhD in organizational psychology f r o m Q u e e n s University (Kingston, ON) and taught for eight years at the University of Guelph In 1999, he moved to Saint Mary's University, where he also holds the position of professor of psychology He was the founding director of the CN Centre for Occupational Health and Safety and the PhD program in business administration (management) He was also a founding principal of the Centre for Leadership Excellence at Saint Mary's An active researcher, he is the author or editor of 12 books and over 150 research articles and chapters He is a fellow of the Association for Psychological Science, the Canadian Psychological Association, and of Society for Industrial and Organizational Psychology Dr Kelloway will be President of the Canadian Psychological Association in 2015-2016, and is a Fellow of the International Association of Applied Psychology 226 USING MPLUS B e n t l e r , P M., FOR & Chou, Sociological Methods Blalock, H M University Bollen, K C & (1964) (1987) in non-experimental research Chapel (1991) with latent variables Conventional wisdom Psychological Bulletin, 110, New York: John Wiley on m e a s u r e m e n t : Boomsma, against A (1983) small sample University models On the size of Groningen, R Cudeck, andfuture A Scientific in T (1995) B r o w n e , M W K (pp 72-141) structures W., A & B M S (2012) (1983) Multivariate Cohen, J., & to S types M., the IL: & A G., H a w k i n s (Ed.), Topics in multi- U n i v e r s i t y Press 24, 445-455 of a s s e s s i n g m o d e l fit Testing structural equation modeling with models (pp In 136-162) Mplus: Basic concepts, applica- W (1983) 18, (2007) (2007) Multivariate I structural (2003) Applied multiple NJ: Cross-validation Lawrence regression! 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review ofhuman Resource Management Review, resource 18, m a n a g e m e n t research using 233-242 W i l l i a m s , L J., V a n d e n b e r g , R J., & E d w a r d s , J (2009) S t r u c t u r a l e q u a t i o n m o d e l i n g in management Annals, Wright, 3, S 161-215 research: A guide for improved analysis Academy ofManagement 543-605 (1934) The method of p a t h c o e f f i c i e n t s Annals of Mathematical Statistics, 5, Index Absolute fit of model, Academy of Management, 22-26 M e t h o d s Division, B r o w n e , M W., Research 17, 28 B y r n e , B M., 16 A d j u s t e d g o o d n e s s - o f - f i t ( A G F I ) test, Causal inference, Affective commitment measure, C a u s a l i t y , d i r e c t i o n of, 130 A G F I ( a d j u s t e d g o o d n e s s - o f - f i t ) test, Centering predictors, A j z e n , I., 5, 23, 30 C F I ( c o m p a r a t i v e f i t i n d e x ) , 27, Akaike i n f o r m a t i o n criterion (AIC), A l l e n , N J., 29 130 (x ) Chi-square 195-196 in absolute fit of model, 22-24 A l t e r n a t i v e fit i n d i c e s , 24 i n c o m p a r a t i v e fit o f m o d e l , ANALYSIS 41 in p a r s i m o n i o u s fit of m o d e l , command, A n d e r s o n , J C., 24, 56, 131 C h o u , C P., A n t o n a k i s , J., Approximation, 132 statistic: 27 29, Cliff, N., root mean of ( R M S E A ) , 17, square 24-25, Autoregressive models, error 132 A s s o c i a t i o n , in c a u s a l i n f e r e n c e , Close fit, t e s t of ( P C L O S E t e s t ) , 25 C l u s t e r i n g of d a t a , 185 C o f f m a n , D L., 17 C o m m a n d file, 177-178 Mplus, 39-42 C o m p a r a t i v e f i t i n d e x ( C F I ) , 27, Comparative B a l l a , J R„ 28 B a r o n , R M., 96, Baseline model, Conditional B a t c h p r o c e s s o r , M p l u s as, information 17, - , Bias-corrected confidence 107-108, 129 B o l l e n , K A., 7, criterion), 29 - , 28, 56, 97, 130 B o n e t t , D G., 28 B o o m s m a , A., of analysis, summary of data, also Multilevel 25-26, 197-198 198-199 m ode ling and Condition tests, 33 Confidence intervals, Confirmatory 17 Bootstrapping c o n f i d e n c e intervals, Brett, J M , 195-196 summary Condition 199-200 200-201 overview, See intervals, 113 (Bayesian i n f o r m a t i o n 196-197 model results, B e n d a h a n , S., B e n t l e r , P M., 106 195-201 m o d e l fit i n f o r m a t i o n , criterion 132 26-28 10-11, models, c o d e for, 16 ( B I C ) , 29 BIC fit of model, Compound paths, 106 26 Bayesian estimators, Bayesian 33 17 107, 220 f a c t o r analysis, 52-93 fit a s s e s s m e n t for, - 107 measurement by, equivalence across time 15 - 231 232 U S I N G MPLUS FOR S T R U C T U R A L E Q U A T I O N M O D E L I N G model i d e n t i f i c a t i o n in, model s p e c i f i c a t i o n in, nested model 56-57 Equality constraints, c o m p a r i s o n s in, p a t h analysis with, E n d o g e n o u s variables, 52-55 30 Estimators, choosing, s a m p l e results section for, 89-93 C o n f i r m a t o r y f a c t o r analysis, o u t p u t for, estimation modification model results, 59 67-69 results, 67 61-63 standardization, as, 63-65 modification from, exploratory item 70-89 structural output, Mplus, model Fit of m o d e l , 14 estimation in, 6-7 and, 176-184 index (CVI), overview, 28 29-35 Formative 28 69-70 indicators, Four-step process, command, 39-40 in Mplus, DEFINE command, 39, confirmatory F r a n c i s , R., 20 Full 41 strategies, in 52 inform ation (FIML) in M p l u s , 37 G e r b i n g , D W., 24, 56, s t r e n g t h of, estim ation, cross-validation of the index), 131 G F I ( g o o d n e s s - o f - f i t ) t e s t , 25, G l y m o u r , B (expected value G., 20 G o o d n e s s - o f - f i t (GFI) test, 28 25 G r a h a m , J W., E d w a r d s , J., 56 "Grounded theory" E f f e c t size, Growth 17 maximum likelihood factor 71-72 Distal relationships, ECVI 56 in mediation, 106-107 37-39 Data-mining techniques, for, 21-22 parsimonious, Five-factor model, (cross-validation index), analysis, models 103-104 R., Disaggregation 69-70 observed variable path analysis Cross-validation DATA 59, 15-17 and,204-205 13, 22, 24 Cross-lagged models, Data file, 199-200 analysis means-as-outcomes 21 Covariance matrix, CVI and, a s s e s s m e n t for, 11-13 35-36 26-2 c o n f i r m a t o r y factor C o s t - b e n e f i t t r a d e - o f f , i n fit o f Cudeck, 21-36 conditional models 22 1 implications in 22-26 comparative, just-identified model, model, estimation, 37 a s s e s s m e n t strategy for, 70-71 absolute fit of m o d e l and, overview, diagram information maximum (full absolute, m atrix: decomposing, path F i s h b e i n , M , 5, 23, 30 equation 71-89 parceling, theory model model 9-10 likelihood) C o n f i r m a t o r y factor analysis, Correlation FIML 58-59 equation 71-89 Factor analysis, 65-67 standardization, cross-validation 28 structural output, results, STDY Exploratory 59-61 of n u m e r i c a l summary, of the E x p l o r a t o r y f a c t o r analysis, indices, standardized model STD Expected value index (ECVI), m o d e l fit i n f o r m a t i o n , 16 E x o g e n o u s v a r i a b l e s , 8, 95 57-69 model 153 - See also Fit of model r i g o r of, quality E s t i m a t i o n a n d fit, 8, 95 115-120, curves, approach, latent, 19 170-176 Index Hypothesis testing approach, 19 LISREL p r o g r a m , 233 25 L o e h l i n , J C., 36 ICC (intraclass correlation L o g i s t i c r e g r e s s i o n , i n Mplus, — c o e f f i c i e n t ) , 189 Identification L o n g , J S., of models: Longitudinal c o n f i r m a t o r y f a c t o r analysis, observed variable path overview, 56-57 analysis, 97 Longitudinal IFI ( i n c r e m e n t a l fit i n d e x ) , 28 I n d e p e n d e n c e model, around, for, c o n f i d e n c e intervals across time, in models, 96-97 151-169 f a c t o r analysis model 152-1 53 e q u a l i t y c o n s t r a i n t s for, Ing, M., 20 153 analysis in, 161-169 summary analysis of, 153-161 correlation coefficient (ICC), 189 M a c C a l l u m , R I s o l a t i o n , in c a u s a l i n f e r e n c e , Item measurement model modifications 107 Indirect relationships Intraclass 170-176 analysis, confirmatory 26 176-184 curves, equivalence I n c r e m e n t a l f i t index (IFI), 151-184 models, latent g r o w t h 13-14 Indirect effect, analysis, cross-lagged parceling, C., 17 M a c D o n a l d , R P., 28 70-71 Manifest variables, Iterative e s t i m a t i o n , by Mplus, 15 M a r c o u l i d e s , G 10 A., 20 M a r s h , H W., 28 J a c q u a r t , P., Maximum J a m e s , L A., 3, 18 l i k e l i h o o d with (MLR) estimator, J a m e s , L R., 3, 18, 25, 29 Just-identified models, Means-as-outcomes 13, 96 c o d e for, 16, results, models: Kelly, K., 20 sample summary K i m , K H., s u m m a r y of data, Known distributional characteristics, alternative fit indices, in See statistics, c o n f i r m a t o r y factor curves, 170-176 Latent variable models, Latent variable path c o n f i r m a t o r y f a c t o r analysis model 129-148 and testing, Latent variable path results for, L e n n o x , R., 10 model 152-153 153 in, 148-151 s u m m a r y analysis Mediation, 40-1 47 130-132 analysis, 161-169 132-140 nonmediated 147-148 testing, complications Latent variables, time, m o d e l m o d i f i c a t i o n s a n a l y s i s for, mediated structural model for, equality constraints for, 130 m e a s u r e m e n t model testing, testing across 151-169 analysis, s p e c i f i c a t i o n in, alternative, model 2-3 Measurement equivalence Latent growth partially 202-203 203 also M u l t i l e v e l m o d e l i n g analysis of, L a l i v e , R., 203-204 analysis, Measurement, 24 204-205 205-206 K e n n y , D A., 96, 106 17 errors 194 201 - 2 m o d e l fit i n f o r m a t i o n , model K e l l o w a y , E K., 52 robust 188, sample of, 153-161 in o b s e r v e d v a r i a b l e path analysis, 06-114 c o n f i d e n c e intervals for, four-step process, Mplus MODEL INDIRECT s u b c o m m a n d for, Mplus output f o r , 107 106-107 107-108 108-114 234 U S I N G MPLUS FOR STRUCTURAL E Q U A T I O N M O D E L I N G Mediation, latent variable and, path analysis Multilevel 147-148 Mediation, multilevel complications unconflated in, modeling and model estimation, m o d e l results, overview, indicators, causes) model, M L M estimators, Multilevel 57 (maximum likelihood with 16, 188, M O D E L c o m m a n d , 41, 43, 55, INDIRECT robust for, 140, 211 model indices equation model parceling, analysis, null m o d e l estimation, Mplus for, e s t i m a t i o n in, BASIC 190-195 option in, 187-190 command, 42 17, Multiple 56 indicators, multiple (MIMIC) model, 37-51 Multisample in, 24-25 39-42 comparative m o d e l fit indices in, causes 57 analysis, in observed variable analysis, - 28 path M u t h e n , B O., 17 27-28 M u t h e n , L K., 17 37-39 l o g i s t i c r e g r e s s i o n by, 47-51 N e s s e l r o a d e , J R., 89 p a r s i m o n i o u s m o d e l f i t i n d i c e s in, r e g r e s s i o n a n a l y s i s by, 29 42-46 s t a n d a r d i z e d s o l u t i o n by, 47 Latent variable Longitudinal modeling; path analysis; analysis; Observed Nested NFI model comparisons, ( n o r m e d fit index), Nonmediated models, C o n f i r m a t o r y factor analysis; path 217-219 in, model TWOLEVEL absolute m o d e l fit indices See also and, 187-195 path Monte Carlo analysis, c o m m a n d file, mediation Multilevel modeling, across 17-20 MODINDICES 202-203 203 modeling, complications 70-71 01-103,106 d a t a file, of data, 219-224 equivalence observed variable Mplus, summary 161-169 overview, 203-204 analysis, unconflated 71-89 time, statistics, summary Multilevel 204-205 205-206 217-224 structural measurement results, sample subcommand, 67-69 output, 201-202 m o d e l fit i n f o r m a t i o n , of models: exploratory item c o d e for, means-as- models: 194 107-108,218 c o n f i r m a t o r y f a c t o r analysis 197-198 198-199 modeling, outcomes 16 errors) estimator, Modification 195-196 s u m m a r y of data, multiple 199-200 200-201 s u m m a r y analysis, (multiple MODEL 196-197 m o d e l fit i n f o r m a t i o n , 219-224 MLR conditional 195-201 c o d e for, 217-219 M e y e r , J P., 130 MIMIC modeling, models, Multilevel variable analysis 97, N o n - n o r m e d fit index, N o r m e d fit index (NFI), N2Mplus 30-34 28 47-1 49 27 28 data t r a n s l a t i o n p r o g r a m , Null model, 26-27, 190-195 M u l a i k , S A., 25 Multilevel modeling, overview, 185-224 185-186 random-slope models, simultaneous, 206-21 O b s e r v e d variable path analysis, 94-128 211-217 39 N u l l B rule, in m o d e l i d e n t i f i c a t i o n , 97 equality constraints, 115-120 m o d e l i d e n t i f i c a t i o n in, 97 Index model specification multisample Observed in, analysis, variable estimation path Qualitative data analysis, Quantitative analysis, output, fit i n f o r m a t i o n , model modifi cation approach, 103-104 99-100, standardized model 104 results, 106 100-101, variable path analysis, theory 107 106-107 O b s e r v e d variables, Management, Respecification p r o c e s s of, RMNET 42, 44 listserv, R M S E A (root mean square approximation), Parsimonious fit of model, Parsimonious goodness-of-fit (PNFI), 17, SABIC 97,147-149 c o r r e l a t i o n s r e p r o d u c e d in, (RMSEA), relationships (sample 33 size-adjusted Bayesian information criterion), Sample 30, overview, d e p i c t e d in, 8-13 Latent variable path analysis; analysis size-adjusted Bayesian information SAMPSTAT command, Saturated models, S c h i e n e s , R., 20 Simple paths, S o p e r , D., Power analysis, 17 Preacher, K.}., 17,219 19 P r e d i c t i o n , p a t h m o d e l s for, Proximal r e l a t i o n s h i p s , s t r e n g t h of, 44-45 13, 24, 16 96 10-11 17 Specification index), 29 Post h o c m o d e l m o d i f i c a t i o n , 42, S a t o r r a - B e n t l e r x c o r r e c t e d value, Ployhart, R E., ( p a r s i m o n i o u s n o r m e d fit criterion 29 PCLOSE test, 25 176 29 16-17 (SABIC), Observed variable path PNFI 132 error of 24-25,132 S a m p l e size, n e s t e d m o d e l c o m p a r i s o n s in, also error o f 17, - , n o r m e d fit index 29 analysis: See square approximation 29 Partially m e d i a t e d m o d e l s , Path Root mean 29-35 28 of A c a d e m y of Management, 14-15 34-35 17-20 R F I ( r e l a t i v e fit i n d e x ) , analysis Parsimonious 24-25 of m o d e l s : M p l u s guidelines for, See C o n f i r m a t o r y O ' K e e f e , D., 52 command, R e s i d u a l s , a n a l y s i s of, 107-108 10 Overidentified models, 42-46 Research M e t h o d s Division, A c a d e m y of 108-114 measure in Mplus, Relative fit i n d e x (RFI), 28 INDIRECT M p l u s o u t p u t for, ( G F I ) test, of (Fishbein in m o d e l identification, Regression analysis, s u b c o m m a n d for, OUTPUT action, Reflective indicators, 56 106-114 MODEL factor model 14, f o u r - s t e p process, OCEAN.20 in 97 and A j z e n ) , Recursive rule, c o n f i d e n c e intervals for, Mplus Reasoned 8-99 mediation, 211-217 R a y k o v , T., 89 101, 104-106 Observed models, R a n k - a n d - o r d e r conditions, identification, q u a l i t y of n u m e r i c a l r e s u l t s , summ ary, 19 Random-slope indices, 106 m o d e l results, 19 g r o u n d e d theory 97-106 model 101-103, 94-97 120-128 235 of models: c o n f i r m a t o r y f a c t o r a n a l y s i s for, 52-55 o b s e r v e d variable p a t h structural equation for, - analysis, 94-97 m o d e l process 236 USING MPLUS FOR S T R U C T U R A L E Q U A T I O N M O D E L I N G Specification of models, p a t h analysis f o r , alternative, latent variable T e m p o r a l order, 129-148 130 TETRAD program, measurement model partially mediated testing, and m o d e l testing, 132-140 Theory nonmediated - 48 See Theory trimming, Time testing complications 130-132 T o m a r k e n , A J., See Spirtes, P., 20 T o m e r , A., SPSS, M p l u s vs., - t rule, SRMR (standardized residual), root mean square 24 command, 42 results, 61-63, analysis, square residual in Mplus, data t r a n s l a t i o n 47 program, 38-39 STD 65-67 Mplus, U l l m a n , J B., 35 Unconstrained models, V a n d e n b e r g , R J., in Mplus, 47 Steiger, J H., 18, 25 equation 24 i d e n t i f i c a t i o n issues in, m o d i f i c a t i o n of models 176 39-40, 15-17 W a l l e r , N G., 17-20 8, 2-4 from, 7-13 "Wastebasket" parameters, 18, 10 161 W i l l i a m s , L J., 56 W L S M V estimator, 17 95 16 W e i g h t e d least s q u a r e d estimator, specification ofmodels 127 8-9 latent and o b s e r v e d or m a n i f e s t , 13-14 from, 120, Variables: in path analysis, 5-7 S u g a w a r a , H M., 13 e n d o g e n o u s and exogenous, modeling: e s t i m a t i o n and f i t f r o m , v a l u e of, r e s p e c i f i c a t i o n of m o d e l s 35 VARIABLE command, STDYX standardization, overview, errors, V a n d e n b e r g , R J., 56 in 63-65 Structural I and, RANDOM 211 in Mplus, STDY standardization, 47, option in Mplus, Underidentified models, standardization, 47, BASIC 56, 97 27 24 Standardized solution, Stat/Transfer i n d e x (TLI), TWOLEVEL Type root m e a n (SRMR), 89 187-190 104-106 Standardized analysis 16 in m o d e l i d e n t i f i c a t i o n , TWOLEVEL STANDARDIZED 34-35 18, Longitudinal Tucker-Lewis 177 Standardized model equation modeling 140-147 in, 19-20 Structural structural model testing, Stability m o d e l s , in causal inference, W r i g h t , Sewall, 7, in Mplus, 11, 106 47 16 SAGE researchmethods The essential world's online tool leading for r e s e a r c h e r s f r o m methods publisher than , 0 pages of book, journal, and r e l e r e n c e contait to support y o r learning Find out more at www.sageresearch methods.com Vr Answer substantive research questions using structural equation modeling techniques with this accessible introduction to Mplus Ideal for researchers and graduate students in the social sciences who require knowledge of structural equation modeling techniques to answer substantive research questions, Using Mplus for S t r u c t u r a l Equation M o d e l i n g provides a reader-friendly introduction to the major types of structural equation models implemented in the Mplus f r a m e w o r k This practical book, which updates author E Kevin Kelloway's 1998 book Using LISREL for Structural Equation Modeling, retains the successful five-step process employed in the earlier book, with a thorough update for use in the Mplus environment Kelloway provides an overview of structural equation modeling techniques in Mplus, including the estimation of confirmatory factor analysis and observed variable path analysis He also covers multilevel modeling for hypothesis testing in real life settings and offers an introduction to the extended capabilities of Mplus, such as exploratory structural equation modeling and estimation and testing of mediated relationships A sample application with the source code, printout, and results is presented for each type of analysis, with data files and code posted on an accompanying, open-access student website "An excellent book on the ins and outs of using Mplus, as well as the practice of structural equation modeling in applied research." — Kevin J Grimm, University of California, Davis MIX Paper responsible »w.feofg I SEN www.sagepublications.com Los Angeles • London • New Delhi • Singapore • Washington DC from sources FSC® C ... path diagrams, all the material is equally relevant to factor analysis, which can be thought of as a special form of path analysis Converting the path diagram to structural equations Path diagrams... estimators are available in Mplus and may be used for different types of models and data For example, the weighted least squares estimator is available for use with categorical data, and Bayesian... read data in a number of formats (e.g., SPSS, Stata) and Chapter 4: Using Mplus 39 prepare an Mplus data file As an added bonus, Stat/Transfer also writes the Mplus data definition statements for