title: author: publisher: isbn10 | asin: print isbn13: ebook isbn13: language: subject publication date: lcc: ddc: subject: Modeling Longitudinal and Multilevel Data : Practical Issues, Applied Approaches, and Specific Examples Little, Todd D Lawrence Erlbaum Associates, Inc 0805830545 9780805830545 9780585346687 English Social sciences Statistical methods, Longitudinal method 2000 HA29.M67 2000eb 300/.1/5195 Social sciences Statistical methods, Longitudinal method Page 3 Modeling Longitudinal and Multilevel Data Practical Issues, Applied Approaches and Specific Examples Edited by Todd D Little Yale University Kai U Schnabel Jürgen Baumert Max Planck Institute for Human Development Copyright © 2000, by Lawrence Erlbaum Associates, Inc All rights reserved No part of the book may be reproduced in any form, by photostat, microform, retrieval system, or any other means, without prior written permission of the publisher Lawrence Erlbaum Associates, Inc., Publishers 10 Industrial Avenue Mahwah, NJ 07430 Cover design by Kathryn Houghtaling Lacey Library of Congress Cataloging-in-Publication Data Modeling longitudinal and multilevel data : practical issues, applied approaches, and specific examples / edited by Todd D Little, Kai-Uwe Schnabel, Jürgen Baumert p cm ISBN 0-8058-3054-5 (cloth : alk paper) Social sciencesStatistical methods Longitudinal method I Little, Todd D II Schnabel, Kai-Uwe III Baumert QA76.76.E95S32 2000 006.3'31dc21 97-5613 CIP Books published by Lawrence Erlbaum Associates are printed on acid-free paper, and their bindings are chosen for strength and durability The final camera copy for this book was prepared by the author and therefore the publisher takes no responsibility for consistency or correctness of typographical style Printed in the United States of America 10 10 Page 5 Contents Preface Modeling Longitudinal and Multilevel Data Kai Uwe Schnabel, Todd D Little, and Jürgen Baumert Multilevel Analyses of Grouped and Longitudinal Data Joop J Hox 15 A Two-Stage Approach to Multilevel Structural Equation Models: Application to Longitudinal Data Chih-Ping Chou, Peter M Bentler, and Mary Ann Pentz 33 Modeling Multivariate Change Robert C MacCallum and Cheongtag Kim 51 An Introduction to Latent Growth Models for Developmental Data Analysis John J McArdle and Richard Q Bell 69 Modeling True Intraindividual Change in Structural Equation Models: The Case of Poverty and Children's Psychosocial Adjustment Rolf Steyer, Ivailo Partchev, and Michael J Shanahan 109 127 Modeling Simultaneously Individual and Group Patterns of Ability Growth or Decline Tenko Raykov 147 Latent Transition Analysis As a Way of Testing Models of Stage-Sequential Change in Longitudinal Data Linda M Collins, Stephanie L Hyatt, and John W Graham Page 6 Testing Cross-Group and Cross-Time Constraints on Parameters Using the General Linear Model Keith F Widaman 163 10 187 Selectivity and Generalizability in Longitudinal Research: On the Effects of Continuers and Dropouts Todd D Little, Ulman Lindenberger, and Heiner Maier 11 Multiple Imputation in Multivariate Research John W Graham and Scott M Hofer 201 12 219 Longitudinal and Multigroup Modeling with Missing Data Werner Wothke 13 241 Customizing Longitudinal and Multiple-Group Structural Modeling Procedures James L Arbuckle 14 Individual Fit, Heterogeneity, and Missing Data in Multigroup Structural Equation Modeling Michael C Neale 249 References 269 Author Index 283 Subject Index 289 About the Authors 293 Page 7 Preface As with any undertaking of this magnitude, the list of persons to whom we are endebted is long and the degree of endebtedness is deep At the beginning and throughout, the generous financial support by the Max Planck Institute for Human Development in Berlin made this project possible The Institute funded the 1998 Berlin Summer School Conference on Multilevel and Longitudinal Modeling, supported the assembly of this volume, and helps to maintain the web page (http://www.mpib-berlin.mpg.de/research_resources/index.html) On the basis of the comments and enthusiasm of the participants as well as the presenters, we felt that a comprehensive volume on these issues was needed We are particularly grateful to Dagmar Stenzel for editing and type-setting the contributions We also appreciate the support and advice of Larry Erlbaum and his crack team at LEA throughout this process Finally, the diligence and timeliness of all contributors can not be thanked enough The efforts, patience, and expertise of all involved has brought a volume that we hope will become a standard reference for social sciences researchers TODD D LITTLE NEW HAVEN, CT, USA KAI U SCHNABEL BERLIN, GERMANY JÜRGEN BAUMERT BERLIN, GERMANY We would like to dedicate this volume to the memory of our friend and colleague Magret Baltes Page 290 E EM algorithm 152, 153, 205210, 220 EQS 27, 42, 43, 44, 46, 48, 244, 250 Error variance 46, 116, 117, 210, 211 Experimental design 11, 163 F F test 169, 170, 173, 175, 178 Factor analysis 15, 65, 88, 107, 128, 131, 132, 147, 148, 155, 174, 220, 245 Factor loading 40, 43, 110, 125, 131, 144, 148, 152, 155 Factorial invariance 75, 90, 95, 174 Fortran 244 G Gender differences 263 General linear model 163 Generalized-least-squares 35 Genetic marker 265 Gompertz model 59 Growth curve 20, 27, 38, 43, 225 H Hierarchical linear model (HML) 12, 13, 15, 33, 36, 4246, 48, 53, 102 Homoscedasticity 34, 38, 194 I Imputation 13, 102, 153, 195, 201, 202, 204209, 211213, 216218, 220, 240, 255 Independence 34, 91, 255, 256 Individual fit 249, 253, 256, 260, 263 Intelligence 15, 25, 128, 139, 146, 178, 190, 196, 199 Interaction 17, 21, 92, 177, 178, 181, 260, 261 Intercept 16, 21, 27, 179181, 183, 197 Interface 226, 242246, 258, 261, 267 Intraclass correlation 19, 21, 25 Invariance of the loadings 197 L Latent class 147149, 151154, 158 Latent growth model 12, 27, 3033, 3739, 42, 45, 48, 65, 70, 72, 74, 81, 82, 8487, 90, 95, 97, 100, 101, 110, 118, 125 Latent status 151, 152, 154156, 158160 Latent transition analysis 13, 149, 206 Latent curve analyses 32 Latent curve approach 31 Likelihood ratio 54, 58, 83, 84, 107, 233, 235, 236, 266 Linear function 53, 55, 59, 60, 232 Linearity 34, 169 LISCOMP 27 LISREL 27, 65, 67, 70, 82, 103, 106, 131, 134, 211, 212, 215, 216, 242, 244, 250 Listwise deletion 203, 204, 220, 222, 240 Loading invariance 90 Longitudinal design 128, 188, 225, 232 M MACS 193, 197 Mahalanobis distance 253, 254, 256, 258, 263 MANOVA 20, 2932, 127, 193, 225 MAR (missing at random) 30, 31, 95, 224, 256 Markov model 153, 232236 Mathcad 244 Maximum likelihood 17, 18, 24, 54, 83, 119, 198, 202, 205, 219, 221, 224, 233, 237, 240, 248250, 252, 255, 256, 258, 260, 262, 264 MCAR (missing completely at random) 30, 31, 202, 255 Measurement invariance 90 Measurement model 110, 120, 147, 238 Meta-analysis 165, 167 Metric invariance 92, 175, 176 MIMIC model 259 Missing data 12, 13, 20, 29, 60, 93, 95, 119, 140, 153, 175, 176, 191, 201209, 211, 217, 219221, 223226, 228, 233, 236240, 246, 255, 256, 258 Mixed model 53 MixReg 20 Mixture distribution 249, 258, 262265, 267 ML3/MLn 33, 62, 67, 102 Monte-Carlo simulation 220, 225227, 229 Multivariate analysis (MANOVA/multilevel) 16, 20, 22, 56, 57, 59, 61 Multivariate normality 17, 35, 107, 219 MUML estimator 24, 49 Mx 30 Page 291 N Neighbor model 113, 124, 125, 126 Nested models 54, 131, 141, 142, 164, 171, 173, 175, 176, 197, 247 Nil hypothesis 164166, 168, 170, 171 NORM 201, 206210, 212, 213, 215 Normality 34, 54, 140, 217, 232, 233, 249, 260 O OLS 63, 167, 169 Optimal curve 84 Ordinary least squares 35, 36, 44, 62, 167, 169 P Pairwise deletion 203205, 219, 220, 222, 240 Parameter invariance 174 Path diagram 39, 65, 71, 73, 81, 88, 90, 95, 105, 106, 113, 232, 233, 239, 261 Path model 27, 32, 43, 81 Pedigree analysis 95 Polynomial functions 10, 22, 54, 55, 97, 135 PRELIS 242 Prevalence rate 38, 156, 189 R Random coefficient model 15, 27, 53 Regression slope 21, 115, 116, 167, 172 Regression weight 3741, 163, 166171, 173182, 184, 233, 236, 238 Reliability 86, 109, 121, 122, 247, 248 Representativeness 187, 188, 191 RMSEA 83, 84, 89, 107, 121, 141, 142, 197 Robustness 11, 191 S Saturated model 121, 171, 232, 234236, 240, 256 Saturation coefficient 81 Scalar invariance 174176, 178 School level 17, 33, 35, 37, 38, 41, 42, 47 School level covariate 42 Selectivity 10, 187200 Sex differences 262 Simulation 203, 208, 220, 225, 226, 228230, 241, 243, 256, 261, 264 Slope of the regression 16 Slopes-as-outcomes 35 SPLIT2 25 SSCP 78 Starting values 209, 259, 263, 264 Static latent variable 151 STREAMS 25, 242, 244 Structural invariance 90 Sums of squares and cross products 78, 169, 206 Superpopulation 192, 193 T Test-wiseness 82 Time-invariant covariate 19 Time-varying covariate 19 U Unbalanced panel design 219 V Validity 187190, 197, 219 VARCL 33, 102 Variance-component model 15 Vector field plot 104 W Wald test 17 Weight variable 130, 131, 133, 137139 WinLTA 152, 160 Page 293 About the Authors James L Arbuckle is Associate Professor in the Psychology Department at Temple University His research interests include the use of structural equation modeling with incomplete, ordinal, and censored data He is a member of the editorial board of the journal, Structural Equation Modeling, and the author of the structural modeling program, Amos Jürgen Baumert is a codirector at the Max Planck Institute for Human Development and director of the Center for Educational Research Noted research projects that he has guided include the Study Educational Processes and Psycho-Social Development in Childhood and Adolescence; the Third International Mathematics and Science Study, Populations 2 and 3; and the Program for International Student Assessment (a project of the Organization for Economic Cooperation and Development) He is a member of the Governing Board of the German Research Foundation Richard Q Bell is Professor Emeritus in the Department of Psychology at the University of Virginia where he has worked since 1974 Bell's substantive research includes a book and a very frequently cited article on the "effects of children on adults and parents," which produced a fundamental change in the direction of research on socialization Bell's methodological work includes seminal articles advocating the statistical reconstruction of longlasting developmental phenomena from shorter observational segments, termed the convergence approach This work inspired several topics in the present volume Peter M Bentler is Professor of Psychology at the University of California, Los Angeles He is past president of the Psychometric Society, the Society of Multivariate Experimental Psychology, and American Psychological Association's Division 5, and has received several awards for distinguished contributions on psychometrics, multivariate statistics, drug and alcohol abuse, and structural equation models Bentler is also chief executive officer of Multivariate Software, Inc., distributors of the EQS Structural Equations Program (http://www.mvsoft.com) Page 294 Chih-Ping Chou is an Assistant Professor of Research in the Department of Preventive Medicine, University of Southern California His research interests include the methodological and statistical issues in substance use prevention and treatment research In 1995, he received the Research Scientist Development Award from the National Institute on Drug Abuse to investigate the applications of advanced statistical techniques for prevention research Linda M Collins is Professor of Human Development and director of The Methodology Center, College of Health and Human Development, Pennsylvania State University She is also director of the Center for the Study of Prevention through Innovative Methodology She is a past president of the Society of Multivariate Experimental Psychology and has won the Cattell Award for outstanding contributions to multivariate psychology Her research interests include prevention research, methodology for longitudinal research, measurement, and categorical latent variable models John W Graham is Professor of Biobehavioral Health in the College of Health and Human Development at Penn State University He is also associate director of the Center for the Study of Prevention through Innovative Methodology, funded by the United States National Institute on Drug Abuse He is a member of the Society of Multivariate Experimental Psychology and the Society for Prevention Research His research interests include social influence and healthrelated behavior in adolescents and adults and development and application of research methodology, including missing data analysis, structural equation modeling, and detection/correction of self-report biases Scott M Hofer is a research associate at the Center for Developmental and Health Genetics at Pennsylvania State University His research interests include individual differences in life-span development and aging, personality and cognitive abilities, and multivariate methodology Joop J Hox is Professor of Social Sciences at Utrecht University and Professor of Methodology at the University of Amsterdam He has taught extensively on topics in methodology and statistics, both domestically and internationally A former Fulbright scholar, he is chair of the Netherlands Organization for Social-Methodological Research and coeditor of the Dutch Journal of Educational Studies His research interests concern survey methodology, data quality, and complex data analysis with multilevel and structural equation techniques Stephanie L Hyatt is a doctoral student in Human Development and Family Studies at Pennsylvania State University Her Master's thesis examined the relationship between the onset of adolescent substance use and parental permissiveness toward alcohol use, and also introduced data augmentation as a method for getting standard errors of parameter estimates in latent transition analysis Her main research interest is in longitudinal methods, including latent transition analysis and growth curve modeling Hyatt's substantive interests include the onset of substance use and deviant be Page 295 haviors in adolescence, change in academic motivation during adolescence, and the transition to adulthood Cheongtag Kim is an Assistant Professor of Psychology at Seoul National University, Korea His main research interest is methodology in psychology, including the areas of covariance-structure modeling and multilevel modeling In particular, his work has investigated methods of incorporating individual differences into models of cognitive processes Ulman Lindenberger is a research scientist at the Max Planck Institute for Human Development in Berlin, Germany His main research interest is in life-span cognitive development, with a special emphasis on the structure, measurement, composition, and development of intellectual abilities across the life span, the relationship between sensory and cognitive development, and issues of cognitive control He also has an interest in development methodology Todd D Little is an Assistant Professor of Psychology at Yale University Prior to joining the Faculty of Psychology at Yale, he was a research scientist for 7 years in the Center for Psychology and Human Development at the Max Planck Institute for Human Development in Berlin, Germany In the Center, he was coprincipal investigator (with Paul Baltes and Gabriele Oettingen) on the Action Control and Child Development project and the Self-Regulation and Social Relations project (with Lothar Krappmann) In addition to his substantive work, he has conducted international workshops on structural equation modeling Robert C MacCallum is a Professor of Psychology at Ohio State University, with joint appointments in the School of Public Health and the Institute for Behavior Medicine Research He is Associate Editor of Multivariate Behavioral Research and Secretary-Treasurer of the Society of Multivariate Experimental Psychology His research interests involve methods for studying the structure in correlational data and for modeling change over time, and the application of those methods in the study of effects of stress on physical and psychological well-being Heiner Maier is a research scientist at the Max Planck Institute for Demographic Research in Rostock, Germany His research interests include social and psychological determinants of mortality and survival in old age, as well as research methods of life-span developmental psychology John J McArdle is Professor of Quantitative Methods in the Department of Psychology at the University of Virginia Most of his methodological research has dealt with the use of linear structural equation models for the analysis of growth and change, especially the use of dynamics and latent growth models His substantive work has included long-term longitudinal studies of cognitive health across the life span, and longitudinal studies of student achievements in the college years He has won the R B Cattell award for distinguished multivariate research (1987), served as president Page 296 of the Society of Multivariate Experimental Psychology (19921993), and is the president of the Federation of Behavioral, Psychological, and Cognitive Sciences (19971999) Michael C Neale is an Associate Professor at Virginia Commonwealth University and the Virginia Institute of Psychiatric and Behavioral Genetics He received his PhD in Psychology from the Institute of Psychiatry, London In 1986, he joined the Department of Human Genetics at Virginia Commonwealth University; in 1992, he moved to the Department of Psychiatry He is known as the developer of the structural equation modeling program, Mx (http://griffin.vcu.edu/mx) He has contributed extensively to methodology for the analysis of genetically informative data, and has authored numerous articles, chapters, and books Ivailo Partchev is an Associate Professor of Sociology and Statistics at the University of Sofia, where he teaches courses on modeling and statistics His research interests focus on statistical modeling and analysis, especially multivariate and multilevel techniques, sampling and variance estimation, psychometrics, public opinion research, and electoral research In addition, he has participated in numerous national and international research projects as a consultant and research fellow Mary Ann Pentz is Director of the Center for Prevention Policy Research and faculty in the Department of Preventive Medicine at the University of Southern California Her research has focused on community and policy approaches to tobacco, alcohol, and drug abuse prevention in youths She has published widely in psychology, public health, and medical journals on the use of multicomponent approaches to community-based prevention that include mass media She serves on the ONDCP's Campaign Design Expert panel to design the new antidrug abuse media campaign Tenko Raykov is a Professor of Psychology at Fordham University Previously, he taught at the universities of Melbourne and Sydney His research interests are statistical modeling of behavioral phenomena, particularly structural equation modeling; longitudinal data analysis and multivariate statistics; and developmental psychology and cognitive aging Kai Uwe Schnabel is a research scientist in the Center for Educational Research at the Max Planck Institute for Human Development in Berlin, Germany In 1998, he spent a year as Visiting Professor at the University of Michigan Together with Jürgen Baumert and Olaf Köller, he is co-investigator on a large-scale longitudinal research project on German adolescents' development Besides his work on motivational development in early adolescence and the transition from school to vocational training, he studies multilevel modeling and its use for latent growth curve analysis Michael J Shanahan is an Assistant Professor of Human Development and Family Studies, Adjunct Professor of Sociology, and Research Affiliate of the Population Research Institute and Methodology Center at Pennsylvania State University He has also served as Visiting Professor of Developmental Psychology at the Friedrich ... Preface Modeling Longitudinal and Multilevel Data Kai Uwe Schnabel, Todd D Little, and Jürgen Baumert Multilevel Analyses of Grouped and Longitudinal Data Joop J Hox 15 A Two-Stage Approach to Multilevel Structural Equation... Multiple Imputation in Multivariate Research John W Graham and Scott M Hofer 201 12 219 Longitudinal and Multigroup Modeling with Missing Data Werner Wothke 13 241 Customizing Longitudinal and Multiple-Group Structural Modeling Procedures... Houghtaling Lacey Library of Congress Cataloging-in-Publication Data Modeling longitudinal and multilevel data : practical issues, applied approaches, and specific examples / edited by Todd D Little, Kai-Uwe Schnabel, Jürgen