Longitudinal Structural Equation Modeling TODD D. LITTLE G P uilford ress e-book Longitudinal Structural Equation Modeling Methodology in the Social Sciences David A. Kenny, Founding Editor Todd D. Little, Series Editor www.guilford.com/MSS This series provides applied researchers and students with analysis and research design books that emphasize the use of methods to answer research questions. Rather than emphasizing statistical theory, each volume in the series illustrates when a technique should (and should not) be used and how the output from available software programs should (and should not) be interpreted. Common pitfalls as well as areas of further development are clearly articulated. RECENT VOLUMES THEORY CONSTRUCTION AND MODEL-BUILDING SKILLS: A PRACTICAL GUIDE FOR SOCIAL SCIENTISTS James Jaccard and Jacob Jacoby DIAGNOSTIC MEASUREMENT: THEORY, METHODS, AND APPLICATIONS Andre A. Rupp, Jonathan Templin, and Robert A. Henson ADVANCES IN CONFIGURAL FREQUENCY ANALYSIS Alexander von Eye, Patrick Mair, and Eun-Young Mun APPLIED MISSING DATA ANALYSIS Craig K. Enders PRINCIPLES AND PRACTICE OF STRUCTURAL EQUATION MODELING, THIRD EDITION Rex B. Kline APPLIED META-ANALYSIS FOR SOCIAL SCIENCE RESEARCH Noel A. Card DATA ANALYSIS WITH Mplus Christian Geiser INTENSIVE LONGITUDINAL METHODS: AN INTRODUCTION TO DIARY AND EXPERIENCE SAMPLING RESEARCH Niall Bolger and Jean-Philippe Laurenceau DOING STATISTICAL MEDIATION AND MODERATION Paul E. Jose LONGITUDINAL STRUCTURAL EQUATION MODELING Todd D. Little INTRODUCTION TO MEDIATION, MODERATION, AND CONDITIONAL PROCESS ANALYSIS: A REGRESSION-BASED APPROACH Andrew F. Hayes Longitudinal Structural Equation Modeling Todd D. Little Foreword by Noel A. Card ThE guiLFoRD PRESS new york London Text © 2013 The Guilford Press A Division of Guilford Publications, Inc. 72 Spring Street, New York, NY 10012 www.guilford.com Figures © 2013 Todd D. Little All rights reserved No part of this book may be reproduced, translated, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the publisher. Printed in the United States of America This book is printed on acid-free paper. Last digit is print number: 98765432 Library of Congress Cataloging-in-Publication Data Little, Todd D. Longitudinal structural equation modeling / Todd D. Little. pages cm. — (Methodology in the social sciences) Includes bibliographical references and index. ISBN 978-1-4625-1016-0 (hardcover : alk. paper) 1. Social sciences—Statistical methods. 2. Longitudinal method. I. Title. HA29.L83175 2013 001.4'33—dc23 2013002924 Foreword Our understanding of a phenomenon can advance only as far as our methodologi cal tools for studying it will allow. Fortunately, we are in a time when methods for understanding human behavior and development are advancing at an extraordinary pace. One side effect of this rapid advancement is that applied researchers are often limited more by their ability to understand the existing methodological tools than by an absence of such tools. Over the past two decades, few have done as much to advance developmental methodology, and scientists’ understanding of these methods, as Todd D. Little. In a number of previous books, through regular workshops on data analytic methods (see statscamp.org), and through active lines of both developmental and quantitative research, Todd has pushed the envelope of methodology. In this book, Todd offers a powerful and flexible set of tools in longitudinal structural equation modeling. The focus is on bringing together two of the most important advanced analytic tools available. Structural equation modeling is a powerful and versatile approach that offers many advantages over traditional manifest variable analysis, including closer attention to measurement, more accurate effect size estimates, and the ability to test questions that simply cannot be tested using traditional methods. This structural equation modeling approach is applied to longitudinal models, which are arguably the most important models for understanding the natural unfolding of processes over time. This book offers readers an understanding of longitudinal structural equation modeling that is simultaneously accessible, broad, and deep. The 10 chapters of the book guide readers from a basic understanding of latent variable modeling (such as that obtained by reading Brown, 2006, or Kline, 2011) through state-of-the-science longitudinal models. Whether you are a beginner or seasoned researcher, this book will expand your data analytic skill set. The first four chapters provide a foundation for subsequent longitudinal model ing. Chapter 1 offers a review of latent variable modeling, and Chapter 2 offers an vi Foreword introduction to design considerations for longitudinal studies. Chapters 3 and 4 fur ther review foundational latent variable principles. Although the material described in these chapters overlaps with that of more general structural equation modeling texts, there are many unique gems of knowledge within these chapters. For instance, Chapter 1 includes a careful consideration of parceling, Chapter 2 offers an insight ful discussion of timing of measurement in longitudinal studies, Chapter 3 attends to the oft-neglected topic of scaling latent variables, and Chapter 4 provokes deeper conceptual thinking about model fit than is typically offered. I anticipate that all readers will learn a considerable amount even in these foundational chapters. The remaining six chapters of this book describe the key analytic models for longitudinal data. Rather than just presenting one favorite model, as do many books, this book offers a balanced approach to describing different types of models, in Chapters 5 (longitudinal CFA), 6 (panel models), Chapter 7 (P-technique for time series), and 8 (growth curve models). Along the way, Todd thoroughly covers issues of multigroup analysis, moderation, mediation, and more complex models (e.g., mul titrait multimethod, bifactor). The coverage within these chapters strikes a remark able balance between big-picture ideas and details, between conceptual understand ing and data analysis examples, and between accessibility and necessary technical aspects of longitudinal modeling. Todd gives a balanced presentation of the advantages and challenges of each of these models. This will allow you to choose the model that best answers your research question, rather than adapting your research question to one model and force-fitting it into one analytic framework. A general theme throughout this book is to help you make informed choices regarding your analyses. Todd teaches you how to choose the most useful of a wide range of data analytic tools, and then to use them well. I am confident that you will find this book a pleasure to read—an extremely rare “page turner” in the quantitative field. Reading this book feels more like taking part in a friendly conversation than listening to a lecture. So, get comfortable, relax, and prepare for the most enjoyable experience that can come from reading a book on advanced data analytic methods. Be sure to have a notepad close by, because the analytic tools described in this book are sure to prompt dozens of research questions that you will soon be able to rigorously test. Noel A. Card University of A rizona Prologue A PERSONAL INTRODUCTION AND WHAT TO EXPECT How Statistics Came into My Life For years, folks have encouraged me to write a book on structural equation model ing (SEM). I’d reply that there are lots of books already out there, especially when it comes to the basics of SEM. Ah, they’d answer back, but there aren’t any that cover it quite the way you do, especially in the context of longitudinal SEM. Mind you, “covering it quite the way I do” does not mean my way is more erudite than those of others, but it is unique and, I hope, somewhat informative and entertaining. I was an English literature major as an undergraduate at the University of California, Riverside. I came to the challenge of learning statistics with trepidation. When I realized that statistics is where logic and common sense intersect, I learned what Bill Bukowski later described as the point at which the poetry of mathematics becomes the elegant prose of statistical reasoning. I discovered that statistics isn’t math but a system of principles to guide my research. Although I was an English literature major, I was also interested in psychol ogy, and in my senior year I thought I would give the intro to statistics course a try. Larry Herringer, the teaching assistant for the course, was patient and worked very hard to explain the concepts in basic terms. He spoke to me. I learned the mate rial well enough to be invited to help Larry with his dissertation research. A few months later, Larry introduced me to a young assistant professor who was interested in recruiting a graduate student to work with him. I spent a few hours talking with Keith Widaman and Larry about what a PhD program in developmental psychology under the mentorship of Keith would be like. I know that I didn’t think it all through, because I was enchanted. What was it, serendipity or a fool’s errand? The deadline to apply for the PhD training program was the next day. I applied. After a few weeks I heard from the graduate admission committee that I could