Latent VariabLe ModeLing with r This book demonstrates how to conduct latent variable modeling (LVM) in R by highlighting the features of each model, their specialized uses, examples, sample code and output, and an interpretation of the results. Each chapter features a detailed example including the analysis of the data using R, the relevant theory, the assumptions underlying the model, and other statis- tical details to help readers better understand the models and interpret the results. Every R com- mand necessary for conducting the analyses is described along with the resulting output which provides readers with a template to follow when they apply the methods to their own data. The basic information pertinent to each model, the newest developments in these areas, and the rele- vant R code to use them are reviewed. Each chapter also features an introduction, summary, and suggested readings. A glossary of the text’s boldfaced key terms and key R commands serve as helpful resources. The book is accompanied by a website with exercises, an answer key, and the in-text example data sets. Latent Variable Modeling with R: • Provides some examples that use messy data providing a more realistic situation readers will encounter with their own data. • Reviews a wide range of LVMs including factor analysis, structural equation modeling, item response theory, and mixture models and advanced topics such as fitting nonlinear structural equation models, nonparametric item response theory models, and mixture regression models. • Demonstrates how data simulation can help researchers better understand statistical meth- ods and assist in selecting the necessary sample size prior to collecting data. • www.routledge.com/9780415832458 provides exercises that apply the models along with annotated R output answer keys and the data that corresponds to the in-text examples so readers can replicate the results and check their work. Intended for use in graduate or advanced undergraduate courses in latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multi- variate statistics taught in psychology, education, human development, and social and health sciences, researchers in these fields also appreciate this book’s practical approach. The book pro- vides sufficient conceptual background information to serve as a standalone text. Familiarity with basic statistical concepts is assumed but basic knowledge of R is not. Brian F. French is a Professor of Measurement, Statistics, and Research Methods at Washington State University. W. Holmes Finch is the George and Frances Ball Distinguished Professor of Educational Psychology and Professor of Statistics and Psychometrics at Ball State University. This page intentionally left blank Latent VariabLe ModeLing with r W. Holmes Finch, Jr. Brian F. French First published 2015 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 27 Church Road, Hove, East Sussex BN3 2FA Routledge is an imprint of the Taylor & Francis Group, an informa business © 2015 Taylor & Francis The right of W. Holmes Finch, Jr. and Brian F. French to be identified as the authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Finch, W. Holmes (William Holmes) Latent variable modeling with R / authored by W. Holmes Finch, Jr. and Brian F. French. pages cm Includes bibliographical references and index. 1. Latent variables. 2. Latent structure analysis. 3. R (Computer program language) I. French, Brian F. II. Title. QA278.6.F56 2015 519.5′35–dc23 2014049475 ISBN: 978-0-415-83244-1 (hbk) ISBN: 978-0-415-83245-8 (pbk) ISBN: 978-1-315-86979-7 (ebk) Typeset in Times New Roman by Out of House Publishing HF: To Maria, my referent indicator. BF: To Sarah, Elise, and Evan, the three paths that fit my life model well. This page intentionally left blank Contents Preface xi Acknowledgments xv About the authors xvii Chapter 1: Introduction to basic data handling in R 1 Introduction 1 The R console and R scripts 1 R libraries 2 Reading data into R 3 Missing data 5 Types of data 6 R Commander and RStudio 7 Summary 8 Further reading 8 References 8 Chapter 2: Exploratory factor analysis 9 Introduction 9 Exploratory factor analysis 10 Factor extraction 13 Factor rotation 13 Statistical methods for determining the optimal number of factors 14 Fitting EFA models using factanal 17 Fitting EFA models using fa 27 Principal components analysis 33 Summary 34 Further reading 35 References 35 viii Contents Chapter 3: Confirmatory factor analysis 37 Introduction 37 Model parameter estimation 39 Assessing model fit 40 Fitting CFA models in R using lavaan 45 Summary 56 Further reading 56 References 56 Chapter 4: Foundations of structural equation modeling 59 Introduction 59 The importance of substantive theory in SEM 60 Fitting the measurement model in R 62 Fitting the structural model in R 65 Fitting alternative SEMs 71 Summary 81 Further reading 82 References 82 Chapter 5: SEM for multiple groups, the MIMIC model, and latent means comparisons 83 Introduction 83 Multiple groups SEM 83 Steps in assessing model invariance 85 Multiple groups CFA with lavaan 87 Comparison of latent means 95 Multiple indicators multiple causes (MIMIC) model 101 Summary 109 Further reading 110 References 110 Chapter 6: Further topics in SEM 112 Introduction 112 Nonrecursive SEM 112 Interactions in latent variable models 117 Structural equation model trees 124 Summary 131 Further reading 132 References 132 Chapter 7: Growth curve modeling 134 Introduction 134 Growth curve models 135 Contents ix Fitting linear growth curve models in R 136 Fitting nonlinear growth curve models in R 141 Including covariates in growth curve models 143 Assessing change over time in multiple variables simultaneously 145 Summary 150 Further reading 150 References 150 Chapter 8: Mixture models 151 Introduction 151 Latent class models 151 Fitting a basic LCA in R 154 Fitting an LCA model with covariates in R 164 Fitting mixture regression models in R 169 Summary 175 Further reading 176 References 176 Chapter 9: Item response theory for dichotomous and polytomous items 177 Introduction 177 Classical test theory in R 178 Dichotomous IRT 180 Polytomous item response theory models 217 Summary 231 Further reading 231 References 231 Chapter 10: Further topics in item response theory 233 Introduction 233 Assessing unidimensionality 233 Assessing local independence 238 Fitting multidimensional models in R 241 Bifactor model 245 Differential item functioning 247 Mokken scaling and nonparametric IRT modeling 265 Kernel smoothing IRT 272 Summary 275 Further reading 276 References 276 Chapter 11: Data simulation for latent variable modeling in R 279 Introduction 279 Simulations for SEM 280