Latent Variable Modeling with R

341 Pages·2015·8.049 MB·English

by  W. Holmes Finch, Brian F. French

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.
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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.
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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