Longitudinal structural equation modeling

410 Pages·2013·13.192 MB·English

by  Little, Todd D

ebook
THE GUILFORD PRESS
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
André 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 A nALySiS: 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: 9 8 7 6 5 4 3 2
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
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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 Arizona
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
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viii Prologue
not be accepted to the graduate training program because I had not taken the Gradu-
ate Record Examinations (GREs), which were not necessary for the master’s pro-
gram in English for which I had been accepted at a nearby state college. The admis-
sion committee at UC Riverside gave me a conditional acceptance if I would take the
GREs and post a combined score that was above their minimum threshold. A session
of the exam was scheduled for 3 weeks after I heard this news. I thought OK, what
the heck. I felt comfortable with the verbal portion of the GREs. I was petrified of
the quantitative portion. I had avoided math courses through my entire undergradu-
ate training (in fact, because of various transfers I made, I somehow got more credit
than I should have for the one intro to algebra course that I did take). My roommate
at the time (now an accomplished neurologist, Bret D. Lindsay, MD) volunteered
considerable amounts of his time to tutor me in math in order to somehow help me
make up for a lifetime of math avoidance.
I took the GREs and waited for the snail mail report on whether I had achieved
the requisite combined score and would be in the PhD program at UC Riverside or
would attend nearby California State University to get a master’s degree in English.
On May 31st I had to notify Cal State of my decision. I had not received my GRE
scores. Again, I acted irrationally. I declined the Cal State offer and waited further.
On June 1st the mail arrived with official word: I was above threshold and, much to
my surprise, my quantitative score was actually better than my verbal score. I imme-
diately went to Larry’s office. We celebrated by splitting a bottle of beer that Larry
had stowed away for a special event. I then informed Keith.
Keith was patient with me for the duration of my graduate training. As I was
Keith’s graduate student, many of the other students presumed that I knew what I
was doing, and I became an unofficial stats consultant. Putting myself in such a posi-
tion forced me to understand statistics more deeply and to find ways to communicate
it better. In 1991, when I was packing my things to take my first academic position
as a research scientist at the Max Planck Institute in Berlin, Germany, I found the
empty bottle of beer that Larry and I had shared. On it are Larry’s initials and the
date of June 1st. The beer was a bottle of Berliner Pils—serendipity again? My 7
years at the Max Planck Institute were incomparable learning years (Herzlichen
Dank an meine Kolleginnen und Kollegen). The empty bottle sits on a shelf in my
office as a reminder of the journey.
My Approach to the Book
If you don’t like math or were never much for equations, don’t panic (and don’t
forget your towel). Throughout this book I do cover the math, but I don’t rely on
it. Plus, I make sure to walk through the equations so you can get a clear sense
of what the elements of the equations mean (hopefully you’ll soon get comfort-
able with them along the way). I have never enjoyed math for math’s sake. As
mentioned, things changed when I took my first statistics course and realized that