Longitudinal Data Analysis using Structural Equation Models

408 Pages·2014·4.341 MB·english

by  John J. McArdle, John R. Nesselroade

LongitudinaL
data anaLysis
using structuraL
Equation ModELs
John J. Mcardle
John r. nesselroade
A M E R I C A N P S Y C H O L O G I C A L A S S O C I AT I O N
WA S H I N G T O N, D C
Copyright © 2014 by the American Psychological Association
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Library of Congress Cataloging-in-Publication Data
McArdle, John J.
Longitudinal data analysis using structural equation models / John J. McArdle and
John R. Nesselroade.
pages cm
Includes bibliographical references and index.
ISBN-13: 978-1-4338-1715-1
ISBN-10: 1-4338-1715-2
1. Longitudinal method. 2. Psychology—Research. I. Nesselroade, John R. II. Title.
BF76.6.L65M33 2014
150.72'1—dc23
2013046896
British Library Cataloguing-in-Publication Data
A CIP record is available from the British Library.
Printed in the United States of America
First Edition
http://dx.doi.org/10.1037/14440-000
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CONTENTS
Preface .......................................................................................................... ix
Overview ....................................................................................................... 3
I. Foundations .......................................................................................... 15
Chapter 1. Background and Goals of Longitudinal Research ........... 17
Chapter 2. Basics of Structural Equation Modeling .......................... 27
Chapter 3. Some Technical Details on Structural
Equation Modeling .......................................................... 39
Chapter 4. Using the Simplified Reticular Action
Model Notation ................................................................... 59
Chapter 5. Benefits and Problems Using Structural Equation
Modeling in Longitudinal Research ................................ 67
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II. Longitudinal SEM for the Direct Identification
of Intraindividual Changes................................................................. 73
Chapter 6. Alternative Definitions of Individual Changes ............. 75
Chapter 7. Analyses Based on Latent Curve Models ........................ 93
Chapter 8. Analyses Based on Time-Series Regression Models ......... 109
Chapter 9. Analyses Based on Latent Change Score Models ......... 119
Chapter 10. Analyses Based on Advanced Latent
Change Score Models ............................................... 133
III. Longitudinal SEM for Interindividual Differences
in Intraindividual Changes ............................................................. 141
Chapter 11. Studying Interindividual Differences
in Intraindividual Changes ........................................... 143
Chapter 12. Repeated Measures Analysis of Variance
as a Structural Model ..................................................... 151
Chapter 13. Multilevel Structural Equation Modeling
Approaches to Group Differences ................................. 159
Chapter 14. Multiple Group Structural Equation Modeling
Approaches to Group Differences ................................. 167
Chapter 15. Incomplete Data With Multiple Group
Modeling of Changes .................................................... 177
IV. Longitudinal SEM for the Interrelationships in Growth ............. 185
Chapter 16. Considering Common Factors/Latent
Variables in Structural Models ...................................... 187
Chapter 17. Considering Factorial Invariance in Longitudinal
Structural Equation Modeling ....................................... 207
Chapter 18. Alternative Common Factors With Multiple
Longitudinal Observations ............................................ 221
Chapter 19. More Alternative Factorial Solutions
for Longitudinal Data .................................................... 231
Chapter 20. Extensions to Longitudinal Categorical Factors ........... 239
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V. Longitudinal SEM for Causes (Determinants)
of Intraindividual Changes............................................................... 253
Chapter 21. Analyses Based on Cross-Lagged
Regression and Changes ................................................ 255
Chapter 22. Analyses Based on Cross-Lagged Regression
in Changes of Factors .................................................... 271
Chapter 23. Current Models for Multiple
Longitudinal Outcome Scores ....................................... 281
Chapter 24. T he Bivariate Latent Change Score Model
for Multiple Occasions .................................................. 291
Chapter 25. Plotting Bivariate Latent Change Score Results ............. 301
VI. Longitudinal SEM for Interindividual Differences in Causes
(Determinants) of Intraindividual Changes .................................. 305
Chapter 26. Dynamic Processes Over Groups................................... 307
Chapter 27. Dynamic Influences Over Groups ................................. 315
Chapter 28. Applying a Bivariate Change Model
With Multiple Groups ................................................... 319
Chapter 29. Notes on the Inclusion of Randomization
in Longitudinal Studies ................................................. 323
Chapter 30. The Popular Repeated Measures Analysis of Variance ..... 329
VII. Summary and Discussion .............................................................. 331
Chapter 31. Contemporary Data Analyses Based
on Planned Incompleteness .......................................... 333
Chapter 32. Factor Invariance in Longitudinal Research ................. 345
Chapter 33. Variance Components for Longitudinal Factor Models .... 351
Chapter 34. Models for Intensively Repeated Measures ................... 355
Chapter 35. Coda: The Future Is Yours! ........................................... 367
References ................................................................................................. 373
Index ......................................................................................................... 401
About the Authors.................................................................................... 425
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PREFACE
George Orwell wrote a lot of important books. At one point, he also
considered the reasons why people write books at all. One conclusion he
reached was that this task was typically undertaken to deal with some demon
in the author’s life. If this is true, and we have no reason to doubt Orwell so
far, then we thought it might be useful to consider the demons that drive us
to take on this seemingly thankless task. The best explanation we have come
up with involves at least three motives.
We have led a workshop on longitudinal data analysis for the past
decade, and participants at this workshop have asked many questions. Our
first motive in writing this book is to answer these questions in an organized
and complete way.
Second, the important advances in longitudinal methodology are
too often overlooked in favor of simpler but inferior alternatives. That is, cer-
tainly researchers have their own ideas about the importance of longitudinal
structural equation modeling (LSEM), including concepts of multip le factorial
invariance over time (MFIT), but we think these are essential ingredients of
useful longitudinal analyses. Also, the use of what we term latent change scores,
which we emphasize here, is not the common approach currently being used
by many other researchers in the field. Thus, a second motive is to distribute
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knowledge about MFIT and the latent change score approach. Most of the
instruction in this book pertains to using computer programs effectively.
A third reason for writing this book is that we are enthusiastic about the
possibilities for good uses of the longitudinal methods described here, some
described for the first time and most never used in situations where we think
they could be most useful. In essence, we write to offer some hope to the next
generation of researchers in this area. Our general approach to scientific dis-
course is not one of castigation and critique of previous work; rather than
attack the useful attempts of others, we have decided to applaud all the prior
efforts and simply lay out our basic theory of longitudinal data analysis. We
hope our efforts will spawn improved longitudinal research.
Our weeklong workshop with the same basic title as this book has been
sponsored every year since 2000 by the Science Directorate of the American
Psychological Association (APA). This APA workshop is based on an earlier
workshop on longitudinal methods started at the Max Planck Institute (MPI)
for Human Development in Berlin in 1986 (at the invitation of the late Paul
Baltes). This book presents the basic theory of longitudinal data analysis
used in the workshop. A forthcoming companion book, titled Applications of
Longitudinal Data Analysis Using Structural Equation Models, will present the
data examples and computer programs used in the workshop.
The current LSEM workshop continues to be sponsored by APA and
is now led by Dr. Emilio Ferrer and Dr. Kevin Grimm at the University of
California at Davis each summer. And near the end of each new workshop,
one of the authors of this book still gives an invited lecture. In this way, the
features of our original LSEM workshop live on.
We have found that the concepts of “change analysis” are wide rang-
ing. We know this book-length treatment will not be definitive, and we just
hope it is viewed as another step along the way. These particular steps were
developed during a time when both authors were teaching faculty of Human
Development at The Pennsylvania State University (PSU) and subsequently
colleagues at the Department of Psychology at the University of Virginia
(UVa), the dates of this collaboration ranging from about 1985 to 2005. Dur-
ing that time, we taught 10 summers of APA-sponsored workshops at UVa
(2000–2009), and we learned some valuable lessons about longitudinal research.
For example, we learned we needed to separate the basic concepts of “growth
and change” in our own approach to data analysis (see McArdle, 2009). We also
learned about the importance of adequate measurement models (see McArdle
& Nesselroade, 2003). It also became apparent that the more the computer
programs changed, the more they stayed the same (to be discussed). Perhaps
it is obvious that our collaboration would not have been possible unless we
were encouraged to work together, so we thank both PSU and UVa for all
the time they allowed us to think about these issues.
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There are many specific people to thank for our collaboration. At the
top of this list we must mention our wives, Carol Prescott and Carolyn Nes-
selroade. These two unusual people gave us critical support that helped us
produce this book, and they continue to allow us the time to work on these
matters. Of course, we have tried to incorporate their ideas into this text
as best we can, and about all we can say now is “thanks.” We know this is
really not enough.
Next in line we thank our wonderful colleagues and graduate students
at UVa, including (in alphabetic order) Steven Boker, Sy-Minn Chow, Ryan
Estabrook, Emilio Ferrer, Kevin Grimm, Paolo Ghisletta, Fumiaki Hama-
gami, Thomas Paskus, Nilam Ram, Lijuan (Peggy) Wang, and Zhiyong
(Johnny) Zhang. Many of these students suggested changes in the materials,
and we tried to use everything they suggested. In particular, Aki helped us
edit the prose you see here and provided most of the figures. Other important
students include Ulman Lindenberger (now MPI, Berlin director) and Karl
Ulrich Mayr (now full professor, University of Oregon). We make special
mention of Drs. Ferrer and Grimm, who have contributed to this material in
more ways than one and who, as mentioned earlier, lead the LSEM workshop
(now at the University of California at Davis) each summer. There are many
others who deserve credit for their comments and questions. All these gradu-
ate students are making important contributions on their own right now, and
this is especially rewarding for us.
As stated earlier, our professional colleagues at UVa were essential to
this effort, and the short list of important supporters includes Richard Bell,
Mavis Heatherington, Richard McCarty, Dennis Profit, Jerry Clore, and
Sandra Scarr. Other colleagues who supported our efforts and made an
important difference in our thinking were many well-known scientists—Paul
Baltes (PSU, MPI), Ray Cattell (UI, UH), John Horn (DU, USC), Ron John-
son (UH), Bill Meredith (UCB), Rod McDonald (OISE, UI), and Bill
Rozeboom (UCA). There is simply no way to adequately thank this unique
group of scientists for taking the time to confide in us things they had just
discovered and what they actually thought about these things. These people
are no longer alive, but we hope their research and their thoughts live on
here. We also thank many members of the Society of Multivariate Experi-
mental Psychology for their continuing support of the development of these
ideas. Finally, we thank all the many participants of our APA-sponsored
workshops and the APA Science Directorate and APA Books staff for the
time and effort they put in toward challenging us to produce a coherent
piece about clearing up some basic concepts about longitudinal research.
In sum, this book is intended as a tribute to the many contributions and
the ideas of many, many others.
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OVERVIEW
Longitudinal data are difficult to collect, but longitudinal research is
popular. And this popularity seems to be growing. The reasons why research-
ers now appear to be enamored with this approach will be questioned,
but there is no doubt the collection of longitudinal data is on the rise. With
this comes the subsequent need for good data analysis methods to analyze
these special kinds of data. Structural equation modeling (SEM) is a valu-
able way to analyze longitudinal data because it is both flexible and useful
for answering common research questions. However, the most appropriate
SEM strategy to use will depend on the specific question you are trying to
answer.
Baltes and Nesselroade’s (1979) seminal chapter identifies five basic
questions or purposes of longitudinal SEM (LSEM):
77 direct identification of intraindividual changes,
77 direct identification of interindividual differences in intra-
individual changes,
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77 examining interrelationships in intraindividual changes,
77 analyses of causes (determinants) of intraindividual changes, and
77 analyses of causes (determinants) of interindividual differences
in intraindividual changes.
We note that “changes” were referred to as “differences” in Baltes and
Nesselroade’s (1979) original text.
In this book, we present the most useful strategies and techniques
for each of these five purposes. We do not offer all kinds of models, just the
selected set of SEM models we have actually put to use. Two important but
underused approaches are emphasized: multiple factorial invariance over
time (MFIT) and latent change scores.
We focus on the big picture approach rather than the algebraic details.
We realize that excessive amounts of linear SEM algebra can get in the way
of big picture thinking, so we have tried to minimize the required algebra and
calculus herein. Thus, we have limited the algebra and calculus to separate
exhibits. We think the defining equations can be studied in some depth
as our main message is presented. To facilitate student learning, a forthcom-
ing companion book will give several fully worked out examples, including
computer scripts.
The remainder of this overview introduces basic topics that are central
to this book. We begin by briefly explaining our approach as developmental
methodologists and how this informs the design and timing of our measures.
Next, we discuss the purpose of SEM in general and LSEM in particular.
Finally, we explain how the rest of this book is organized in relation to Baltes
and Nesselroade’s (1979) five purposes of LSEM.
OUR APPROACH AS DEVELOPMENTAL METHODOLOGISTS
Who are developmental methodologists anyway? And why should any-
one listen to them? These are two questions that have been of interest to us
for a long time, probably because we fit into this small category of scientists!
Methodologists study the many ways researchers evaluate evidence. It
is clear that some formal methods are better than others, and the key role of
the methodologist is to point this out to others. There is no real need for a
methodologist to actually find any facts (i.e., collect empirical data), and this
seems to put these people in a special category. One would think this makes
the task much easier. But it is also clear that other people seem to find it very
hard to listen to a person who does not know all the troubles and nuances of
doing “real” research. So, in this book, we will not use computer simulation
to prove our points here; we have done so elsewhere, but only to check on
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