Applied Longitudinal Data Analysis - Modeling Change and Event Occurrence

867 Pages·2003·11.991 MB·English

by  Judith D. Singer and John B. Willett

Title Pages
University Press Scholarship Online
Oxford Scholarship Online
Applied Longitudinal Data Analysis: Modeling
Change and Event Occurrence
Judith D. Singer and John B. Willett
Print publication date: 2003
Print ISBN-13: 9780195152968
Published to Oxford Scholarship Online: September 2009
DOI: 10.1093/acprof:oso/9780195152968.001.0001
Title Pages
(p.i) APPLIED LONGITUDINAL DATA ANALYSIS (p.ii)
(p.iii) Applied Longitudinal Data Analysis
2003
(p.iv)
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Title Pages
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Library of Congress Cataloging-in-Publication
Data
Singer, Judith D.
Applied longitudinal data analysis : modeling
change and event
occurrence/by Judith D. Singer and John B.
Willett.
p. cm.
Includes bibliographical references and index.
ISBN 0-19-515296-4
1. Longitudinal methods. 2. Social sciences—
Research.
I. Willett, John B. II. Title.
H62 .S47755 2002
001.4’2—dc21
2002007055
9 8 7 6 5 4 3 2 1
Printed in the United States of America
on acid-free paper
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Preamble
(p.v)
University Press Scholarship Online
Oxford Scholarship Online
Applied Longitudinal Data Analysis: Modeling
Change and Event Occurrence
Judith D. Singer and John B. Willett
Print publication date: 2003
Print ISBN-13: 9780195152968
Published to Oxford Scholarship Online: September 2009
DOI: 10.1093/acprof:oso/9780195152968.001.0001
Preamble
(p.v)
Time, occasion, chance and change.
To these all things are subject.
—Percy Bysshe Shelley
Questions about change and event occurrence lie at the heart of
much empirical research. In some studies, we ask how people
mature and develop; in others, we ask whether and when events
occur. In their two-week study of the effects of cocaine exposure on
neurodevelopment, Espy, Francis, and Riese (2000) gathered daily
data from 40 premature infants: 20 had been exposed to cocaine,
20 had not. Not only did the cocaine-exposed infants have slower
rates of growth, but the effect of exposure was greater the later the
infant was delivered. In his 23-year study of the effects of wives’
employment on marital dissolution, South (2001) tracked 3523
couples to examine whether and, if so, when they divorced. Not
only did the effect of wives’ employment become larger over time
(the risk differential was greater in the 1990s than in the 1970s), it
increased the longer a couple stayed married.
In this book, we use concrete examples and careful
explanation to demonstrate how research questions about
change and event occurrence can be addressed with
longitudinal data. In doing so, we reveal research
opportunities unavailable in the world of cross-sectional data.
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Preamble
(p.v)
In fact, the work of Espy and colleagues was prompted, at
least in part, by the desire to improve upon an earlier cross-
sectional study. Brown, Bakeman, Coles, Sexson, and Demi
(1998) found that gestational age moderated the effects of
cocaine exposure. But with only one wave of data, they could
do little more than establish that babies born later had poorer
functioning. They could not describe infants’ rates of
development, nor establish whether change trajectories were
linear or nonlinear, nor determine whether gestational age
affected infants’ functioning at birth. With 14 waves of data,
on the other hand, Espy and colleagues could do this and
(p.vi) more. Even though their study was brief—covering just
the two weeks immediately after birth—they found that
growth trajectories were nonlinear and that the trajectories of
later-born babies began lower, had shallower slopes, and had
lower rates of acceleration.
South (2001), too, laments that many researchers fail to
capitalize on the richness of longitudinal data. Even among
those who do track individuals over time, “relatively few …
have attempted to ascertain whether the critical
socioeconomic and demographic determinants of divorce and
separation vary across the marital life course” (p. 230).
Researchers are too quick to assume that the effects of
predictors like wives’ employment remain constant over time.
Yet as South points out, why should they? The predictors of
divorce among newlyweds likely differ from those among
couples who have been married for years. And concerning
secular trends, South offers two cogent, but conflicting,
arguments about how the effects of wives’ employment might
change over time. First, he argues that the effects might
diminish, as more women enter the labor force and working
becomes normative. Next, he argues that the effects might
increase, as changing mores weaken the link between
marriage and parenthood. With rich longitudinal data on
thousands of couples in different generations who married in
different years, South carefully evaluates the evidence for, and
against, these competing theories in ways that cross-sectional
data do not allow.
Not all longitudinal studies will use the same statistical
methods—the method must be matched to the question.
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Preamble
(p.v)
Because these two studies pose different types of research
questions, they demand different analytic approaches. The
first focuses on a continuous outcome—neurological
functioning—and asks how this attribute changes over time.
The second focuses on a specific event—divorce—and asks
about its occurrence and timing. Conceptually, we say that in
the first study, time is a predictor and our analyses assess how
a continuous outcome varies as a function of time and other
predictors. In the second study, time is an object of study in its
own right and we want to know whether, and when, events
occur and how their occurrence varies as a function of
predictors. Conceptually, then, time is an outcome.
Answering each type of research question requires a different
statistical approach. We address questions about change using
methods known variously as individual growth modeling
(Rogosa, Brandt, & Zimowski, 1982; Willett, 1988), multilevel
modeling (Goldstein, 1995), hierarchical linear modeling
(Raudenbush & Bryk, 2002), random coefficient regression
(Hedeker, Gibbons, & Flay, 1994), and mixed modeling
(Pinheiro & Bates, 2000). We address questions about event
occurrence using methods known variously as survival analysis
(Cox & Oakes, 1984), event history (p.vii) analysis (Allison,
1984; Tuma & Hannan, 1984), failure time analysis (Kalbfleish
& Prentice, 1980), and hazard modeling (Yamaguchi, 1991).
Recent years have witnessed major advances in both types of
methods. Descriptions of these advances appear throughout
the technical literature and their strengths are well
documented. Statistical software is abundant, in the form of
dedicated packages and preprogrammed routines in the large
multipurpose statistical packages.
But despite these advances, application lags behind.
Inspection of substantive papers across many disciplines, from
psychology and education to criminology and public health,
suggests that—with exceptions, of course—these methods
have yet to be widely and wisely used. In a review of over 50
longitudinal studies published in American Psychological
Association journals in 1999, for example, we found that only
four used individual growth modeling (even though many
wanted to study change in a continuous outcome) and only one
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Preamble
(p.v)
used survival analysis (even though many were interested in
event occurrence; Singer & Willett, 2001). Certainly, one
cause for this situation is that many popular applied statistics
books fail to describe these methods, creating the
misimpression that familiar techniques, such as regression
analysis, will suffice in these longitudinal applications.
Failure to use new methods is one problem; failure to use
them well is another. Without naming names, we find that
even when individual growth modeling and survival analysis
are used in appropriate contexts, they are too often
implemented by rote. These methods are complex, their
statistical models sophisticated, their assumptions subtle. The
default options in most computer packages do not
automatically generate the statistical models you need.
Thoughtful data analysis requires diligence. But make no
mistake; hard work has a payoff. If you learn how to analyze
longitudinal data well, your approach to empirical research
will be altered fundamentally. Not only will you frame your
research questions differently but you will also change the
kinds of effects that you can detect.
We are not the first to write on these topics. For each method
we describe, there are many excellent volumes well worth
reading and we urge you to consult these resources. Current
books on growth modeling tend to be somewhat technical,
assuming advanced knowledge of mathematical statistics (a
topic that itself depends on probability theory, calculus, and
linear algebra). That said, Raudenbush and Bryk (2002) and
Diggle, Liang, and Zeger (1994) are two classics we are proud
to recommend. Goldstein (1995) and Longford (1993) are
somewhat more technical but also extremely useful. Perhaps
because of its longer history, there are several accessible
books on survival analysis. Two that we (p.viii) especially
recommend are Hosmer and Lemeshow (1999) and Collett
(1994). For more technically oriented readers, the classic
Kalbfleisch and Prentice (1980) and the newer Therneau and
Grambsch (2000) extend the basic methods in important ways.
Our book is different from other books in several ways. To our
knowledge, no other book at this level presents growth
modeling and survival analysis within a single, coherent
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Preamble
(p.v)
framework. More often, growth modeling is treated as a
special case of multilevel modeling (which it is), with repeated
measurements “grouped” within the individual. Our book
stresses the primacy of the sequential nature of the empirical
growth record, the repeated observations on an individual
over time. As we will show, this structure has far-reaching
ramifications for statistical models and their assumptions.
Time is not just “another” predictor; it has unique properties
that are key to our work. Many books on survival analysis, in
contrast, treat the method itself as an object of study in its
own right. Yet isolating one approach from all others conceals
important similarities among popular methods for the analysis
of longitudinal data, in everything from the use of a person-
period data set to ways of interpreting the effects of time-
varying predictors. If you understand both growth modeling
and survival analysis, and their complementarities, you will be
able to apply both methods synergistically to different
research questions in the same study.
Our targeted readers are our professional colleagues (and
their students) who are comfortable with traditional statistical
methods but who have yet to fully exploit these longitudinal
approaches. We have written this book as a tutorial—a
structured conversation among colleagues. In its pages, we
address the questions that our colleagues and students ask us
when they come for data analytic advice. Because we have to
start somewhere, we assume that you are comfortable with
linear and logistic regression analysis, as well as with the
basic ideas of decent data analysis. We expect that you know
how to specify and compare statistical models, test
hypotheses, distinguish between main effects and interactions,
comprehend the notions of linear and nonlinear relationships,
and can use residuals and other diagnostics to examine your
assumptions. Many of you may also be comfortable with
multilevel modeling or structural equation modeling, although
we assume no familiarity with either. And although our
methodological colleagues are not our prime audience, we
hope they, too, will find much of interest.
Our orientation is data analytic, not theoretical. We explain
how to use growth modeling and survival analysis via careful
step-by-step analysis of real data. For each method, we
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Preamble
(p.v)
emphasize five linked phases: identifying research questions,
postulating an appropriate model and understanding (p.ix) its
assumptions, choosing a sound method of estimation,
interpreting results, and presenting your findings. We devote
considerable space—over 150 tables and figures—to
illustrating how to present your work not just in words but
also in displays. But ours is not a cookbook filled with
checklists and flowcharts. The craft of good data analysis
cannot be prepackaged into a rote sequence of steps. It
involves more than using statistical computer software to
generate reams of output. Thoughtful analysis can be difficult
and messy, raising delicate problems of model specification
and parameter interpretation. We confront these thorny issues
directly, offering concrete advice for sound decision making.
Our goal is to provide the short-term guidance you need to
quickly start using the methods in your own work, as well as
sufficient long-term advice to support your work once begun.
Many of the topics we discuss are rooted in complex statistical
arguments. When possible, we do not delve into technical
details. But if we believe that understanding these details will
improve the quality of your work, we offer straightforward
conceptual explanations that do not sacrifice intellectual rigor.
For example, we devote considerable space to issues of
estimation because we believe that you should not fit a
statistical model and interpret its results without
understanding intuitively what the model stipulates about the
underlying population and how sample data are used to
estimate parameters. But instead of showing you how to
maximize a likelihood function, we discuss heuristically what
maximum likelihood methods of estimation are, why they make
sense, and how the computer applies them. Similarly, we
devote considerable attention to explicating the assumptions
of our statistical models so that you can understand their
foundations and limitations. When deciding whether to include
(or exclude) a particular topic, we asked ourselves: Is this
something that empirical researchers need to know to be able
to conduct their analyses wisely? This led us to drop some
topics that are discussed routinely in other books (for
example, we do not spend time discussing what not to do with
longitudinal data) while we spend considerable time
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Preamble
(p.v)
discussing some topics that other books downplay (such as
how to include and interpret the effects of time-varying
predictors in your analyses).
All the data sets analyzed in this book—and there are many—
are real data from real studies. To provide you with a library of
resources that you might emulate, we also refer to many other
published papers. Dozens of researchers have been
extraordinarily generous with their time, providing us with
data sets in psychology, education, sociology, political science,
criminology, medicine, and public health. Our years of
teaching convince us that it is easier to master technical
material when it is embedded in real-world applications. But
we hasten to add that the methods are (p.x) unaware of the
substance involved. Even if your discipline is not represented
in the examples in these pages, we hope you will still find
much of analytic value. For this reason, we have tried to
choose examples that require little disciplinary knowledge so
that readers from other fields can appreciate the subtlety of
the substantive arguments involved.
Like all methodologists writing in the computer age, we faced
a dilemma: how to balance the competing needs of illustrating
the use of statistical software with the inevitability that
specific advice about any particular computer package would
soon be out of date. A related concern that we shared was a
sense that the ability to program a statistical package does not
substitute for understanding what a statistical model is, how it
represents relationships among variables, how its parameters
are estimated, and how to interpret its results. Because we
have no vested interest in any particular statistical package,
we decided to use a variety of them throughout the book. But
instead of presenting unadulterated computer output for your
perusal, we have reformatted the results obtained from each
program to provide templates you can use when reporting
findings. Recognizing that empirical researchers must be able
to use software effectively, however, we have provided an
associated website that lists the data sets used in the book, as
well as a library of computer programs for analyzing them,
and selected additional materials of interest to the data
analyst.
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Preamble
(p.v)
The book is divided into two major parts: individual growth
modeling in the first half, survival analysis in the second.
Throughout each half, we stress the important connections
between the methods. Each half has its own introduction that:
(1) discusses when the method might be used; (2)
distinguishes among the different types of research questions
in that domain; and (3) identifies the major statistical features
of empirical studies that lend themselves to the specified
analyses. Both types of analyses require a sensible metric for
clocking time, but in growth modeling, you need multiple
waves of data and an outcome that changes systematically,
whereas in survival analysis, you must clearly identify the
beginning of time and the criteria used to assess event
occurrence. Subsequent chapters in each half of the book walk
you through the details of analysis. Each begins with a chapter
on data description and exploratory analysis, followed by a
detailed discussion of model specification, model fitting, and
parameter interpretation. Having introduced a basic model,
we then consider extensions. Because it is easier to
understand the path that winds through the book only after
important issues relevant for each half have been introduced,
we defer discussion of each half’s outline to its associated
introductory chapter.
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