IV. STATISTICAL ANALYSIS (continued)
A. Statistical Models and Data Analysis
7. Classification (Configural
- von Eye, A. Configural frequency analysis of longitudinal
multivariate responses. In: von Eye, A., ed. Statistical Methods
in Longitudinal Research, Vol. II: Time Series and Categorical Longitudinal
Data. New York: Academic Press, 1990.
Configural frequency analysis (CFA) is a method of analyzing
single cells in contingency tables, which are called configurations.
CFA tests whether a configuration forms a type or an antitype. The
chapter discusses methods for analysis of longitudinal multivariate
responses with CFA. To tackle the problem of unmanageable numbers
of contingency table cells in longitudinal categorical data, three
methods of reducing the number of cells are discussed. The chapter
gives data examples for each of these approaches.
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8. Classification (Latent
- Clogg, C.C. Latent class models. In: Arminger, G.,
Clogg, C.C., & Sobel, M.E., eds. Handbook of Statistical Modeling
for the Social and Behavioral Sciences. New York: Plenum Press,
1995, pp. 311-359.
The chapter reviews developments of latent class models
(LCM) since the late 1970s, including the work by Goodman and Haberman.
It includes mainly methodological or statistical references. The author
refers to promising developments in the models, the methods, and the
applications in the field. The chapter is a comprehensive and informative
introduction to the topic.
- Clogg, C.C., & Goodman, L.A. Latent structure analysis
of a set of multidimensional contingency tables. J Am Stat Assoc
The paper presents a general framework for simultaneous
latent structure analysis of a set of two or more multidimensional
contingency tables. The authors consider three basic types of models:
(1) models that assume complete homogeneity across tables, (2) models
that allow partial homogeneity across tables, and (3) models that
allow complete heterogeneity. The authors then use two different sets
of data to illustrate the procedures for model testing and parameter
- Collins, L.M., Fidler, P.L., Wugalter, S.E., &
Long, J.D. Goodness-of fit testing for latent class models. Multivariate
Behav Res 28:375-389, 1993.
Latent class models with sparse contingency tables can
present problems for model comparison and selection, because under
these conditions the distributions of goodness-of-fit indices are
often unknown. The authors present a simulation study to investigate
the distributions of the likelihood ratio statistics G2,
the Pearson statistic X2 , and a new goodness-of-fit
index suggested by Read and Cressie (1988). In general, the mean of
the distribution of a statistic was closer to the expectation of the
chi-squared distribution when the average cell expectation was large,
there were fewer indicator items, and the latent class measurement
parameters were less extreme. Based on the results they got, the authors
argue that one solution to the problem of spare tables is to forego
reliance on theoretical distributions for expectations and quantiles
of goodness-of-fit statistics and to turn to empirical central or
noncentral distributions obtained from Monte Carlo sampling procedures.
- Collins, L.M., Graham, J.W., Long, J.D., & Hansen,
W.B. Cross-validation of latent class models of early substance use
onset. Multivariate Behav Res, 29(2):165-183, 1994.
The purpose of this paper is to expand on Cudeck and
Brownes (1983) work in two directions. The first direction of
expansion is into testing of latent class models. The second direction
of expansion involves using cross-validation to examine differences
between groups, where groups may be formed by gender, ethnicity, region,
etc. In this article cross-validation is used to help select models
of early substance use onset in a sample of young adolescents. The
result suggests that double cross-validation is to be preferred over
- Goodman, L.A. Exploratory latent structure analysis
using both identifiable and unidentifiable models. Biometrika
The paper considers a wide class of latent structure
models, which serve as possible explanations of the observed relationships
among a set of m manifest polytomous variables. The author
considers both models that are identifiable and those that are not.
For each of the models, the method is presented for calculating the
maximum likelihood estimate of the expected frequencies and for determining
whether the model is identifiable. In addition, the author discusses
how to assess model fit and deal with unidentifiable models.
- Haberman, S.J. Qualitative Data Analysis. Vol. 2,
New Developments. New York: Academic Press, 1979.
Together with volume one of the series, the book provides
a thorough introduction to linear models and to latent-class models.
This volume explores models for qualitative data that go beyond the
hierarchical log-linear models and logit models. Topics covered include
multinomial response models, incomplete tables, symmetrical tables,
adjustment of data, and latent-class models.
- Langeheine, R., & Rost, J., eds. Latent Trait
and Latent Class Models. New York: Plenum, 1988.
The edited volume presents a synthesis of latent trait
and latent class models, which have been developed independently in
different research areas and yet share a lot in common. An introductory
chapter gives an overview of both types of models. In parts I and
II of the book, there are papers that deal with specific topics in
each of the models. Part III contains papers that compare the latent
trait models to the latent class models. Part IV of the book describes
applications of the two models to real data.
- Lazarsfeld, P.F., & Henry, N.W. Latent Structure
Analysis. Boston: Houghton Mifflin, 1968.
The book is a classic text on latent class modeling.
It starts with a discussion of the concept of latent structure analysis
and then deals with the mathematical aspects of the latent class models.
Chapter 5 deals with the problem of ordered classes. Chapters 6 and
7 describe various latent structure models with continuous latent
space, such as the latent content model and the polynomial traceline
models. Chapters 8 and 9 discuss more general latent structure models:
latent profile analysis and latent Markov chain models.
- McCutcheon, A.C. Latent Class Analysis. Beverly
Hills, CA: Sage Publications, 1987.
The text introduces the reader to latent class analysis,
which enables a characterization of categorical latent variables from
an analysis of the structure of the relationships among several categorical
manifest variables. The author first discusses the logic and application
of the formal latent class model. He then describes exploratory and
confirmatory applications of LCA. Chapter 4 covers the use of the
latent class model for examining the scaling properties of a set of
survey items. Chapter 5 is devoted to the use of LCA to model simultaneously
the latent structure of two or more populations.
- Rost, J. Rating scale analysis with latent class models.
Psychometrika 53:327-348, 1988.
The article describes a general approach for analyzing
rating data with latent class models. Previous rating scale analysis
was associated with latent trait models. The author proposes a general
model and a two-parameter model with location and dispersion parameters.
The latter is analogous to Andrichs Disloc-model. Parameter
estimation is done via EM-algorithm. The article contains two examples
that illustrate the application of the models and their statistical
control. Model restriction through equality constraints are discussed,
and multiparameter generalizations are outlined.
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B. Statistical Analyses for
1. General References
- Collins, L.M., & Hom, J.L., eds. Best Methods
for the Analysis of Change: Recent Advances, Unanswered Questions,
Future Directions. Washington, DC: American Psychological Association,
The volume presents findings reported at an October
1989 conference entitled "Best Methods for the Analysis of Change"
held at the University of Southern California. The major purpose of
the conference was to identify significant problems of design and
data analysis in research on change. The editors of the book organize
chapters into the following themes: (1) Issues in Applied SettingsThese
chapters discuss methodological issues that have arisen in substantive
applications; (2) Psychometric and Distributional Properties of VariablesThese
chapters address special problems presented by the measurement of
change; (3) Design and AnalysisChapters in this group explore
important factors to consider in designing good studies to measure
change and in analyzing data; (4) New MethodologiesThis section
includes latest developments in growth curve analysis, measurement
methodologies, survival analysis, and time series analysis; and (5)
Latent Variable ModelingA number of chapters touch on various
aspects of latent variable modeling.
- Dwyer, J.H., Feinleib, M., Lippert, P., & Hoffmeister,
H., eds. Statistical Models for Longitudinal Studies of Health.
New York: Oxford University Press, 1992.
Most of the chapters in this volume are derived from
papers presented at the Workshop on the Analysis of Longitudinal Data
held in Berlin in 1987. The workshop tried to bring together statisticians
from different health related fields that conduct longitudinal studies.
It aimed to gain understanding of the fundamental statistical issues
that confront longitudinal researchers in epidemiology and the social
sciences. Part 1 deals with models for continuous variables. Part
2 examines models for categorical data. Part 3 deals with special
problems in the modeling of longitudinal observations. Part 4 consists
of two chapters that discuss future directions researchers can take
in analyzing longitudinal data.
- Gottman, J.M., ed. The Analysis of Change. Mahwah,
NJ: Lawrence Erlbaum Associates, Inc., 1995.
As its title suggests, this edited volume deals with
the latest developments in the study of change. It puts forward new
ideas about how one would think about change and how it should be
analyzed. The book is divided into two sections. The first section
deals with designs that analyze change in multiple subjects, and the
second section deals with change in single subjects and an interacting
system. Some topics covered in the book include myths about longitudinal
research, hierarchical regression analysis, introduction to latent
growth curve models, using hierarchical linear models to study contextual
effects, survival analysis, accelerated short-term longitudinal design,
autoregressive effects in structural equation models, sequential analysis,
time-series analysis, and dynamic modeling.
- Cohen, P. A source of bias in longitudinal investigations
of change. In: Collins, L.M., & Hom, J.L., eds. Best Methods
for the Analysis of Change: Recent Advances, Unanswered Questions,
Future Directions. Washington, DC: American Psychological Association,
1991, pp. 18-30.
In this chapter, Cohen raises the problem of the "premature
covariate," which arises when a covariate is changing over time.
Cohen shows that, quite apart from any measurement error considerations,
if a covariate is not measured at the time it exerts its causal influence,
it may not be an effective covariate; that is statistical analysis
may not partial out all of the effect of the covariate on the dependent
- von Eye, A., ed. Statistical Methods in Longitudinal
Research, Vols. I & II: Principles and Structuring Change.
New York: Academic Press, 1990.
The main goal of the two volumes of work is to narrow
the gap between methodological advances in longitudinal investigation
and the application of them in social sciences. The target audience
of the work includes students of development and change. Each of the
16 chapters in the two volumes presents new aspects of methodology
or statistics. Volume I contains section 1 and 2, and volume II consists
of sections 3 and 4. Section 1 covers problems of general interest
in longitudinal research, such as the process of change, missing data,
and approaches to repeated measurement analysis. Section 2 includes
chapters on the structuring of change. It includes chapters on longitudinal
factor analysis, structural equation modeling, and methods of scaling.
Section 3 covers the analysis of time series. It consists of chapters
that discuss the use of event history analysis, spectral analysis,
and "tukerizing curves." Section 4 discusses developments
in the analysis of repeatedly observed categorical data. It includes
chapters on the use of log-linear modeling, latent class analysis,
and finite mixture distribution, and prediction analysis in contingency
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2. Analysis of Repeated Measurement Data
- Davidian, M., & Giltinan, D.M. Nonlinear Models
for Repeated Measurement Data. London: Chapman & Hall, 1995.
This book provides the first unified development of
methods and models for data of this type, with a detailed treatment
of inference for the nonlinear mixed effects model and its extensions.
A practical strength of the book is the inclusion of several detailed
case studies from the areas of population pharmacokinetics and pharmacodynamics,
immunoassay and bioassay development, and the analysis of growth curves.
- Greenhouse, S.W., & Geisser, S. On methods in analysis
of profile data. Psychometrika 24:95-112, 1959.
This paper is concerned with methods for analyzing quantitative,
noncategorical profile datae.g., a battery of tests given to
individuals in one or more groups. It is assumed that the variables
have a multinormal distribution with an arbitrary variance-covariance
matrix. Approximate procedures based on classical analysis of variance
are presented, including an adjustment to the degrees of freedom resulting
in conservative F tests. These can be applied to the case where
the variance-covariance matrices differ from group to group. In addition,
exact generalized multivariate analysis methods are discussed.
- Hand, D.J., & Crowder, M.J. Practical Longitudinal
Data Analysis. London: Chapman and Hall, 1996.
A multitude of techniques are available for analyzing
repeated-measures data. The book describes the whole spectrum of approaches,
beginning with very simple and crude methods, working through intermediate
techniques commonly used by consultant statisticians, and concluding
with more recent and advanced methods. Multiple testing, response
feature analysis, univariate analysis of variance approaches, multivariate
analysis of variance approaches, regression models, two-stage linear
models, approaches to categorical data, and techniques for analyzing
crossover designs are covered. The theory is illustrated with examples,
using real data brought to the authors during their work as statistical
- Hertzog, C., & Rovine, M. Repeated-measures analysis
of variance in developmental research: Selected issues. Child Development
This paper presents a review of developments in statistical
techniques for repeated-measures analysis of variance. The authors
present an updated perspective on the nature of the mixed model assumptions
and their implications for mixed model, adjusted mixed model, or multivariate
significance test. However, the central theme of the review is that
the validity of mixed model assumptions is but one consideration in
selection of an appropriate method of repeated-measures ANOVA. In
particular, the authors recommend the avoidance of omnibus significance
tests in favor of specific planned comparisons whenever hypotheses
more specific than the omnibus null hypothesis may be formulated a
- Lindsey, J.K. Models for Repeated Measurement.
Oxford: Oxford University Press, 1995.
This book will be of interest to research statisticians
in agriculture, medicine, economics, and psychology and to the many
consulting statisticians who want an up-to-date expository account
of this important topic. The book is organized into four parts. In
the first part, the general context of repeated measurements is presented.
The three basic types of response variables, continuous (normal),
categorical and count, and duration, are introduced. The ways in which
such repeated observations are interdependent, through heterogeneity
and time dependence, are discussed. A framework for constructing suitable
models is developed, with the introduction of the necessary concepts
of multivariate distributions and stochastic processes. In the following
three parts, a large number of concrete examples, including data tables,
are presented to illustrate the models available. Each of these parts
corresponds to one to the types of responses mentioned above.
- Rogan, J.C., Keselman, H.J., & Mendoza, J.L. Analysis
of repeated measurements. Br J Math Stat Psychol 32:269-286,
The literature demonstrates that uniformity of population
variances and covariances is a sufficient but not a necessary requirement
for valid F ratios in repeated measures designs; the tests
will be valid if the less restrictive condition of circularity is
satisfied. The circularity assumptions of various repeated-measures
designs are presented, and the empirical literature is reviewed and
interpreted in light of these assumptions. An empirical investigation
compares numerous data analytic strategies when circularity assumptions
have been violated. Results indicate that adjusted univariate and
multivariate tests are comparable with respect to type I error control
and power. Furthermore, it is shown that by formulating planned comparisons,
researchers can bypass all or some circularity constraints.
- Vonesh E.F., & Chinchilli, V.M. Linear and Nonlinear
Models for the Analysis of Repeated Measurements. New York: Marcel
Dekker, Inc., 1997.
The book integrates the latest theory, methodology,
and applications related to the design and analysis of repeated measurementscovering
a broad range of topics including the analysis of repeated-measures
designs, general crossover designs, and linear and nonlinear regression
models. The topics covered in the book include generalized multivariate
analysis of variance, the random coefficient growth curve, the linear
mixed effects models, a nonlinear version of the generalized multivariate
analysis of variance model, a Gaussian-based nonlinear mixed effects
model, a generalized nonlinear mixed effects model, and generalized
estimating equations for various estimating techniques.
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3. General Estimating Equations
- Diggle, P.J., Liang, K.-Y., & Zeger, S.L. Analysis
of Longitudinal Data. Oxford: Oxford University Press, 1994.
This book describes statistical models and methods for
the analysis of longitudinal data. It covers both the underlying statistical
theory of each method and its application to a range of examples from
the agricultural and biomedical sciences. Major topics in the book
are design issues, exploratory methods of analysis, linear models
for continuous data, general linear models for discrete data, and
models and methods for handling data with missing values.
- Liang, K.-Y., & Zeger, S.L. Longitudinal data analysis
using generalized linear models. Biometrika 73:13-22, 1986.
This paper proposes an extension of generalized linear
models to the analysis of longitudinal data. The authors introduce
a class of estimating equations that give consistent estimates of
the regression parameters and of their variance under mild assumptions
about time dependence. The estimating equations are derived without
specifying the joint distribution of a subjects observations
yet they reduce to the score equations for multivariate Gaussian outcomes.
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4. Latent Growth Curve Analysis
- Bryk, A.S., & Raudenbush, S.W. Application of hierarchical
linear model to assessing change. Psychol Bull 101(1):147-158,
The two authors use a two-stage model of change to model
individual change. In the first stage, the within-subject stage, an
individuals status on some trait is modeled as a function of
an individual growth trajectory plus random error. At the second,
or between-subjects stage, the parameters of the individual growth
trajectories vary as a function of differences between subjects in
background characteristics, instructional experiences, and possibly
experimental treatments. The authors, using data on Head Start children,
illustrate how this two-stage conceptualization allows investigators
to model individual change, predict future development, assess the
quality of measurement instruments for distinguishing among growth
trajectories, and study systematic variation in growth trajectories
as a function of background characteristics and experimental treatments.
- Duncan, T.E., Duncan, S.C., Alpert, A., Hops, H., Stoolmiller,
M., & Muthen, B. Latent variable modeling of longitudinal and
multilevel substance use data. Multivariate Behavioral Research
The authors of this article use the Multilevel Latent
Growth Modeling (MLGM) approach, which is a latent variable growth
analysis that takes into account cluster sampling, to analyze longitudinal
and multilevel data for adolescent and parent substance use measured
at four annual time points. The authors model the shape of the growth
curve and the extent of individual differences in the common trajectory
over time. The effects of marital and family status and socio-economic
status on family levels of substance use are also examined.
- Francis, D.J., Fletcher, J.M., Stuebing, K.K., Davidson,
K.C., & Thompson, N.M. Analysis of change: Modeling individual
growth. J Consult Clin Psychol 59(1):27-37, 1991.
Research on change is complicated by problems of measurement
and analysis stemming from a conceptualization of change as a series
of accumulating increments and decrements. In contrast, individual
growth curves depict change as a continuous process underlying individual
performance. These two perspectives are reviewed, and some problems
with the use of difference scores in the study of change are clarified.
Traditional methods are contrasted with growth curve analysis for
the purpose of measuring change and studying its correlates. An illustrative
example of the use of growth curves is provided from research on recovery
of cognitive function following pediatric closed head injury.
- MacCallum, R.C., Kim, C., Malarkey, W.B., & Kiecolt-Glaser,
J.K. Studying multivariate change using multilevel models and latent
curve models. Multivariate Behavioral Research 32(3):215-253,
The paper proposes methods to study relationships between
patterns of change on different variables. The authors show that multilevel
modeling framework, which is often used to study univariate change,
can be extended to the multivariate case to yield estimates of covariances
of parameters representing aspects of change on different variables.
The paper also considers extension of latent curve models to the multivariate
case, and shows how such models are related to multivariate multilevel
- McArdle, J.J., & Epstein, D. Latent growth curves
within developmental structural equation models. Child Development
The authors use structural equation modeling to combine
ideas from repeated-measures ANOVA with ideas from longitudinal factor
analysis, and present a longitudinal model that includes correlations,
variances, and means. McArdle et al. name the approach latent growth
curve model (LGM). They show that the technique permits the estimation
of parameters representing both individual and group dynamics. Aspects
of the latent growth models are illustrated with a set of longitudinal
WISC data from young children.
- Meredith, W., & Tisak, J. Latent curve analysis.
Psychometika 55(1):107-122, 1990.
The authors describe the latent curve analysis, which
contains individual parameters and a structure on both the first and
second moments of the random variables reflecting growth. The paper
also describes the ML estimation procedures and the asymptotic tests
associated with the procedure. The authors also show the relationship
between the procedure and standard repeated measures ANOVA as well
as first-order-autoregressive methods. The latent curve analysis also
encompasses cohort sequential designs and it allows for period or
- Rogosa, D.R., Brandt, D., & Zimowski, M. A growth
curve approach to the measurement of change. Psychol Bull 92(3):726-748,
The authors approached the measurement of individual
change from the standpoint of individual time paths and statistical
models for individual change. The paper also considers both the psychometric
properties of measures of individual change and examines measures
of change for data with more than two observations on each individual.
The author found that many of their results are at odds with previous
literature in the behavioral sciences.
- Rogosa, D.R., & Willet, J.B. Understanding correlates
of change by modeling individual differences in growth. Psychometrika
The paper proposes an approach to model systematic individual
differences in growth. It consists of two parts: (1) a model for individual
growth, and (2) a model for the dependence of parameters in the individual
growth models on individual characteristics. The paper begins with
explicit representations of correlates of change that are constructed
for various models of individual growth. Then the authors discuss
the special case of initial status as a correlate of change. Lastly,
the shortcomings of previous approaches to the assessment of correlates
of change are demonstrated. In particular, correlations of residual
change measures with exogenous individual characteristics are shown
to be poor indicators of systematic individual differences in growth.
- Sayer, A.G., & Willet, J.B. A cross-domain model
for growth in adolescent alcohol expectancies. Multivariate Behav
Res 33:509-543, 1998.
The authors demonstrate how the methods of individual
growth modeling and covariance structure analysis can be integrated
and used to investigate the interrelationships among simultaneous
individual changes in two domainspositive and negative alcohol
expectanciesover the course of early to mid-adolescence, for
both boys and girls. Sayer et al. represent individual change over
time in positive expectancies with a piecewise growth model, and in
negative expectancies with a straight-line growth model. Then they
use multisample covariance structure analysis to ask whether individual
changes in positive and negative expectancies are related to each
other and whether the pattern of interrelationships differs by gender.
- Willett, J.B. Measuring change more effectively by
modeling individual change over time. In: Husen, T., & Postlethwaite,
T.N., eds. The International Encyclopedia of Education, 2nd
ed. Oxford, England: Pergamon Press, 1994.
In this chapter Willett provides an overview about the
various methods of measuring change in social sciences research. He
first points out why change can be reasonably measured if one goes
beyond the traditional "before and after," or "two
wave," design. A discussion on the proper use of the difference
score is also provided. Then the author shows how that can be done
by fitting growth models to within-person changes and between-person
differences in change.
- Willett, J.B., Ayoub, C.C., & Robinson, D. Using
growth modeling to examine systematic differences in growth: An example
of change in the functioning of families at risk of maladaptive parenting,
child abuse, or neglect. J Consult Clin Psychol 59(1):38-47,
This longitudinal study provides an example of the use
of exploratory growth modeling to examine changes over time in the
functioning of 172 families who underwent treatment in an innovative
prevention program, Project Good Start. Two types of research question
are addressed: a within-family question (Does family functioning
change over time in families at risk of maltreatment who are receiving
special early support services?) and a between-family question
(Are changes in family functioning systematically related to selected
characteristics of family background and treatment?). Results of the
study highlight the heterogeneity across families in the direction
and rate of family function change and its systematic relationship
with the family profile on entry into intervention. Although treatment
seems successful in stabilizing and improving the family functioning
of most at-risk families, problems of violence/maltreatment, and distressed
parenting act to defer successful treatment.
- Willet, J.B., & Sayer, A.G. Using covariance structure
analysis to detect correlates and predictors of individual change
over time. Psychol Bull 116(2):363-381, 1994.
The article explains how the individual growth models
can be reformatted to correspond to the measurement and structural
components of the general LISREL model with mean structures and illustrates
how the new method can be applied to a sample of longitudinal panel
data. The integration of the two techniques brings the flexibility
of covariance analysis into growth curve modeling.
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5. Time Series Analysis
- Aoki, M. State Space Modeling of Time Series.
Berlin: Springer-Verlag, 1987.
In this book, the author adopts a state space approach
to time series modeling to provide a new, computer-oriented method
for building models for vector-valued time series. Background material
leading up to the two types of estimators of the state space models
is collected and presented coherently in four consecutive chapters.
Expositions are given of conversion of ARMA models into state space
forms, of properties of state space models, and how two alternative
decompositions of Hankel matrices are used in constructing estimators.
Later chapters explain in detail different types of innovation models.
- Jones, R.H. Longitudinal Data With Serial Correlation:
A State-Space Approach. London: Chapman & Hall, 1993.
The emphasis of the book is on methods for analyzing
unbalanced repeated measures or longitudinal data with possible serial
correlation. The basic model is a mixed fixed and random effects model
often referred to as the Laird-Ware model. Both maximum likelihood
and restricted maximum likelihood methods of estimation are discussed
in detail in the book. Methods of model selection and the testing
of contrasts of the fixed coefficients are discussed. The Kalman filter
is presented as a method for calculating likelihoods for this class
of models. The book also contains nonlinear models.
- Lütkepohl, H. Introduction to Multiple Time Series
Analysis, 2nd ed. New York: Springer-Verlag, 1993.
The book is based on the authors lecture notes
in a course on multiple time series analysis for graduate students
in business and economics. Chapters 1 to 4 contain an introduction
to the vector autoregressive methodology. Chapters 5 to 9 deal with
mixed autoregressive moving average models. Chapter 10 reviews econometric
dynamic simultaneous equations models; chapter 11 considers cointegration
topic; chapter 12 discusses models with systematically varying coefficients;
and chapter 13 describes the state space model.
- McCleary, R., & Hay, R.A., Jr. Applied Time
Series Analysis for the Social Sciences. Beverly Hills, CA: Sage
The authors introduce the readers to univariate ARIMA
models (emphasizing the Box-Jenkins iterative cycle of model identification,
estimation, and diagnosis), impact assessments, and forecasts. This
is followed by chapters on multivariate ARIMA models and ARIMA estimation
- Molenaar, P.C.M. A dynamic factor model for the analysis
of multivariate time series. Psychometrika 50:181-202, 1985.
To circumscribe the deficiency of the P-technique in
handling lagged covariance structure, the author proposes a new statistical
technique, the dynamic factor analysis. The technique accounts for
the entire lagged covariance function of an arbitrary second order
stationary time series. Besides, dynamic factor analysis is shown
to be applicable to a relatively short stretch of observations, and
the author suggests that it will be useful for a lot of psychological
- Molenaar, P.C.M., De Gooijer, J.G., & Schmitz,
B. Dynamic factor analysis of nonstationary multivariate time series.
Psychometrika 57:333-349, 1992.
The authors propose a dynamic factor model for the analysis
of multivariate nonstationary time series in the time domain. The
article deals with a mild form of nonstationarity often relevant in
analyzing socioeconomic time series. Such nonstationarity in the series
is represented by a linear time dependent mean function. By extending
Molenaars stationary dynamic factor analysis methods, the authors
incorporate the effect of nonstationarity on the latent factor series,
forming the dynamic nonstationary factor model (DNFM). The authors
further demonstrate the properties of the DNFM model and its application.
- Ostrom, C.W., Jr., Time Series Analysis: Regression
Techniques, 2nd ed. Thousand Oaks, CA: Sage Publications, 1990.
The monograph serves as an in-depth introduction to
a variation of the basic regression model that utilizes data from
time series. Ostrom shows how to diagnose the autocorrelation problem,
starting with the simple first-order autoregression process and working
up to higher order, moving average, and mixed error processes. Further,
he spells out estimation procedures for overcoming autocorrelation
difficulties. Several useful Generalized Least Squares approaches
are discussed. The book also addresses important special topics: Box-Jenkins
versus classical regression approaches; endogenous and exogenous lagged
variables; and ex-post and ex-ante forecasting.
- Rao, T.S. Developments in Time Series Analysis:
In Honour of Maurice B. Priestley. London, Chapman & Hall,
This volume contains 27 papers, written by well-known
time series analysts, dealing with statistical theory, methodology
and applications. The emphasis is on the recent developments in the
analysis of linear, nonlinear (non-Gaussian), stationary, and nonstationary
time series. The topics include cointegration, estimation and asymptotic
theory, Kalman filtering, nonparametric statistical inference, long
memory models, nonlinear models, and spectral analysis of stationary
and nonstationary processes.
- Shumway, R.H. Applied Statistical Time Series Analysis.
New Jersey: Prentice Hall, 1988.
The book is an expanded version of lectures from a course
in applied time series for graduate studies. Topics covered in the
book include characteristics of time series, spectral analysis and
filtering, time domain regression methods, frequency domain regression,
pattern recognition and discriminant analysis, and time series computing.
- Velicer, W.F., & McDonald, R.P. Cross-sectional
time series designs: A general transformation approach. Multivariate
Behav Res 26:247-254, 1991.
Cross-sectional time series designs assess the generalizability
of intervention effects across different units. The article extends
the general transformation approach proposed by the same authors in
1984 to the analysis of multiple unit data by the development of a
patterned transformation matrix. A sequence of tests of the parameters
permits the assessment of between-unit differences. The resulting
procedure includes several alternative approaches as special cases
and is easily implemented with only minor revisions in existing computer
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6. Survival Analysis
- Blossfeld, H.P., & Rohwer, G. Event History
Analysis: Statistical Theory and Application in the Social Sciences.
Mahwah, NJ: Lawrence Erlbaum Associates, 1995.
The book gives a comprehensive introductory account
of event history modeling techniques and their usefulness for causal
analysis in the social sciences. Besides, the volume deals with continuous-time
models. It is both a student textbook and a reference book for research
scientists. The book also introduces the reader to the Transition
Data Analysis (TDA) program, which estimates the sorts of models most
frequently used with longitudinal data, in particular, event history
- Kalbfleisch, J.D., & Prentice, R.L. The Statistical
Analysis of Failure Time Data. New York: Wiley, 1980.
The main purpose of the book is to collect and unify
some statistical models and methods that have been proposed for analyzing
failure time data. Special attention has been paid to problems arising
in the biomedical sciences. Chapter 1 deals with the basic formulation
of survival models and elementary methods of analysis. Chapter 2 presents
common survival models for homogeneous populations. Chapter 3 deals
with parameter estimation. The proportional hazards model is considered
in chapter 4. Chapters 5 to 8 deal with more specialized topics.
- Petersen, T. Analysis of event histories. In: Arminger,
G., Clogg, C.C., & Sobel, M.E., eds. A Handbook for Statistical
Modeling in the Social and Behavioral Sciences. New York: Plenum,
1992, pp. 453-517.
This chapter on event history analysis focuses on three
types of failure-time or jump processes. The first is the single-state
nonrepeatable event process, which is obtained when there is a single
state that can be occupied only once. The second is the multistate
process, in which the state currently occupied can be left for several
distinct reasons. The third is the repeatable-event process. In such
a process, a person can occupy a state several times. In all three
types of failure-time processes the objective of the empirical analysis
is to analyze the determinants of the amount of time that elapses
between changes and the value of the destination state once a change
occurs. The chapter is organized into 17 sections, covering various
topics in event history analysis, like various kinds of hazard-rate
models, the influence of unobserved variables and time-aggregation
bias, and how to deal with life censoring.
- Singer, J.D., & Willett, J.B. Modeling the days
of our lives: Using survival analysis when designing and analyzing
studies of duration and the timing of events. Psychol Bull
The article describes the use of survival analysis in
answering psychological research questions, especially those that
study whether and when events occur. One fundamental problem for such
studies is the presence of censored observations. The article focuses
on two aspects of survival analysis: study design and data analysis.
It shows how psychologists have used the methods during the past decade
and identifies new directions for future applications. Examples are
drawn from research on mental health, addiction, social interaction,
and the life course.
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7. Latent Transition Analysis
- Collins, L.M., Flaherty, B.P., Hyatt, S.L. & Schafer,
J.L. WinLTA User's Guide. Version 2.0. The Methodology Center,
The Pennsylvania State University, 1999.
The manual describes in detail how to fit latent transition
models to data. It provides an overview of the mathematical model
underlying LTA and the way parameters are estimated in the method.
It also contains working examples that guide users in setting up LTA
- Collins, L.M., Graham, J.W., Rousculp, S.C., &
Hansen, W.B. Heavy caffeine use and the beginning of the substance
use onset process: An illustration of latent transition analysis.
In: Bryant, K.J., Windle, M., & West, S.G., eds. The Science
of Prevention: Methodological Advances from Alcohol and Substance
Abuse Research. Washington, DC: American Psychological Association,
The chapter introduces the readers to latent transition
analysis (LTA) and demonstrates the usefulness of the technique in
alcohol prevention research. The authors begin with a description
of the LTA model, both in conceptual and statistical terms. Then they
present the results of a study that use LTA to model the drug use
of adolescents who participated in a survey conducted as part of the
Adolescent Alcohol Prevention Trial (AAPT; Graham, Rohrbach, Hansen,
Flay, & Johnson, 1989).
- Collins, L.M., & Wugalter, S.E. Latent class models
for stage-sequential dynamic latent variables. Multivariate Behav
Res 27:131-157, 1992.
The authors present the latent transition analysis (LTA)
technique that can model stage-sequential dynamic latent variables
in longitudinal studies. LTA expands the latent Markov model to allow
applications to more complex latent variables and the use of multiple
indicators. Because complex latent class models result in sparse contingency
tables, which may lead to poor parameter estimation, a simulation
study was conducted in order to determine whether model parameters
are recovered adequately by LTA and whether additional indicators
result in better measurement or in impossibly sparse tables. The results
indicated that parameter recovery was satisfactory overall, although
as expected the standard errors were large in some conditions with
- Graham, J.W., Collins, L.M., Wugalter, S.W., Chung,
N.K., & Hansen, W.B. Modeling transitions in latent stage-sequential
processes: A substance use prevention example. J Consult Clin Psychol
This article illustrates the use of latent transition
analysis (LTA), a methodology for testing stage-sequential models
of individual growth. LTA is an outgrowth of latent class theory and
is a particular type of latent Markov model emphasizing the use of
multiple manifest indicators. LTA is used to compare the fit of two
models of early adolescent substance use onset and to assess the effects
of a school-based substance use prevention program on Ss measured
in 7th grade and again in 8th grade.
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