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A. Statistical Models and Data Analysis (continued)

7. Classification (Configural Frequency Analysis)

  1. 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 Class Analysis)

  1. 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.

  1. Clogg, C.C., & Goodman, L.A. Latent structure analysis of a set of multidimensional contingency tables. J Am Stat Assoc 79:762-771, 1984.

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 estimation.

  1. 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.

  1. 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 Browne’s (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 single cross-validation.

  1. Goodman, L.A. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61:215-231, 1974.

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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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 Andrich’s 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 Longitudinal Data

1. General References

  1. 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.

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 Settings—These chapters discuss methodological issues that have arisen in substantive applications; (2) Psychometric and Distributional Properties of Variables—These chapters address special problems presented by the measurement of change; (3) Design and Analysis—Chapters in this group explore important factors to consider in designing good studies to measure change and in analyzing data; (4) New Methodologies—This section includes latest developments in growth curve analysis, measurement methodologies, survival analysis, and time series analysis; and (5) Latent Variable Modeling—A number of chapters touch on various aspects of latent variable modeling.

  1. 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.

  1. 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.

  1. 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 variable.

  1. 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 tables.

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2. Analysis of Repeated Measurement Data

  1. 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.

  1. 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 data—e.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.

  1. 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 consultants.

  1. Hertzog, C., & Rovine, M. Repeated-measures analysis of variance in developmental research: Selected issues. Child Development 56:787-809, 1985.

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 priori.

  1. 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.

  1. Rogan, J.C., Keselman, H.J., & Mendoza, J.L. Analysis of repeated measurements. Br J Math Stat Psychol 32:269-286, 1979.

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.

  1. 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 measurements—covering 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 (G.E.E.)

  1. 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.

  1. 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 subject’s observations yet they reduce to the score equations for multivariate Gaussian outcomes.

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4. Latent Growth Curve Analysis

  1. Bryk, A.S., & Raudenbush, S.W. Application of hierarchical linear model to assessing change. Psychol Bull 101(1):147-158, 1987.

The two authors use a two-stage model of change to model individual change. In the first stage, the within-subject stage, an individual’s 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.

  1. 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 32(3):275-318, 1997.

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.

  1. 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.

  1. 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, 1997.

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 models.

  1. McArdle, J.J., & Epstein, D. Latent growth curves within developmental structural equation models. Child Development 58:110-133, 1987.

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.

  1. 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 practice effects.

  1. Rogosa, D.R., Brandt, D., & Zimowski, M. A growth curve approach to the measurement of change. Psychol Bull 92(3):726-748, 1982.

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.

  1. Rogosa, D.R., & Willet, J.B. Understanding correlates of change by modeling individual differences in growth. Psychometrika 50:203-228, 1985.

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.

  1. 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 domains—positive and negative alcohol expectancies—over 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.

  1. 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.

  1. 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, 1991.

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.

  1. 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

  1. 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.

  1. 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.

  1. Lütkepohl, H. Introduction to Multiple Time Series Analysis, 2nd ed. New York: Springer-Verlag, 1993.

The book is based on the author’s 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.

  1. McCleary, R., & Hay, R.A., Jr. Applied Time Series Analysis for the Social Sciences. Beverly Hills, CA: Sage Publications, 1980.

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 algorithms.

  1. 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 research.

  1. 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 Molenaar’s 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.

  1. 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.

  1. Rao, T.S. Developments in Time Series Analysis: In Honour of Maurice B. Priestley. London, Chapman & Hall, 1993.

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.

  1. 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.

  1. 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 software.

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6. Survival Analysis

  1. 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 data.

  1. 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.

  1. 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.

  1. 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 110(2):268-290, 1991.

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

  1. 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 models.

  1. 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, 1997.

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).

  1. 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 few subjects.

  1. 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 59:48-57, 1991.

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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