Latent Curve Models

KENNETH A. BOLLEN, PhD, is Henry Rudolph Immerwahr Distinguished Professor of Sociology, Director of the Odum Institute for Research in Social Science, and an Adjunct Professor of Statistics at The University of North Carolina at Chapel Hill. He is the author of two books, including Structural Equations with Latent Variables (Wiley), and more than 100 scholarly papers. PATRICK J. CURRAN, PhD, is Associate Professor of Psychology in the L. L. Thurstone Psychometric Laboratory at The University of North Carolina at Chapel Hill. He has made contributions to the development and application of new quantitative methodologies in the social sciences through his integrated program of research, writing, and teaching.

"This useful new text on growth curve modeling fills a critical gap in the applied methodological literature in longitudinal modelling. ... We see it as an important text for those working in longitudinal modeling to own and be able to refer to in the context of model development and instruction." (Psychometrika, 2011) "…an authoritative account of the subject…" (Journal of the American Statistical Association, December 2007)

• Preface. 1 Introduction.1.1 Conceptualization and Analysis of Trajectories.1.2 Three Initial Questions About Trajectories.1.3 Brief History of Latent Curve Models.1.4 Organization of the Remainder of the Book.2 Unconditional Latent Curve Model.2.1 Repeated Measures.2.2 General Model and Assumptions.2.3 Identification.2.4 Case-By-Case Approach.2.5 Structural Equation Model Approach.2.6 Alternative Approaches to the SEM.2.7 Conclusions.Appendix 2A: Test Statistics, Nonnormality, and Statistical Power.3 Missing Data and Alternative Metrics of Time.3.1 Missing Data.3.2 Missing Data and Alternative Metrics of Time.3.3 Conclusions.4 Nonlinear Trajectories and the Coding of Time.4.1 Modeling Nonlinear Functions of Time.4.2 Nonlinear Curve Fitting: Estimated Factor Loadings.4.3 Piecewise Linear Trajectory Models.4.4 Alternative Parametric Functions.4.5 Linear Transformations of the Metric of Time.4.6 Conclusions.Appendix 4A: Identification of Quadratic and Piecewise Latent Curve Models.4A.1 Quadratic LCM.4A.2 Piecewise LCM.5 Conditional Latent Curve Models.5.1 Conditional Model and Assumptions.5.2 Identification.5.3 Structural Equation Modeling Approach.5.4 Interpretation of Conditional Model Estimates.5.5 Empirical Example.5.6 Conclusions.6 The Analysis of Groups.6.1 Dummy Variable Approach.6.2 Multiple-Group Analysis.6.3 Unknown Group Membership.6.4 Conclusions.Appendix 6A: Case-by-Case Approach to Analysis of Various Groups.6A.1 Dummy Variable Method.6A.2 Multiple-Group Analysis.6A.3 Unknown Group Membership.6A.4 Appendix Summary.7 Multivariate Latent Curve Models.7.1 Time-Invariant Covariates.7.2 Time-Varying Covariates.7.3 Simultaneous Inclusion of Time-Invariant and Time-Varying Covariates.7.4 Multivariate Latent Curve Models.7.5 Autoregressive Latent Trajectory Model.7.6 General Equation for All Models.7.7 Implied Moment Matrices.7.8 Conclusions.8 Extensions of Latent Curve Models.8.1 Dichotomous and Ordinal Repeated Measures.8.2 Repeated Latent Variables with Multiple Indicators.8.3 Latent Covariates.8.4 Conclusions.References.Author Index.Subject Index.