Latent Curve Models: A Structural Equation Perspective

Abstract

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.