Latent Variable Models for Longitudinal Data with Flexible Measurement Schedule

This chapter provides a survey of the development of latent variable models that are suitable for analyzing unbalanced longitudinal data. This chapter begins with an introduction, in which the marginal modeling approach (without the use of latent variable) for correlated responses such as repeatedly measured longitudinal data is described. The concepts of random effects and latent variables are introduced at the beginning of Sect. 41.1. Section 41.1.1 describes the linear mixed models of Laird and Ware for continuous longitudinal response; Sect. 41.1.2 discusses generalized linear mixed models (with latent variables) for categorical response; and Sect. 41.1.3 covers models with multilevel latent variables. Section 41.2.1 presents an extended linear mixed model of Laird and Ware for multidimensional longitudinal responses of different types. Section 41.2.2 covers measurement error models for multiple longitudinal responses. Section 41.3 describes linear mixed models with latent class variables—the latent class mixed model that can be useful for either a single or multiple longitudinal responses. Section 41.4 studies the relationships between multiple longitudinal responses through structural equation models. Section 41.5 unifies all the above varieties of latent variable models under a single multilevel latent variable model formulation.