Multivariate longitudinal data analyses

This chapter delves into multivariate longitudinal analyses of complex datasets, focusing on unobservable constructs measured through categorical discrete indicators across multiple occasions. Such analyses, relevant in fields such as psychology, sociology, education, and medicine, often rely on latent variable models to interpret data from questionnaires, exams, or other assessments. The chapter explores explicitly generalized linear latent variable models (GLLVMs) as a versatile framework for analyzing multidimensional, longitudinal data with binary indicators, addressing challenges such as item-specific effects, serial dependence, and the categorical nature of responses. By capturing temporal associations and accounting for unobserved heterogeneity via random effects, GLLVMs facilitate an in-depth examination of how latent constructs evolve. Various modeling approaches within the GLLVM framework, including unstructured factor covariances, latent growth curves, and autoregressive processes, provide tools for incorporating serial dependence across items. An empirical application using data from the Health and Retirement Study showcases the utility of GLLVMs in modeling the dynamics of depressive symptoms, particularly the interrelationship between anhedonia and negative affect.