Mixed-Effects Models with Crossed Random Effects for Multivariate Longitudinal Data

Multivariate models for longitudinal data attempt to examine change in multiple variables as well as their interrelations over time. In this study, we present a Mixed-Effects Model with Crossed Random effects (MEM-CR) for individuals and variables, and compare it with two existing structural equation models for multivariate longitudinal data, namely the Curve-of-Factor-Scores (CUFFS) and the Factor-of-Curve-Scores (FOCUS). We compare these models in two types of longitudinal studies based on balanced and unbalanced data: panel studies and cohort-sequential designs, respectively. We illustrate the performance of these statistical techniques using empirical data from two studies (MHS, a panel study, and NLSY79, a cohort-sequential design) with discrete and continuous time metric modeling, respectively. We conclude that MEMs-CR provides relevant information about the developmental trajectories of individuals and variables in multivariate longitudinal data under either type of data condition. We discuss the theoretical and methodological implications of our findings.