Latent Ornstein-Uhlenbeck models for Bayesian analysis of multivariate longitudinal categorical responses

We propose a Bayesian latent Ornstein-Uhlenbeck (OU) model to analyze unbalanced longitudinal data of binary and ordinal variables, which are manifestations of fewer continuous latent variables. We focus on the evolution of such latent variables when they continuously change over time. Existing approaches are limited to data collected at regular time intervals. Our proposal makes use of an OU process for the latent variables to overcome this limitation. We show that assuming real eigenvalues for the drift matrix of the OU process, as is frequently done in practice, can lead to biased estimates and/or misleading inference when the true process is oscillating. In contrast, our proposal allows for both real and complex eigenvalues. We illustrate our proposed model with a motivating dataset, containing patients with amyotrophic lateral sclerosis disease. We were interested in how bulbar, cervical, and lumbar functions evolve over time.