Title: Latent Ornstein-Uhlenbeck models for Bayesian analysis of multivariate longitudinal categorical responses
Authors: Emmanuel Lesaffre - University of Leuven (Belgium) [presenting]
Trung Dung Tran - KULeuven (Belgium)
Abstract: To explore the association of oral health with general health information obtained from a registry done on the elderly population in Belgium, we propose a Bayesian latent vector autoregressive (LVAR) model. This model handles multivariate balanced longitudinal data of binary and ordinal variables (items) as a function of a small number of continuous latent variables. We focus on the evolution of the latent variables while taking into account the correlation structure of the responses. Often local independence is assumed. Local independence implies that, given the latent variables, the responses are assumed mutually independent cross-sectionally and longitudinally. However, conditioning on the latent variables may not remove the dependence of the responses. We address local dependence by further conditioning on item-specific random effects. In a second step we extend the previous model to the unbalanced case. This model is then generalized to analyse multivariate unbalanced longitudinal data. We show that assuming real eigenvalues for the drift matrix of the OU process, as is frequently done, can lead to biased estimates and/or misleading inference when the true process is oscillating. Our proposal allows for both real and complex eigenvalues. We illustrate our model with a dataset containing patients with amyotrophic lateral sclerosis disease. We were interested in how bulbar, cervical, and lumbar functions evolve over time. Simulations showed a good behaviour.