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Bayesian inference on dependence in multivariate longitudinal data

In many applications, it is of interest to assess the dependence structure in multivariate longitudinal data. Discovering such dependence is challenging due to the dimensionality involved. By concatenating the random effects from component models for each response, dependence within and across longitudinal responses can be characterized through a large random effects covariance matrix. Motivated by the common problems in estimating this matrix, especially the off-diagonal elements, we propose a Bayesian approach that relies on shrinkage priors for parameters in a modified Cholesky decomposition. Without adjustment, such priors and previous related approaches are order-dependent and tend to shrink strongly toward an ARtype structure. We propose moment-matching (MM) priors to mitigate such problems. Efficient Gibbs samplers are developed for posterior computation. The methods are illustrated through simulated examples and are applied to a longitudinal epidemiologic study of hormones and oxidative stress.