Models for the Covariance Matrix of Multivariate Longitudinal and Repeated Measures Data

We present flexible, fully Bayesian models for the covariance structure of unbalanced multivariate repeated measures data. A typical setting involves measurements on many subjects taken at any of a large number of possible times. Unstructured covariance matrices have too many parameters to be fit to this sort of data, so researchers have typically relied on structured covariance matrices which depend on a small set of unknown parameters. We introduce prior distribution families for unstructured covariance matrices that allow the data to determine a compromise between unstructured and parametric matrices. Applications to data from the UCLA Brain Injury Research Center are discussed.