A Bayesian Approach on the Effect of Different Covariance Structures on Repeated Measures Data

Abstract

The correlation between pairs of repeated measures influences the estimation of the within-subject fixed
factor effect. Bayesian approach considers the correlations as random in reality unlike in classical approach where they are assumed constants. Multivariate Wishart distribution is assumed prior for the covariance structure of the measurements, but this distribution is influenced by the scale matrix parameter. This study investigates the effect of three scale matrices namely the Identity matrix (ID), Variance Component matrix (VC) and Compound Symmetry matrix (SC) on the distribution and estimates of model under the Bayesian framework. Simulated data set for different sample sizes and a real repeated measures data set were both analysed for the three covariance structure models and comparisons of the models were made using deviance information criterion (DIC) and residual sum of squares (RSS). The results from the simulation study indicate that the data-based VC and SC prior specifications performed better compared to the ID, only in small sample size situations, as all three converge in large sample size. The SC scale matrix fits the real data set better than VC matrix and can be used as suitable prior for Wishart distribution on correlation of measurements in repeated measures data in Bayesian analysis.