Bayesian Mixture Model of Extended Redundancy Analysis

Extended redundancy analysis (ERA), a generalized version of redundancy analysis (RA), has been proposed as a useful method for examining interrelationships among multiple sets of variables in multivariate linear regression models. As a limitation of the extant RA or ERA analyses, however, parameters are estimated by aggregating data across all observations even in a case where the study population could consist of several heterogeneous subpopulations. In this paper, we propose a Bayesian mixture extension of ERA to obtain both probabilistic classification of observations into a number of subpopulations and estimation of ERA models within each subpopulation. It specifically estimates the posterior probabilities of observations belonging to different subpopulations, subpopulation-specific residual covariance structures, component weights and regression coefficients in a unified manner. We conduct a simulation study to demonstrate the performance of the proposed method in terms of recovering parameters correctly. We also apply the approach to real data to demonstrate its empirical usefulness.