Bayesian multi-way balanced nested MANOVA models with random effects and a large number of the main factor levels

Abstract

This article considers the balanced nested multi-way multivariate analysis of variance (MANOVA) models with random effects and a large number of main factor levels under certain prior assumptions. Two different parametrizations for the MANOVA models with random effects and the corresponding explicit asymptotics are established. The asymptotic approximations are then compared with those obtained from the classical large-sample approximation and Markov chain Monte Carlo method via a balanced nested two-way MANOVA model with random effects. Simulation results demonstrate that our approach is superior to the classical approximation method on estimating the posterior standard deviations of variance component parameters.