A Bayesian Multiple Comparison Procedure for Simple Order-Restricted Mixed Models with Missing Values

Abstract

A Bayesian hierarchical model is developed for multiple comparisons in mixed models with missing values where the population means satisfy a simple order restriction. We employ the Gibbs sampling and Metropolis-within-Gibbs sampling techniques to obtain parameter estimates and estimates of the posterior probabilities of the equality of the mean pairs. The latter estimates are used to test whether any two means are significantly different, and to test the global hypothesis of the equality of all means. The performance of the model is investigated in simulations by means of both multiple imputations and ignoring missingness. We also illustrate the utility of the model in a real data set. The results show that the proposed hierarchical model can effectively unify parameter estimation, multiple imputations, and multiple comparisons in one setting.