Application of Faulkenberry (2018) Bayes Factor to a Balanced Two Way Analysis of Variance with Random Effects

Abstract

The Analysis of Variance technique estimates variance components by comparing their mean squares to their expected values. Nevertheless, this method could give variance component estimates that are found outside the parameter space, i.e. negative estimates. In a bid to overcome this deficiency, alternate approaches are essential, and likelihood-based approaches have become common over time. Bayesian techniques have also been proposed and Bayes factors developed for examining various models. We applied the Bayes factor proposed by Faulkenberry (2018) to a Balanced Two Way ANOVA under three (3) cases, namely Case 1: the levels of the two factors are fixed; Case 2: the levels of the two factors are random; and Case 3: the levels of one factor are considered as fixed, while the levels of the other factor are considered as random. We realized that when the levels of the two factors are fixed, the Bayesian conclusion about the variability in the effects is in line with that of a frequentist. But when the same data set was considered to be wholly or partly as sample observations drawn randomly from a given population of interest, the Bayesian conclusion differed slightly from that of the frequentist.

Keywords: Bayes Factor; Bayesian; Frequentist, Fixed; Random.