Model Discrimination in Meta - Analysis - ABayesian

In wanting to summarise evidence from a number of studies a variety of statistical methods have been proposed. Of these the most widely used is the so-called xed effect model in which the individual studies are estimating a single, but unknown, overall population e ect. When there is `considerable' heterogeneity, in terms of the e ect sizes, between the studies the use of a random e ect model has been advocated in which each individual study is assumed to be estimating its own, unknown, true e ect. Discrimination between xed and random e ect models has been advocated by means of a 2 test for heterogeneity, which it is accepted has low statistical power. Recent interest has been shown in the use of Bayes Factors as an alternative. The use of Bayes factors is illustrated using a number of previously published meta-analyses in which there are varying degrees of heterogeneity. It is shown how the use of Bayes Factors leads to a more intuitive assessment of the evidence in favour of the various models than conventional Classical techniques. Their extension to the case when there are potentially important covariates is also considered within the framework of a GLMM. Abbreviated Title: Bayesian Model Discrimination