Bayesian testing of informative hypotheses on (co)variance parameters
10 / 2011 - 09 / 2013
When investigating the effect of a new treatment of depression, researchers will typically quantify the treatment effect as the average change in the subjects? depression scores. However, not only the average change is important for the evaluation of a treatment, but also the variation of the change between subjects is relevant. It is not desirable to have a treatment with a highly varying effect, which for some patients may even be negative. The degree of individual variation can be captured by a variance parameter. Statistical methods for comparing variances, however, are completely underdeveloped. In this project, I will develop methods for testing hypotheses on (co)variances that can be used in the analysis of data from repeated measures studies, within-subject experiments, and multilevel studies. The specific approach adopted in this project will be on the evaluation of informative hypotheses (hypotheses implying inequalities) using a Bayesian testing procedure called Bayes factors. Bayes factors quantify the degree of support for a specific hypothesis (or theory) compared to alternative hypotheses (or theories). User-friendly software will be developed that allows applied researchers who are not familiar with the technical details of Bayesian statistical modelling to test their scientific expectations regarding the within- and between-subject variation.