Bayesian model selection for constrained multivariate normal linear models

Abstract

The expectations that researchers have about the structure in the data can often be formulated in terms of equality constraints and/or inequality constraints on the parameters in the model that is used. In a (M)AN(C)OVA model, researchers have expectations about the differences between the (adjusted) group means; in a repeated measures model, expectations can be stated between the measuremenet means over time; and in a (multivariate) regression model, expectations can be stated between the (standardized) regression coefficients. Based on different theories, different expectations can be formulated into a set of competing equality and inequality constrained models. The researcher is then interested which model receives most support from the data. This dissertation explores how the Bayes factor, a Bayesian model selection, can be used for this purpose.