Bayesian Testing of Scientific Expectations under Multivariate Normal Linear Models

Abstract

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated measures analysis. Statistical criteria for a model selection problem where models may have equality as well as order constraints on the model parameters based on scientific expectations are limited however. This paper presents a default Bayes factor for this inference problem using fractional Bayes methodology. Group specific fractions are used to properly control prior information. Furthermore the fractional prior is centered on the boundary of the constrained space to properly evaluate order-constrained models. The criterion enjoys various important properties under a broad set of testing problems. The methodology is readily usable via the R package ‘BFpack’. Applications from the social and medical sciences are provided to illustrate the methodology.