  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 procedures for model selection where
the models may have equality and order constraints on the model parameters of
interest are limited however. This paper presents a default Bayes factor for
this model selection problem. The default Bayes factor is based on generalized
fractional Bayes methodology where different fractions are used for different
observations and where the default prior is centered on the boundary of the
constrained space under investigation. First, the method is fully automatic and
therefore can be applied when prior information is weak or completely
unavailable. Second, using group specific fractions, the same amount of
information is used from each group resulting in a minimally informative
default prior having a matrix Cauchy distribution, resulting in a consistent
default Bayes factor. Third, numerical computation can be done using
parallelization which makes it computationally cheap. Fourth, the evidence can
be updated in a relatively simple manner when observing new data. Fifth, the
selection criterion can be applied relatively straightforwardly in the presence
of missing data that are missing at random. Applications for the social and
behavioral sciences are used for illustration.
