Simple Bayesian testing of scientific expectations in linear regression models

Abstract

Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the second predictor, and the second predictor is expected to be larger than the third predictor. The goal is then to test such expectations against competing scientific expectations or theories. In this paper, a simple default Bayes factor test is proposed for testing multiple hypotheses with equality and order constraints on the effects of interest. The proposed testing criterion can be computed without requiring external prior information about the expected effects before observing the data. The method is implemented in R-package called ‘lmhyp’ which is freely downloadable and ready to use. The usability of the method and software is illustrated using empirical applications from the social and behavioral sciences.