Testing equality of regression coefficients in heteroscedastic normal regression models

This article addresses the problem of testing whether the vectors of regression coefficients are equal for two independent normal regression models when the error variances are unknown. This problem poses severe difficulties both to the frequentist and Bayesian approaches to statistical inference. In the former approach, normal hypothesis testing theory does not apply because of the unrelated variances. In the latter, the prior distributions typically used for the parameters are improper and hence the Bayes factor-based solution cannot be used.We propose a Bayesian solution to this problem in which no subjective input is considered. We first generate “objective” proper prior distributions (intrinsic priors) for which the Bayes factor and model posterior probabilities are well defined. The posterior probability of each model is used as a model selection tool. This consistent procedure of testing hypotheses is compared with some of the frequentist approximate tests proposed in the literature.