TESTING RESTRICTIONS IN NORMAL DATA MODELS USING GIBBS SAMPLING

The problem of testing a set of restrictions R(q)=0 in a complex hierarchical model is considered. We propose a different approach from the standard PO ratio test, which can be viewed as the Bayesian analogous to the classical Wald type test. With respect to the PO ratio, it has the advantage of being easier to implement and, unlike the PO ratio test, it can be computed also when some prior in the hierarchy is diffuse. Several Monte Carlo simulations show that the procedure scores very well both in terms of power and unbiasedness, generally doing as well as the standard PO ratio approach, or even better in cases where the degree of coefficient heterogeneity is not high.