Generalization of the Order-Restricted Information Criterion for Multivariate Normal Linear Models.

Abstract

The generalized order-restricted information criterion (goric) is a model selection criterion which can, up to now, solely be applied to the analysis of variance models and, so far, only evaluate restrictions of the form , where is a vector of k group means and R a matrix. In this paper, we generalize the goric in two ways: (i) such that it can be applied to t-variate normal linear models and (ii) such that it can evaluate a more general form of order restrictions: , where is a vector of length tk, r a vector of length cm, and R a matrix of full rank (when ). At the end, we illustrate that the goric is easy to implement in a multivariate regression model.