Generalization of the order-restricted information criterion for multivariate normal linear models

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 R θ ≤ 0 , where θ is a vector of k group means and R a c m × k 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: R θ ≤ r , where θ is a vector of length tk, r a vector of length cm, and R a c m × tk matrix of full rank (when r ≠ 0 ). At the end, we illustrate that the goric is easy to implement in a multivariate regression model.