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