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≤0$R\theta \le 0$, where θ$\theta$ is a vector of k group means and R   a _cm×k$c_m\times k$ 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≤r$R\theta \le r$, where θ$\theta$ is a vector of length tk, r a vector of length c_m, and R   a _cm×tk$c_m\times \mathit{tk}$ matrix of full rank (when r≠0$r\ne 0$). At the end, we illustrate that the goric is easy to implement in a multivariate regression model.