The generalized order-restricted information criterion (GORIC) is a generalization of the Akaike information criterion such that it can evaluate hypotheses that take on specific, but widely applicable, forms (namely, closed convex cones) for multivariate normal linear models. It can examine the traditional hypotheses H0: β1,1 = = βt,k and Hu: β1,1,..., βt,k and hypotheses containing simple order restrictions Hm: β1,1 ≥... ≥ βt,k, where any "≥" may be replaced by "=" and m is the model/hypothesis index; with βh,j the parameter for the h-th dependent variable and the j-th predictor in a t-variate regression model with k predictors (which might include the intercept). But, the GORIC can also be applied to restrictions of the form Hm: R1β = r1; R2β ≥ r2, with β a vector of length tk, R1 a cm1 × tk matrix,r1 a vector of length cm1, R2 a cm2 × tk matrix, and r2 a vector of length cm2. It should be noted that [R1T, R2T]T should be of full rank when [R1T, R2T]T ≠ 0. In practice, this implies that one cannot examine range restrictions (e.g., 0 < β1,1 < 2 or β1,2 < β1,1 < 2β1,2) with the GORIC. A Fortran 90 program is presented, which enables researchers to compute the GORIC for hypotheses in the context of multivariate regression models. Additionally, an R package called goric is made by Daniel Gerhard and the first author.
Kuiper, R. M., & Hoijtink, H. (2013). A fortran 90 program for the generalized order-restricted information criterion. Journal of Statistical Software, 54(8), 1–19. https://doi.org/10.18637/jss.v054.i08