A Fortran 90 Program for the Generalized Order-Restricted Information Criterion

Abstract

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: β_1,1 = … = β_t,k and H_u: β_1,1, …, β_t,k and hypotheses containing simple order restrictions H_m: β_1,1 ≥ … ≥ β_t,k, where any "≥" may be replaced by "=" and m is the model/hypothesis index; with β_h,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 H_m: R₁β = r₁; R₂β ≥ r₂, with β a vector of length tk, R₁ a c_m1 × tk matrix, r₁ a vector of length c_m1, R₂ a c_m2 × tk matrix, and r₂ a vector of length c_m2. It should be noted that [R₁^T, R₂^T]^T should be of full rank when [R₁^T, R₂^T]^T ≠ 0. In practice, this implies that one cannot examine range restrictions (e.g., 0 < β_1,1 < 2 or β_1,2 < β_1,1 < 2β_1,2) 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.