## 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 H_{0}: 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 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 ≥ r_{2}, with β a vector of length tk, R_{1} a c_{m1} × tk matrix,r1 a vector of length c_{m1}, R_{2} a c_{m2} × tk matrix, and r_{2} a vector of length c_{m2}. It should be noted that [R_{1}^{T}, R_{2}^{T}]^{T} should be of full rank when [R_{1}^{T}, R_{2}^{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.

Original language | English |
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Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Journal of Statistical Software |

Volume | 54 |

Issue number | 8 |

DOIs | |

Publication status | Published - Sept 2013 |

## Keywords

- Fortran 90
- Inequality constraint
- Model selection
- Order restriction
- R
- Regression model