# GORIC

This site informs you about the research output with respect to two information criteria that can evaluate theory-based hypotheses: GORIC and GORICA.

* Theory-based hypotheses*

Researchers are often interested in *theory-based hypotheses*: for example, medicine A works better than medicine B, which works better than a placebo (in an anova model: µ_{A} > µ_{B} > µ_{Placebo}); or number of children is a stronger predictor for happiness than income (in a regression model with standardized parameters: β_{NC} > β_{Inc}). These theory-driven hypotheses can be evaluated with generalizations of the Akaike information criterion (AIC): the GORIC (Generalized Order-Restricted Information Criterion) and the GORICA (an *a*pproximation of the GORIC). These AIC-like criteria can examine *inequality constraints* / *order restrictions* as in the examples. They evaluate a set of competing hypotheses (which are thus based on expectations as opposed to a set of all possible combinations which are examined when exploring for theories). The GORIC or GORICA then select the best model/hypothesis out of a set.

**1. GORIC**

Currently, the GORIC is applicable to multivariate normal linear models .

In case you are interested in applying the GORIC to evaluate informative hypotheses (also in the context of replicating studies), you might be interested in the following **Postgraduate course** (in July): Theory Based Hypothesis Evaluation Using the P-value, Bayes Factor, and Information Criteria.

GORIC is also a **software package** that calculates the GORIC for traditional and order-restricted hypotheses.

GORIC is licensed under the GNU General Public License Version >=2

**Click here **to download the stand-alone version of GORIC (of Rebecca M. Kuiper).

**Click here** to download GORIC with a Windows user interface (of Rebecca M. Kuiper).

Click here to visit the download page of the R-package for GORIC (of Daniel Gerhard and Rebecca M. Kuiper).

If you use GORIC, you give credits to the developers by **referring to**:

- Kuiper, R. M., & Hoijtink, H. (2013). A Fortran 90 program for the generalization of the order restricted information criterion.
*Journal of Statistical Software, 54*(8)*,*1-19.

Other GORIC literature:

- Kuiper, R.M., Hoijtink, H. and Silvapulle, M.J. (2011). An Akaike type information criterion for model selection under inequality constraints.
*Biometrika, 98,*495-501. doi: 10.1093/biomet/asr002 - Kuiper, R.M., Hoijtink, H. and Silvapulle, M.J. (2012). Generalization of the order restricted information criterion for multivariate normal linear models.
*Journal of Statistical Planning and Inference, 142,*2454-2463. doi: 10.1016/j.jspi.2012.03.007 - Kuiper, Rebecca M., Gerhard, Daniel & Hothorn, Ludwig A. (2014). Identification of the Minimum Effective Dose for Normally Distributed Endpoints Using a Model Selection Approach.
*Statistics in Biopharmaceutical Research*, 6 (1), (pp. 55-66) (12 p.). - Otava, M., Sengupta, R., Shkedy, Z., Lin, D., Pramana, S., Verbeke, T., Haldermans, P., Hothorn, L. A., Gerhard, G., Kuiper, R. M., Klinglmueller, F. and Kasim, A. (2017). IsoGeneGUI – Multiple approaches for dose-response analysis of microarray data using R.
*The R Journal*, 9 (1), (pp. 14-26) (13 p.).

**2. GORICA**

The GORICA can be applied to **a broad range of models**.

Upcoming GORICA literature:

- Yasin Altınısık, Esther Nederhof, Herbert Hoijtink, Albertine J. Oldehinkel, and Rebecca M. Kuiper (unpublished). Evaluation of Inequality Constrained Hypotheses Using a Generalization of the AIC.
- Yasin Altınısık, Roy Hessels, and Rebecca M. Kuiper (unpublished). An AIC-based Information Criterion Evaluating (In)equality Constrained Hypotheses for Contingency Tables.
- Yasin Altınısık and Rebecca M. Kuiper (unpublished). The GORICA Applied: An AIC-Based Information Criterion for Evaluating Informative Hypotheses.