This site informs you about the research output with respect to two information criteria that can evaluate theory-based hypotheses: GORIC and GORICA.
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: µA > µB > µPlacebo); or number of children is a stronger predictor for happiness than income (in a regression model with standardized parameters: βNC > βInc). 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 approximation 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.
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.).
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.