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. Below, you find more information about both information criteria.
In case you are interested in applying the GORIC(A) to evaluate informative hypotheses (also in the context of replicating studies), you might be interested in the following Postgraduate course (in July): Hypothesis testing 3.0 (previously called: Theory Based Hypothesis Evaluation Using the P-value, Bayes Factor, and Information Criteria). We (Herbert Hoijtink and Rebecca M. Kuiper) or I (Rebecca M. Kuiper) can also offer such a workshop on request.
Currently, the GORIC is applicable to multivariate normal linear models .
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 goric (of Daniel Gerhard and Rebecca M. Kuiper).
Click here to visit the tutorial page on using the goric function in the R-package restriktor (of Leonard Vanbrabant and Rebecca M. Kuiper).
If you use GORIC, you give credits to the developers by referring to:
- 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. (2013). A Fortran 90 program for the generalization of the order restricted information criterion. Journal of Statistical Software, 54(8), 1-19.
- The reference to the software you use.
Other GORIC literature:
- 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.
gorica is also a software package that calculates the GORICA for traditional and order-restricted hypotheses.
gorica is licensed under the GNU General Public License Version >=2
Click here to download the gorica R function (of Yasin Altınısık) with example files (and Supplementary Material).
Click here for the R package gorica (in development; of Caspar van Lissa, Yasin Altınısık, and Rebecca M. Kuiper).
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.