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Informative Hypotheses

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: 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-type criteria can examine inequality constraints / order restrictions as in the examples above. 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 selects the best model/hypothesis out of a set.

In case the hypotheses in the set do not cover all possible hypothesis (i.e., the whole parameter space), then a fail-safe hypothesis should be included to prevent selecting the best out of a set of weak hypotheses. Preferably, the complement of the hypotheses in the set (i.e., all possible hypotheses except those in the set) should be included, which is currently only available for one hypothesis; otherwise, the unconstrained hypothesis which covers all possible hypothesis (i.e., the whole parameter space) should be included.

Below, you find more information about both information criteria.

 

Course & Workshops

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.

 

Software GORIC & GORICA

1. GORIC

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); the restriktor package can be installed from CRAN.

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.
  • In case of using the complement of a hypothesis: Vanbrabant, L., Van Loey, N., and Kuiper, R. M. (2020). Evaluating a theory-based hypothesis against its complement using an AIC-type information criterion with an application to facial burn injury. Psychological Methods, 25(2), 129–142.
  • The reference to the software you use.

Other GORIC literature:

 

2. GORICA

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 (of Caspar van Lissa, Yasin Altınısık, and Rebecca M. Kuiper); which can be installed from CRAN.

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

  • 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, Caspar van Lissa and Rebecca M. Kuiper (unpublished). The GORICA Applied: An AIC-Based Information Criterion for Evaluating Informative Hypotheses.
  • In case of using the complement of a hypothesis: Vanbrabant, L., Van Loey, N., and Kuiper, R. M. (2020). Evaluating a theory-based hypothesis against its complement using an AIC-type information criterion with an application to facial burn injury. Psychological Methods, 25(2), 129–142.
  • In case of using it for contingency tables: Yasin Altınısık, Caspar van Lissa, Roy Hessels, and Rebecca M. Kuiper (unpublished). An AIC-based Information Criterion Evaluating (In)equality Constrained Hypotheses for Contingency Tables.
  • The reference to the software you use.