# 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-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 courses** (in the summer): “A gentle introduction to Bayesian Statistics” and “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 and (upcoming) articles 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 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:

- 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.). - Heck, D. W., Boehm, U., Böing-Messing, F., Bürkner, P.-C., Derks, K., Dienes, Z., Fu, Q., Gu, X., Karimova, D., Kiers, H., Klugkist, I.,
**Kuiper, R. M.**, Lee, M. D., Leenders, R., Leplaa, H. J., Linde, M., Ly, A., Meijerink-Bosman, M., Moerbeek, M., Mulder, J., Palfi, B., Schönbrodt, F., Tendeiro, J., van den Bergh, D., van Lissa, C. J., van Ravenzwaaij, D., Vanpaemel, W., Wagenmakers, E.-J., Williams, D. R., Zondervan-Zwijnenburg, M., & Hoijtink, H. (in press). A review of applications of the Bayes factor in psychological research.*Psychological Methods*. https://psyarxiv.com/cu43g

**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).

**2. GORICA**

The GORICA can be applied to **a broad range of statistical 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 ** 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**:

- Altınısık, Y., Nederhof, E., Van Lissa, C. J., Hoijtink, H., Oldehinkel, A. J., and Kuiper, R. M. (in press). Evaluation of Inequality Constrained Hypotheses Using a Generalization of the AIC.
- Altınısık, Y., Van Lissa, C. J., and Kuiper, R. M. (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: Altınısık, Y., Van Lissa, C. J., Hessels, R., and Kuiper, R. M. (unpublished). An AIC-based Information Criterion Evaluating (In)equality Constrained Hypotheses for Contingency Tables.
- The reference to the software you use.

Other GORICA literature:

- Kuiper, R. M. (2021). AIC-type theory-based model selection for structural equation models.
*Structural Equation Modeling: A Multidisciplinary*Journal. - Kuiper, R. M. (2021). Evaluating causal dominance of CTmeta-analyzed lagged regression estimates.
*Structural Equation Modeling: A Multidisciplinary*Journal.

**Click here **to download the gorica R function (of Yasin Altınısık) with example files (and Supplementary Material).

**Other GORICA in R**

The GORICA can be applied to the overall standardized estimates of a (longitudinal) cross-lagged model resulting from a meta-analysis (CTmeta). This can be used to quantify the support for, for instance, a causal dominance hypothesis regarding the cross-lagged relationships. Example R code to apply the GORICA on a CTmeta result can be found in R as follows:

*library(devtools)*

*install_github(“rebeccakuiper/CTmeta”)*

*library(CTmeta)*

*?CTmeta*

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

*citation(“gorica”) or [goric function of Vanbrabant & Kuiper in] citation(“restriktor”)**citation(“CTmeta”)*- Kuiper, R. M. and Ryan, O. (2020). Meta-analysis of lagged regression models: A continuous-time approach.
*Structural Equation Modeling: A Multidisciplinary Journal*, 27(3), 396–413. - Kuiper, R. M. (2021). Evaluating causal dominance of CTmeta-analyzed lagged regression estimates.
*Structural Equation Modeling: A Multidisciplinary*Journal.