Informative Hypotheses

Informative Hypotheses

GORIC and GORICA

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 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 for tutorials and example files on using the GORIC and GORICA via 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. doi: 10.18637/jss.v054.i08
  • In case of using the complement of a hypothesis: Vanbrabant, L., Van Loey, N., & 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. https://doi.org/10.1037/met0000238
  • The reference to the software you use (e.g. goric function and restriktor package).

Other GORIC literature:

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).

 

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 tutorials and example files on using the GORIC and GORICA. The R package gorica (of Caspar van Lissa, Yasin Altınısık, and Rebecca M. Kuiper) can be installed from CRAN.

 

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

  • Altınısık, Y., Van Lissa, C. J., Hoijtink, H., Oldehinkel, A. J., and Kuiper, R. M. (2021). Evaluation of inequality constrained hypotheses using a generalization of the AIC. Psychological Methods, 26(5), 599-621. doi: 10.1037/met0000406.
  • 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., & 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. https://doi.org/10.1037/met0000238
  • 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:

Corresponding R scrips: R scripts for SEM and R scripts for CTmeta.

 

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:

  • [goric function of Vanbrabant & Kuiper in] citation(“restriktor”) or citation(“gorica”)
  • 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. doi: 10.1080/10705511.2019.1652613
  • Kuiper, R. M. (2021). Evaluating Causal Dominance of CTmeta-Analyzed Lagged Regression Estimates, Structural Equation Modeling: A Multidisciplinary Journal, 28(6), 951-963. doi: 10.1080/10705511.2020.1823228