gorica: An R Package to Evaluate Informative Hypotheses

This manuscript is currently under review in the Multivariate Behavioral Research (0027-3171/1532-7906) journal with the submission ID 242077517. The manuscript is not the last version of the paper and may not exactly replicate the final document. Please do not copy or cite without author's permission.}The use of informative hypotheses has received considerable attention in psychology. Evaluation of these hypotheses using model selection criteria allows researchers to focus directly on theories (based on the results of previous studies and/or their own expectations). In their simplest form, informative hypotheses contain only equality constraints that can be evaluated by Akaike's information criterion (AIC) in a model selection framework. However, informative hypotheses often have more complex functional forms, including inequality constraints. The generalized order restricted information criterion approximation (GORICA) is an AIC-type information criterion that can be used to evaluate hypotheses containing equality and/or inequality constraints for many statistical models. We discuss and illustrate the evaluation of informative hypotheses for educational psychologists in the context of Poisson regression modeling, multilevel regression modeling, structural equation modeling, and logistic regression modeling. To evaluate hypotheses, the GORICA needs the estimates of (standardized) model parameters and their covariance matrix. We use three methods to estimate these (standardized) parameters and their covariance matrix: maximum likelihood estimation (MLE), nonparametric bootstrapping (NB), and Gibbs sampling (GS). In the online Supplementary material, we demonstrate how to obtain the results presented in this paper using the gorica package in R.