Altinisik, YasinHessels, Roy S.Van Lissa, Caspar J.Kuiper, Rebecca M.2025-03-232025-03-2320251554-351X1554-3528https://doi.org/10.3758/s13428-024-02570-6https://hdl.handle.net/11486/4653Researchers face inevitable difficulties when evaluating theory-based hypotheses in the context of contingency tables. Log-linear models are often insufficient to evaluate such hypotheses, as they do not provide enough information on complex relationships between cell probabilities in many real-life applications. These models are usually used to evaluate the relationships between variables using only equality restrictions between model parameters, while specifying theory-based hypotheses often also requires inequality restrictions. Moreover, high-dimensional contingency tables generally contain low cell counts and/or empty cells, complicating parameter estimation in log-linear models. The presence of many parameters in these models also causes difficulties in interpretation when evaluating the hypotheses of interest. This study proposes a method that simplifies evaluating theory-based hypotheses for high-dimensional contingency tables by simultaneously addressing each of the above problems. With this method, theory-based hypotheses, which are specified using equality and/or inequality constraints with respect to (functions of) cell probabilities, are evaluated using an AIC-type information criterion, GORICA. We conduct a simulation study to evaluate the performance of GORICA in the context of contingency tables. Two empirical examples illustrate the use of the method.eninfo:eu-repo/semantics/openAccessAICContingency tablesGORICA(In)equality constraintsTheory-based hypothesesArticle57210.3758/s13428-024-02570-6398437252-s2.0-85216607677Q1WOS:001404746900002Q1