Altinisik Yasin, Hessels Roy S, Van Lissa Caspar J, Kuiper Rebecca M
Department of Statistics, Sinop University, Osmaniye Mahallesi, Selanik Caddesi (Kuzey Kampüs), No:52G, 57000, Sinop, Türkiye.
Experimental Psychology, Helmholtz Institute, Utrecht University, Utrecht, The Netherlands.
Behav Res Methods. 2025 Jan 22;57(2):70. doi: 10.3758/s13428-024-02570-6.
Researchers 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.
在列联表的背景下评估基于理论的假设时，研究人员面临不可避免的困难。对数线性模型往往不足以评估此类假设，因为在许多实际应用中，它们无法提供足够的关于单元格概率之间复杂关系的信息。这些模型通常仅使用模型参数之间的等式约束来评估变量之间的关系，而指定基于理论的假设通常还需要不等式约束。此外，高维列联表通常包含低单元格计数和/或空单元格，这使得对数线性模型中的参数估计变得复杂。这些模型中存在许多参数，在评估感兴趣的假设时也会导致解释困难。本研究提出了一种方法，通过同时解决上述每个问题，简化对高维列联表基于理论的假设的评估。使用这种方法，使用关于单元格概率（的函数）的等式和/或不等式约束指定的基于理论的假设，通过AIC型信息准则GORICA进行评估。我们进行了一项模拟研究，以评估GORICA在列联表背景下的性能。两个实证例子说明了该方法的使用。
