Previous studies indicated that the assumption of logistic form of parametric item response functions (IRFs) is violated often enough to be worth checking. Using nonparametric item response theory (IRT) estimation methods with the posterior predictive model checking method can obtain significance probabilities of fit statistics in a Bayesian framework by accounting for the uncertainty of the parameter estimation and can indicate the location and magnitude of misfit for an item. The purpose of this study is to check the performance of the Bayesian nonparametric method to assess the IRF fit of parametric IRT models for mixed-format tests and compare it with the existing bootstrapping nonparametric method under various conditions. The simulation study results show that the Bayesian nonparametric method can detect misfit items with higher power and lower type I error rates when the sample size is large and with lower type I error rates compared with the bootstrapping method for the conditions with nonmonotonic items. In the real-data study, several dichotomous and polytomous misfit items were identified and the location and magnitude of misfit were indicated.

中文翻译：

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使用贝叶斯非参数项响应函数估计来检查参数模型拟合。

先前的研究表明，经常违反逻辑形式的参数项响应函数（IRF）的假设，因此值得检查。将非参数项目响应理论（IRT）估计方法与后验预测模型检查方法结合使用，可以通过考虑参数估计的不确定性来获得贝叶斯框架中拟合统计的显着概率，并且可以指示项目不匹配的位置和大小。这项研究的目的是检查贝叶斯非参数方法的性能，以评估用于混合格式测试的参数IRT模型的IRF拟合，并将其与现有的自举非参数方法在各种条件下进行比较。仿真研究结果表明，与自举法相比，对于非单调项目，当样本量较大且I型错误率较低时，贝叶斯非参数方法可以检测出具有较高功效和I型错误率的失配项目。在实际数据研究中，确定了两个二分法和多分法不匹配项，并指出了不匹配的位置和大小。