A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

中文翻译：

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基于分数的测量不变性检查项目响应理论中的贝叶斯最大后验估计。

近年来提出了一系列基于分数的测试，用于评估项目反应理论 (IRT) 的几个模型中模型参数的不变性。这些测试最初是在最大似然框架中开发的。本研究讨论了贝叶斯最大后验估计和多组 IRT 模型的类似测试。我们提出了两类统计检验，它们基于使用合并方差法的近似值，或基于基于渐近结果的模拟方法。通过模拟研究评估了由此产生的测试，该模拟研究调查了它们对关于两参数和三参数逻辑模型中分类或连续人协变量的差异项目功能的敏感性。