Nonparametric item response models provide a flexible framework in psychological and educational measurements. Douglas (2001) established asymptotic identifiability for a class of models with nonparametric response functions for long assessments. Nevertheless, the model class examined in Douglas (2001) excludes several popular parametric item response models. This limitation can hinder the applications in which nonparametric and parametric models are compared, such as evaluating model goodness-of-fit. To address this issue, We consider an extended nonparametric model class that encompasses most parametric models and establish asymptotic identifiability. The results bridge the parametric and nonparametric item response models and provide a solid theoretical foundation for the applications of nonparametric item response models for assessments with many items.

翻译：非参数项目反应模型为心理与教育测量提供了灵活的分析框架。Douglas（2001）建立了一类具有非参数响应函数的长评估模型的渐近可识别性。然而，Douglas（2001）所考察的模型类别排除了若干常用的参数项目反应模型。这一局限性可能阻碍非参数模型与参数模型进行比较的应用场景，例如模型拟合优度评估。为解决该问题，我们考虑了一个包含大多数参数模型的扩展非参数模型类别，并证明了其渐近可识别性。研究结果弥合了参数与非参数项目反应模型之间的鸿沟，为多项目评估中应用非参数项目反应模型提供了坚实的理论基础。