Multilevel bifactor item response theory (IRT) models are commonly used to account for features of the data that are related to the sampling and measurement processes used to gather those data. These models conventionally make assumptions about the portions of the data structure that represent these features. Unfortunately, when data violate these models' assumptions but these models are used anyway, incorrect conclusions about the cluster effects could be made and potentially relevant dimensions could go undetected. To address the limitations of these conventional models, a more flexible multilevel bifactor IRT model that does not make these assumptions is presented, and this model is based on the generalized partial credit model. Details of a simulation study demonstrating this model outperforming competing models and showing the consequences of using conventional multilevel bifactor IRT models to analyze data that violate these models' assumptions are reported. Additionally, the model's usefulness is illustrated through the analysis of the Program for International Student Assessment data related to interest in science.

中文翻译：

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一种更灵活的贝叶斯多级双因素项响应理论模型

多级双要素项目响应理论（IRT）模型通常用于说明与用于收集那些数据的采样和测量过程有关的数据特征。通常，这些模型对代表这些功能的数据结构部分进行假设。不幸的是，当数据违反这些模型的假设但无论如何都使用这些模型时，可能会得出关于聚类效应的错误结论，并且可能无法检测到潜在的相关维度。为了解决这些常规模型的局限性，提出了一种不做这些假设的更加灵活的多级双因素IRT模型，该模型基于广义的部分信用模型。报告了模拟研究的详细信息，该研究证明了该模型优于竞争模型，并显示了使用常规多级双因子IRT模型分析违反这些模型假设的数据的后果。此外，通过对与科学兴趣有关的国际学生评估计划数据的分析，说明了该模型的有用性。