Ludwig-Maximilians-Universität München, Akademiestraße 1, 80799, Munich, Germany.
Psychometrika. 2022 Dec;87(4):1238-1269. doi: 10.1007/s11336-022-09865-7. Epub 2022 Apr 27.
A comprehensive class of models is proposed that can be used for continuous, binary, ordered categorical and count type responses. The difficulty of items is described by difficulty functions, which replace the item difficulty parameters that are typically used in item response models. They crucially determine the response distribution and make the models very flexible with regard to the range of distributions that are covered. The model class contains several widely used models as the binary Rasch model and the graded response model as special cases, allows for simplifications, and offers a distribution free alternative to count type items. A major strength of the models is that they can be used for mixed item formats, when different types of items are combined to measure abilities or attitudes. It is an immediate consequence of the comprehensive modeling approach that allows that difficulty functions automatically adapt to the response distribution. Basic properties of the model class are shown. Several real data sets are used to illustrate the flexibility of the models.
提出了一个全面的模型类，可用于连续、二项、有序分类和计数类型的响应。项目的难度由难度函数来描述，这些函数替代了通常在项目反应模型中使用的项目难度参数。它们关键地决定了响应分布，使得模型在覆盖的分布范围方面非常灵活。该模型类包含了几个广泛使用的模型，如二项式 Rasch 模型和分级响应模型作为特例，允许简化，并为计数类型项目提供了一种无分布的替代方案。这些模型的一个主要优势是，它们可以用于混合项目格式，当不同类型的项目组合起来测量能力或态度时。这种全面的建模方法可以自动适应响应分布，这是模型的一个重要特点。该模型类的基本性质得到了展示。几个真实的数据集被用来说明模型的灵活性。
