Department of Statistics, TU Dortmund University.
Institute of Psychology in Education, University of Münster.
Multivariate Behav Res. 2024 May-Jun;59(3):502-522. doi: 10.1080/00273171.2023.2288577. Epub 2024 Feb 13.
In psychology and education, tests (e.g., reading tests) and self-reports (e.g., clinical questionnaires) generate counts, but corresponding Item Response Theory (IRT) methods are underdeveloped compared to binary data. Recent advances include the Two-Parameter Conway-Maxwell-Poisson model (2PCMPM), generalizing Rasch's Poisson Counts Model, with item-specific difficulty, discrimination, and dispersion parameters. Explaining differences in model parameters informs item construction and selection but has received little attention. We introduce two 2PCMPM-based explanatory count IRT models: The Distributional Regression Test Model for item covariates, and the Count Latent Regression Model for (categorical) person covariates. Estimation methods are provided and satisfactory statistical properties are observed in simulations. Two examples illustrate how the models help understand tests and underlying constructs.
在心理学和教育学中，测试（例如阅读测试）和自我报告（例如临床问卷）会产生计数，但与二值数据相比，相应的项目反应理论 (IRT) 方法还不够发达。最近的进展包括双参数 Conway-Maxwell-Poisson 模型 (2PCMPM)，它推广了 Rasch 的 Poisson 计数模型，具有项目特定的难度、区分度和分散参数。解释模型参数的差异可以为项目构建和选择提供信息，但这方面的关注很少。我们引入了两个基于 2PCMPM 的解释计数 IRT 模型：项目协变量的分布回归测试模型和（分类）个体协变量的计数潜在回归模型。提供了估计方法，并在模拟中观察到令人满意的统计性质。两个示例说明了这些模型如何帮助理解测试和潜在结构。
