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Hierarchical and Higher-Order Factor Structures in the Rasch Tradition: A Didactic

机译：Rasch传统中的分层和高阶因子结构：一个教学法

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In this paper, we consider hierarchical and higher-order factor models and the relationship between them, and, in particular, we use Rasch models to focus on the exploration of these models. We present these models, their similarities and/or differences from within the Rasch modeling perspective and discuss their use in various settings. One motivation for this work is that certain well-known similarities and differences between the equivalent models in the two-parameter logistic model (2PL) approach do not apply in the Rasch modeling tradition. Another motivation is that there is some ambiguity as to the potential uses of these models, and we seek to clarify those uses. In recent work in the Item Response Theory (IRT) literature, the estimation of these models has been mostly presented using the Bayesian framework: here we show the use of these models using traditional maximum likelihood methods. We also show how to re-parameterize these models, which in some cases can improve estimation and convergence. These alternative parameterizations are also useful in "translating" suggestions for the 2PL models to the Rasch tradition (since these suggestions involve the interpretation of item discriminations, which are required to be unity in the Rasch tradition). Alternative parameterizations can also be used to clarify the relationship among these models. We discuss the use of these models for modeling multidimensionality and testlet effects and compare the interpretation of the obtained solutions to the interpretation for the multidimenisional Rasch model - a more common approach for accounting multidimensionality in the Rasch tradition. We demonstrate the use of these models using the partial credit model.
机译：在本文中，我们考虑了层次和高阶因子模型及其之间的关系，特别是，我们使用Rasch模型来重点研究这些模型。我们从Rasch建模角度介绍这些模型，它们的相似性和/或差异，并讨论它们在各种环境中的使用。进行这项工作的动机是，两参数对数模型（2PL）方法中等效模型之间的某些众所周知的异同在Rasch建模传统中不适用。另一个动机是对于这些模型的潜在用途存在一些歧义，我们试图澄清这些用途。在项目响应理论（IRT）文献的最新工作中，这些模型的估计大部分是使用贝叶斯框架进行的：在这里，我们展示了使用传统最大似然方法对这些模型的使用。我们还将展示如何重新参数化这些模型，在某些情况下可以改善估计和收敛。这些替代参数化在将2PL模型“翻译”为Rasch传统的建议中也很有用（因为这些建议涉及对项目歧视的解释，这在Rasch传统中需要统一）。也可以使用其他参数化来阐明这些模型之间的关系。我们讨论了使用这些模型对多维和睾丸效应进行建模的方法，并将获得的解决方案的解释与多维Rasch模型的解释进行了比较，这是Rasch传统中解决多维问题的一种更为常见的方法。我们使用部分信用模型演示了这些模型的使用。

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