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

Journal of applied measurement Pub Date : 2018-01-01
Perman Gochyyev, Mark Wilson
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Abstract

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.

拉希传统中的等级和高阶因子结构:一种说教。
在本文中,我们考虑了层次和高阶因子模型以及它们之间的关系,特别是我们使用Rasch模型来重点探索这些模型。我们从Rasch建模的角度介绍了这些模型,它们的相似性和/或差异,并讨论了它们在各种环境中的使用。这项工作的一个动机是,在双参数逻辑模型(2PL)方法中,等效模型之间的某些众所周知的相似性和差异性并不适用于Rasch建模传统。另一个动机是,这些模型的潜在用途有一些模糊,我们试图澄清这些用途。在最近的项目反应理论(IRT)文献中,这些模型的估计主要是使用贝叶斯框架提出的:在这里,我们展示了使用传统的最大似然方法来使用这些模型。我们还展示了如何重新参数化这些模型,这在某些情况下可以改善估计和收敛性。这些可选的参数化在将2PL模型的建议“翻译”到Rasch传统中也很有用(因为这些建议涉及对项目区分的解释,这在Rasch传统中需要是统一的)。还可以使用其他参数化来澄清这些模型之间的关系。我们讨论了这些模型对多维度和测试效应建模的使用,并将所获得的解的解释与多维Rasch模型的解释进行了比较-这是Rasch传统中用于计算多维度的一种更常见的方法。我们使用部分信用模型来演示这些模型的使用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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