The Problem With the Step Metaphor for Polytomous Models for Ordinal Assessments
The Problem With the Step Metaphor for Polytomous Models for Ordinal Assessments
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序数评估的多分模型的步骤隐喻问题
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
D. Andrich
中科院分区：
文献类型：
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作者：
D. Andrich
P恩菲尔德（2014）的“多分类项目反应理论模型的教学模块”从对二分类反应模型的回顾开始。他将这些称为多分类IRT模型的构建块：阶跃函数。这些模型的数学和它们与多分类模型的相互关系是正确的。不幸的是，他用来解释有序范畴的两类最常用的多分类模型的二分反应的步骤特征与这些模型的数学结构不相容。这两类模型在彭菲尔德的论文中被称为相邻类别模型和累积模型。在最好的情况下，从采取步骤的动态意义上来看，步骤隐喻导致对模型的肤浅理解，仅仅是对数据的描述;在最坏的情况下，它导致对模型的误解，以及如何使用它们来评估类别的经验排序是否与预期的排序一致。本文的目的是解释为什么步骤隐喻与这两种模型都不兼容，并总结每种模型的不同过程。它还显示，与具体的例子，这些模型之一，可以应用于更好地理解有序类别的评估。
P enfield’s (2014) “Instructional Module on Polytomous Item Response Theory Models” begins with a review of dichotomous response models. He refers to these as The Building Blocks of Polytomous IRT Models: The Step Function. The mathematics of these models and their interrelationships with the polytomous models is correct. Unfortunately, the step characterization for dichotomous responses, which he uses to explain the two most commonly used classes of polytomous models for ordered categories, is incompatible with the mathematical structure of these models. These two classes of models are referred to in Penfield’s paper as adjacent category models and cumulative models. At best, taken in the dynamic sense of taking a step, the step metaphor leads to a superficial understanding of the models as mere descriptions of the data; at worst it leads to a misunderstanding of the models and how they can be used to assess if the empirical ordering of the categories is consistent with the intended ordering. The purpose of this note is to explain why the step metaphor is incompatible with both models and to summarize the distinct processes for each. It is also shows, with concrete examples, how one of these models can be applied to better understand assessments in ordered categories.