Kyngdon Andrew
University of New South Wales, Sydney, Australia.
J Appl Meas. 2006;7(3):260-77.
Despite its 55 year presence in the field of mathematical psychology, the theory of unidimensional unfolding remains an enigma for many psychometricians and applied practitioners. This paper is the first of a three part series; and it aims to introduce unidimensional unfolding theory. The paper begins with a simple hypothetical example presenting an idealised distinction between responses to cumulative and unfolding dichotomous items. This followed by an accessible presentation of the theory of unidimensional unfolding as first articulated by Clyde H. Coombs (1950, 1964). The concept of the single peaked preference function (Coombs and Avrunin, 1977) which underpins unfolding theory is then presented. The article then progresses to the class of Rasch (1960) based IRT models developed by Andrich (1995) and Luo (2001). It was shown these models propose arguments not inconsistent with Coombs's (1964) original theory. The presumption of additive structure in psychological attributes was concluded to be the key weakness of the theories of unidimensional unfolding discussed.
尽管单维展开理论在数学心理学领域已存在55年，但对许多心理测量学家和应用实践者来说，它仍是一个谜。本文是一个三部分系列文章中的第一篇，旨在介绍单维展开理论。文章开篇通过一个简单的假设示例，展示了对累积二分项目和展开二分项目的反应之间的理想化区别。接下来以通俗易懂的方式介绍了由克莱德·H·库姆斯（1950年、1964年）首次阐述的单维展开理论。随后介绍了支撑展开理论的单峰偏好函数概念（库姆斯和阿夫鲁宁，1977年）。文章接着探讨了由安德里奇（1995年）和罗（2001年）基于拉施（1960年）开发的IRT模型类别。结果表明，这些模型提出的观点与库姆斯（1964年）的原始理论并不矛盾。心理属性中加法结构的假设被认为是所讨论的单维展开理论的关键弱点。
