An introduction to the theory of unidimensional unfolding

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.