Relationships between the Thurstone, Coombs, and Rasch approaches to item scaling

Abstract

Andrich (1978) derived a formal equivalency between Thurstone’s Case V specialization of the law of comparative judgment for paired comparisons, with a logistic function substituted for the normal, and the Rasch model for direct responses. The equivalency was corroborated by a specific substantial-psychological interpretation of the Rasch binary item response probability. Studying the relationships between the Thurstone and Rasch models from another perspective than Andrich’s, namely, from a data-theoretical point of view, it appears that the equivalency is based on an implicit assumption with respect to the subject population. This assumption (1) is rather restrictive, and therefore its empirical validity seems to be low, and (2) seems to contradict the substantial reasoning corroborating the Thurstone-Rasch equivalency. It is argued that the Thurstone model cannot be considered the sample-independent pair comparison counterpart of the Rasch model. An alternative pair comparison equivalent of the Rasch model is tentatively proposed. Finally, the theoretical and practical implications of Andrich’s and of the present study are discussed.