Relationships Between the Thurstone,Coombs,and Rasch Approaches to Itenl Scaling

Abstract

Andrich (1978) derived a formal equivalency be tween 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-psychologi cal 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 popula tion. This assumption (1) is rather restrictive, and therefore its empirical validity seems to be low, and (2) seems to contradict the substantial reasoning corro borating 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 equiva lent of the Rasch model is tentatively proposed. Fi nally, the theoretical and practical implications of An drich's and of the present study are discussed.