The application of an unfolding model of the PIRT type to the measurement of attitude

Abstract

Unfolding data for unidimensional variables constructed from direct responses (e.g., agreement or disagreement) are characterized by single peaked functions involving the locations of each person and each stimulus. A continuous discrirninal process, of the form postulated by Thurstone when he proposed his Law of Comparative Judgment, is suggested. This process is transformed to a qualitative dichotomous response in which the probability of endorsement is governed by the square of the distance between the locations of the person and the stimulus. Maximum likelihood estimates of the parameters are derived, and it is shown that the information associated with any response is a bimodal function of the difference between the person and stimulus locations. The feasibility of parameter estimation is demonstrated with a limited simulation study. The model is applied to a set of statements designed to measure attitudes toward capital punishment and scaled by the methods of Thurstone. The responses conformed to the unfolding mechanism, and the scale values of the statements are statistically equivalent to those obtained by Thurstone’s methods. Index terms: Attitude measurement, Developmental data, Discriminal process, Item response theory, Person response theory, Thurstone scaling, Unfolding data, Unidimensional scaling.