The Application of an Unfolding Model of the PIRT Type to the Measurement of Attitude

Abstract

Unfolding data for unidimensional variables con structed from direct responses (e.g., agreement or dis agreement) are characterized by single peaked func tions 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 re sponse in which the probability of endorsement is governed by the square of the distance between the lo cations of the person and the stimulus. Maximum like lihood estimates of the parameters are derived, and it is shown that the information associated with any re sponse 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 capi tal punishment and scaled by the methods of Thur stone. The responses conformed to the unfolding mechanism, and the scale values of the statements are statistically equivalent to those obtained by Thur stone's methods. Index terms: Attitude measure ment, Developmental data, Discriminal process, Item response theory, Person response theory, Thurstone scaling, Unfolding data, Unidimensional scaling.