THE GRADED UNFOLDING MODEL: A UNIDIMENSIONAL ITEM RESPONSE MODEL FOR UNFOLDING GRADED RESPONSES

Binary or graded disagree‐agree responses to attitude items are often collected for the purpose of attitude measurement. Although such data are sometimes analyzed with cumulative measurement models, recent investigations suggest that unfolding models are more appropriate (Roberts, 1995; Van Schuur & Kiers, 1994). Advances in item response theory (IRT) have led to the development of several parametric unfolding models for binary data (Andrich, 1988; Andrich & Luo, 1993; Hoijtink, 1991), but IRT models for unfolding graded responses have not been addressed in the psychometric literature. A parametric IRT model for unfolding either binary or graded responses was developed in this study. The model, called the graded unfolding model (GUM), is a generalization of Andrich & Luo's (1993) hyperbolic cosine model for binary data. A joint maximum likelihood procedure was implemented to estimate GUM parameters, and a subsequent recovery simulation showed that reasonably accurate estimates could be obtained with minimal data demands (e.g., as few as 100 subjects and 15 to 20 6‐category items). The applicability of the GUM to common attitude testing situations was illustrated with real data on student attitudes toward capital punishment. Index terms: attitude measurement, graded unfolding model, hyperbolic cosine model, ideal point process, item response theory, Likert scale, Thurstone scale, unidimensional scaling, unfolding model .