A unidimensional item response model for unfolding responses from a graded disagree-agree response scale

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 studies 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); however, IRT models for unfolding graded responses have not been proposed. A parametric IRT model for unfolding either binary or graded responses is developed here. The graded unfolding model (GUM) is a generalization of Andrich & Luo’s 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 respondents and 15 to 20 six-category items). The applicability of the GUM to common attitude testing situations is 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, unfolding model, unidimensional scaling