A Unidimensional Item Response Model for Unfolding Responses From a Graded Disagree-Agree Response Scale

Abstract

Binary or graded disagree-agree responses to atti tude items are often collected for the purpose of attitude measurement. Although such data are sometimes ana lyzed with cumulative measurement models, recent studies suggest that unfolding models are more appro priate (Roberts, 1995; van Schuur & Kiers, 1994). Ad vances 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 re sponses is developed here. The graded unfolding model (GUM) is a generalization of Andrich & Luo's hyperbolic cosine model for binary data. A joint maximum likeli hood procedure was implemented to estimate GUM pa rameters, and a subsequent recovery simulation showed that reasonably accurate estimates could be obtained with minimal data demands (e.g., as few as 100 respon dents and 15 to 20 six-category items). The applicability of the GUM to common attitude testing situations is illus trated 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, Thur stone scale, unfolding model, unidimensional scaling.