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

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