A Q3 statistic for unfolding item response theory models:: Assessment of unidimensionality with two factors and simple structure

Although there are many methods available for dimensionality assessment for items with monotone item response functions, there are few methods available for unfolding item response theory models. In this study, a modification of Yen's Q(3) statistic is proposed for the case of these nonmonotone item response models. Through a simulation study, the method demonstrates some promise for use as a test of the hypothesis of unidimensionality and local independence. A positive bias seems to occur in some cases, however. The new statistic appears to have properties that would also make it useful in the construction of dissimilarity measures for use in clustering and multidimensional scaling algorithms. A real data analysis is also provided to demonstrate how the proposed methods could be used in practice.