Selection of unidimensional scales from a multidimensional item bank in the polytomous Mokken IRT model

Abstract

An automated item selection procedure for selecting unidimensional scales of polytomous items from multidimensional datasets is developed for use in the context of the Mokken item response theory model of monotone homogeneity (Mokken & Lewis, 1982). The selection procedure is directly based on the selection procedure proposed by Mokken (1971, p. 187) and relies heavily on the scalability coefficient H (Loevinger, 1948; Molenaar, 1991). New theoretical results relating the latent model structure to H are provided. The item selection procedure requires selection of a lower bound for H. A simulation study determined ranges of H for which the unidimensional item sets were retrieved from multidimensional datasets. If multidimensionality is suspected in an empirical dataset, well-chosen lower bound values can be used effectively to detect the unidimensional scales. Index terms: item response theory, Mokken model, multidimensional item banks, nonparametric item response models, scalability coefficient H, test construction, unidimensional scales.