Multidimensional modeling with unidimensional approximations

Abstract

This paper advances nonparametric multidimensional item response theory by reporting experimental results on the use of nonmetric multidimensional scaling (MDS) to synthesize a multidimensional model from several approximating one-dimensional models. A two-dimensional simulation data set contains items in which the two-component traits combine linearly (dominance model items) and items in which the two-component traits combine quadratically (ideal point items). Several unidimensional approximations of the two-dimensional model were obtained by running unidimensional estimation software on the simulated data set. The graphs reconstructed from MDS of the unidimensional approximations at selected points clearly separate dominance items from ideal point items, and also various types of dominance or ideal point models. MDS also succeeded in determining the dimensionality of the simulation model items from the observable item responses.