On multidimensional item response theory – a coordinate free approach

Abstract

A coordinate system free definition of complex structure multi-dimensional item response theory (MIRT) for dichotomously scored items is presented. The point of view taken emphasizes the possibilities and subtleties of understanding MIRT as a multidimensional extension of the “classical” unidimensional item response theory models. The main theorem of the paper is that every monotonic MIRT model looks the same; they are all trivial extensions of univariate item response theory. © 2007, Ashdin Publishing. All rights reserved.