ON MULTIDIMENSIONAL ITEM RESPONSE THEORY: A COORDINATE‐FREE APPROACH
Tamás Antal · ETS Research Report Series · 2007
ABSTRACT A coordinate‐free definition of complex‐structure multidimensional 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.