Open AccessON MULTIDIMENSIONAL ITEM RESPONSE THEORY: A COORDINATE‐FREE APPROACH
Author(s) -
Antal Tamás
Publication year - 2007
Publication title -
ets research report series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.235
H-Index - 5
ISSN - 2330-8516
DOI - 10.1002/j.2333-8504.2007.tb02072.x
Subject(s) - item response theory , univariate , monotonic function , extension (predicate logic) , point (geometry) , mathematics , algebra over a field , computerized adaptive testing , computer science , mathematical economics , theoretical computer science , calculus (dental) , statistics , multivariate statistics , pure mathematics , psychometrics , mathematical analysis , geometry , medicine , dentistry , programming language
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.