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On Multidimensional Item Response Theory: A Coordinate-Free Approach IRT

Author(s):
Antal, Tamas
Publication Year:
2007
Report Number:
RR-07-30
Source:
ETS Research Report
Document Type:
Report
Page Count:
17
Subject/Key Words:
Multidimensional Item Response Theory (MIRT), Item Response Theory (IRT)

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.

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