On multidimensional item response theory -- a coordinate free approach

Details On multidimensional item response theory -- a coordinate free approach On multidimensional item response theory -- a coordinate free approach

2007-07-19

arxiv.org/abs/0707.2884v1

Electronic Journal of Statistics 2007, Vol. 1, 290-306

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/07-EJS016 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS016

A coordinate system 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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