On multidimensional item response theory -- a coordinate free approach

TL;DR

This paper introduces a coordinate-free framework for multidimensional item response theory (MIRT), revealing that all monotonic MIRT models are essentially trivial extensions of univariate IRT models, emphasizing their fundamental similarities.

Contribution

It provides a coordinate-free definition of complex MIRT models and proves that all monotonic MIRT models are trivial extensions of univariate IRT models.

Findings

All monotonic MIRT models are trivial extensions of univariate IRT.

The coordinate-free approach clarifies the structure of MIRT models.

Highlights the fundamental similarity among monotonic MIRT models.

Abstract

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.