Graphical Representation of Multidimensional Item Response Theory Analyses

Paradoxical Results in Multidimensional Item Response Theory

In multidimensional item response theory (MIRT), it is possible for the estimate of a subject’s ability in some dimension to decrease after they have answered a question correctly. This paper investigates how and when this type of paradoxical result can occur. We demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of line...

Likelihood and Fairness in Multidimensional Item Response Theory

In multidimensional item response theory, it is possible for the estimate of a subject’s ability in some dimension to decrease after they have answered a question correctly. When this occurs, the fairness of the estimate may be called into question. This paper investigates how and when this form of non-monotonicity occurs. We demonstrate that many response models and statistical estimates can p...

On multidimensional item response theory -- a coordinate free approach

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 ...

Item Response Theory

DOCUMENT RESUME

Tools for graphical representation of multidimensional data in SIAT