Digital Module 29: Multidimensional Item Response Theory Equating

Selection the best Method of Equating Using Anchor-Test Design‎ in Item Response Theory ‎‎

Explaining the problem. The equating process is used to compare the scores of the two different tests with the same theme‎. ‎The goal of this research is finding the best method of equating data using Logistic model. ‎ Method. we are using the data of Ph.D‎. ‎test in Statistic major for two consecutive years 92 and 93‎. ‎For analyzing‎, ‎we are specifically using the tests of Statistics major ...

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...

A Practitioner’s Introduction to Equating with Primers on Classical Test Theory and Item Response Theory

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 ...