Multidimensional Item Response Theory models for practical application in large tests designed to measure multiple constructs.. (2017)
In this project, we propose to extend and spread the Multidimensional Item Response Theory (MIRT) models, by introducing and developing new models, based on some of those developed for the unidimensional case. Furthermore, we will study the problem where one item could be measuring more than one construct. The project has been designed to attack several problems existing when a large test is thought to measure more than one construct, and it is applied to a big population. Examples of such tests are those applied by Unversidad Nacional and ICFES. Specifically, we propose the development of MIRT models for including random effects in the item parameters for modeling the differential functioning of the items in the presence of several populations; the modeling of longitudinal data in the case of multidimensional data in tests that are repeated in the time and the introduction of latent regressions for explaining the responses of multidimensional tests by means of explanatory variables based on available socio-demographic information of the responders. Additionally, we propose the introduction of some statistical descriptive tools for detecting the dimensionality of the latent traits and for confirmatory analysis. We propose not only the theoretically development of the models, but also, their implementation in a package for the R statistical system.