Constrained Multidimensional Computerized Adaptive Testing with Polytomously scored items and Shadow Tests.

Abstract

A method is presented for constrained multidimensional computer- ized adaptive testing with polytomously scored items. Constraints are imposed using the Shadow Test approach. It is shown that Posterior Expected Kullback-Leibler divergence of a multidimensional item response theory model is linear in the items, which makes it a suitable as an objective function for item selection in combination with the Shadow Test approach. Simulation studies are presented to illustrate the performance of the proposed method. We conclude that the combination of Posterior Expected Kullback- Leibler divergence and the Shadow Test approach performs well in all simulations. Finally, an R-package implementing the approach is presented.