TitleKullback-Leibler information in multidimensional adaptive testing: theory and application
Publication TypeBook Chapter
Year of Publication2009
AuthorsWang, C, Chang, H-H
CityD. J. Weiss (Ed.), Proceedings of the 2009 GMAC Conference on Computerized Adaptive Testing.

Built on multidimensional item response theory (MIRT), multidimensional adaptive testing (MAT) can, in principle, provide a promising choice to ensuring efficient estimation of each ability dimension in a multidimensional vector. Currently, two item selection procedures have been developed for MAT, one based on Fisher information embedded within a Bayesian framework, and the other powered by Kullback-Leibler (KL) information. It is well-known that in unidimensional IRT that the second derivative of KL information (also termed “global information”) is Fisher information evaluated atθ 0. This paper first generalizes the relationship between these two types of information in two ways—the analytical result is given as well as the graphical representation, to enhance interpretation and understanding. Second, a KL information index is constructed for MAT, which represents the integration of KL nformation over all of the ability dimensions. This paper further discusses how this index correlates with the item discrimination parameters. The analytical results would lay foundation
for future development of item selection methods in MAT which can help equalize the item exposure rate. Finally, a simulation study is conducted to verify the above results. The connection between the item parameters, item KL information, and item exposure rate is demonstrated for empirical MAT delivered by an item bank calibrated under two-dimensional IRT.