The asymptotic posterior normality of the latent trait for polytomous IRT models

Chang and Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous IRT models. This paper presents an extention of their results to polytomous IRT models in a fairly straightforward manner. In addition, a global information function is defined, and the relationship between the global information function and the currently used information functions is discussed. An information index that combines both the global and local information is proposed for adaptive testing applications.This research was partially supported by Educational Testing Service Allocation Project No. 79424. The author wishes to thank Charles Davis, Xuming He, Frank Jenkins, Spence Swinton, William Stout, Ming-Mai Wang, and Zhiliang Ying for their helpful comments and discussions. The author particularly wishes to thank the Editor, Shizuhiko Nishisato, the Associate Editor, and three anonymous reviewers for their thoroughness and thoughtful suggestions.