IRT Information Function of Polytomously Scored Items under the Graded Response Model

Abstract

Computerized adaptive testing(CAT) is one of the ultimate areas in the field of item response theory(IRT).Many high stake tests,such as GRE and TOEFL,have their CAT versions. Item selection strategy is the core content of CAT.And item information function(IIF) always is the important index of item selection.Although item information of dichotomously scored items has been extensively studied,item information of polytomously scored items receives much less attention. However,due to the advantages inbred in Computerized adaptive testing(CAT) with polytomously scored items,it gains more and more attention now.But the item selection strategies implemented under such situations are not systematically proved to be efficient.Many researchers use the degree of closeness between trait level and the average of item category parameters as the index of item selection strategy,or other strategies such as the degree of closeness between trait level and the median of item category parameters,etc. Up to now,seldom research had systematically concerned about the inherent relationship between the trait level and item category parameters under polytomously scored item types,and its effect on item information. The primary purpose of this research is to systematically investigate the relations of item information to item category parameters and subject trait levels. In this study,we simulated 121 trait values that distributed uniformly between the ranges of-3 to 3.Also,we simulated 504 sets of item parameters,with 4 sets of discrimination parameters which separately matched the 126 sets of difficulty parameters.Each item is graded in terms of 5 categories with differential degrees of difficulty. Based on the results of item information of simulated data,we find that the trait value that correspondence to the maximum item information matches the difficulty parameter group with high-frequency item categories.We call this principal as "item category parameter priority rule".Such principle is very different from the previous item selection strategies under computerized adaptive testing situations. The results of this research will be very useful for the construction of computerized adaptive testing with polytomously scored items.