A Recursive Algorithm for IRT Weighted Observed Score Equating

Abstract

There are various reasons for placing different weights on items of test forms such as increasing test reliability or validity and improving measurement precision. Different weighting schemes have been used to accommodate different purposes under different testing situations. However, when the items are weighted, the question is how to equate the test forms containing those weighted items. Under IRT, there are two commonly used equating methods—IRT true score equating and IRT observed score equating. Applying the weights on items to IRT true score equating is straightforward and the software WITSE (Chien and Shin, WITSE: A program for weighted IRT true score equating, Version 1.0. Iowa City, IA: Pearson, 2008) had been specifically developed for weighted scores using IRT true score equating. Yet, currently, there is no procedure or algorithm available for the IRT weighted observed score equating due to the great complexity augmented by imposing weights on items. The regular IRT observed score equating constructs the estimated observed score distributions for two test forms, which are typically obtained using recursive algorithm. However, when items have different weights, the recursive algorithm is no longer feasible. Therefore, an extended recursive algorithm based on the recursive algorithm is proposed in this paper to construct the estimated observed score distribution and is illustrated with a real data set.