Comparison of Kernel Equating and Kernel Local Equating in Item Response Theory Observed Score Equating

Abstract

The present study aims to compare the Kernel equating and Kernel local equating methods in observed score equating. Functions and error estimates regarding the difference between raw and equated scores and the scores equated by Stocking-Lord and Haebara true-score equating methods in Kernel local equating and Kernel equating were examined in Item Response Theory Observed Score Equating. Therefore, 5, 10, and 15 external anchor items were used, and scores were obtained from two forms based on the 2PL model. R (version 3.5.3.) programming software was used for IRT assumptions, item parameters, calibration, and equating analyses. The results revealed that Stocking-Lord and Haebara true-score equating methods yielded similar results. Moreover, if the equating method is the same, estimation errors decreased when the number of anchor items increased. The mean scores obtained by Kernel equation 5 and 15 anchor items were lower than Kernel local equating, while means of Kernel equating of 10 anchor items were higher. As the number of items increased, estimation errors decreased, and Kernel local equating revealed the lowest errors in the medium score scale. Kernel equating can be used based on the related ability level if the individual’s ability distribution is known.