Comparison of Different Bandwidth Determination Methods in Kernel Equating

Abstract

The study aims to compare the presented methods for determining the bandwidth parameter in the kernel equating method on a real data set. A bandwidth parameter needs to be determined when kernel equating is used to equate two test forms. The bandwidth parameters determine the smoothness of the continuousized score distributions, so their effect on equating results is inevitable. Gaussian Kernel, Logistic Kernel and Uniform Kernel methods were used for bandwidth selection and the results were compared according to the Percentage Relative Error (PRE), the Standard Error and the Standard Error of Equating Difference (SEED). The findings of the study show that the three different approaches to minimizing the penalty function have similar results. Although the standard errors of the equated scores obtained with the uniform kernel method were slightly smaller, the results were almost the same as the other two approaches. When the three equating methods are compared according to the percent relative error, the distribution obtained from Gaussian kernel equating is more consistent with the population distribution.