COMPARING ALTERNATIVE KERNELS FOR THE KERNEL METHOD OF TEST EQUATING: GAUSSIAN, LOGISTIC, AND UNIFORM KERNELS

Abstract

ABSTRACTThe kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile‐like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile‐rank, equating method carries out the continuization step by linear interpolation, in principle the kernel equating methods could use various kernel smoothings to replace the discrete score distributions.This paper expands the work of von Davier et al. (2004) in investigating alternative kernels for equating practice. To examine the influence of different kernel functions on the equating results, this paper focuses on two types of kernel functions: the logistic kernel and the continuous uniform distribution (known to be the same as the linear interpolation). The Gaussian kernel is used for reference. By employing an equivalent‐groups design, the results of the study indicate that the tail properties of kernel functions have great impact on the continuized score distributions. However, the equated scores based on different kernel functions do not vary much, except for extreme scores.The results presented in this paper not only support the previous findings on the efficiency and accuracy of the existing continuization methods, but also enrich the information on observed‐score equating models.