Wiberg M., Gonzalez J., von Davier A.A. Generalized Kernel Equating with Applications in R

Boca Raton: CRC Press, 2025. — 267 p.Generalized Kernel Equating is a comprehensive guide for statisticians, psychometricians, and educational researchers aiming to master test score equating. This book introduces the Generalized Kernel Equating (GKE) framework, providing the necessary tools and methodologies for accurate and fair score comparisons.The book presents test scores equating as a statistical problem and covers all commonly used data collection designs. It details the five steps of the GKE framework: pre-smoothing, estimating score probabilities, continuation, equating transformation, and evaluating the equating transformation. Various smoothing strategies are explored, including log-linear models, item response theory models, beta4 models, and discrete kernel estimators. The estimation of score probabilities when using IRT models is described and Gaussian kernel continuation is extended to other kernels such as uniform, logistic, Epanechnikov, and adaptive kernels. Several bandwidth selection methods are described. The kernel equating transformation and its variants are defined, and both equating-specific and statistical measures for evaluating equating transformations are included. Real data examples, guiding readers through the GKE steps with detailed R code and explanations are provided. Readers are equipped with advanced knowledge and practical skills for implementing test score-equating methods.Different equating methods are described throughout this book, and illustrations are given in Chapters 9 and 10. A unique feature of this book compared with the von Davier et al. book is that R code is provided for the described equating methods. Essentially, we have used the R packages equate, which implements both KE and IRT KE, and SNSequate, which implements both traditional and KE methods.Other R packages are used for models and methods that are helpful in particular stages for some of the equating methods. When implementing smoothing with discrete kernels, we utilized the R package SNSequate. The functions within this package are built on top of functions from the Ake package. To perform IRT KE, the packages ltm and mirt are used to estimate the IRT models of interest. Finally, psych is used to examine the IRT model fit.The book is divided into three parts. The first part, which includes this chapter and Chapter 2, introduces the definitions and the basic elements of the generalized kernel equating (GKE) framework. The second part, which consists of Chapters 3 – 8, is focused on the GKE framework. More specifically, it involves smoothing, estimation of score probabilities, the continuation of the test score distributions through the use of convolutions, bandwidth selection for the kernels, the equating transformation, and the evaluation of the equating transformation. The third part of the book (Chapters 9 and 10) describes how some of the methodology presented in the previous chapters can be applied to empirical examples, what practical considerations need to be made, and how R code can be used.The book concludes with two appendices. Appendix A contains instructions on the installation of R, a list of R packages with version numbers used within the book, as well as a brief description of how to read test data. Appendix B describes which R packages can be used to perform the different steps in GKE and also refers to where different examples can be found.