KE is applied to the four major equating designs and to both Chain Equating and Post-Stratification Equating for the Non-Equivalent groups with Anchor Test Design. It will be an important reference for several groups: (a) Statisticians (b) Practitioners and (c) Instructors in psychometric and measurement programs. The authors assume some familiarity with linear and equipercentile test equating, and with matrix algebra.
This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating results. The results of the kernel chained equatings using a large fixed bandwidth were nearly identical to the results from the chained linear equatings whereas the comparisons of the kernel poststratification equatings using a large bandwidth showed differences from both Tucker and Levine observed score equating results, although for most of the score range those differences were small. Similarly, the differences were small for most of the score range in the comparisons of kernel poststratification equatings and kernel chained equatings using the optimal bandwidth with chained equipercentile equatings. (Contains 5 tables and 14 figures.).
This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others.
This study compares the accuracy of NEAT-design IRT true score equating (TIRT) and kernel equating (KE) in different conditions. The relative accuracy of three methods (Stocking-Lord transformation based TIRT (SL TIRT), kernel chain equipercentile equating (KE CE) and kernel post-stratification equating (KE PSE)) are examined in specific and general conditions. Simulated data are used for the analysis. 60 different specific conditions are generated and the relative performances of the methods in each condition are compared using ANOVA. Then the error of each equating line is summarized with RMSD. 180 RMSD values in 60 conditions are categorized into 20 general conditions. RMSD values in each level of the general condition are compared with RMSD. All findings have led to the conclusion that KE CE is the superior equating method for all general and specific conditions. Compared to KE PSE and SL TIRT, it produces more accurate and stable results. Closer examination shows how KE CE is consistently less affected by various adverse conditions, how SL TIRT is more affected, and how KE PSE is drastically affected. Hence, among the three methods, KE CE is preferred over KE PSE and SL TIRT, while SL TIRT is preferred over KE PSE.
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 score equating as a statistical problem and covers all commonly used data collection designs. It details the five steps of the GKE framework: presmoothing, estimating score probabilities, continuization, equating transformation, and evaluating the equating transformation. Various presmoothing 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 continuization is extended to other kernels such as uniform, logistic, epanechnikov and adaptive kernels. Several bandwidth selection methods are described. The kernel equating transformation and variants of it 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 an advanced knowledge and practical skills for implementing test score equating methods.
By providing an introduction to test equating which both discusses the most frequently used equating methodologies and covering many of the practical issues involved, this volume expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking.
