Linear Equating for the NEAT Design: A Rejoinder and Some Further Comments

This article presents the authors' rejoinder to commentaries on linear equating and the NEAT design. The authors appreciate the insightful work of the commentary writers. Each has made a number of interesting points, many of which the authors had not considered at all. Before responding to some of those points, the authors reiterate what they see as the main results of their work. First, they developed five distinct linear equating models within a common framework. Second, their results indicate that the choice of relationship between total test scores and anchor test scores can make a big difference in the equating relationships and in the degree of bias in these relationships. Third, they found that when the groups differ in performance, the Levine methods make the largest adjustments, the "Tucker" methods make the smallest adjustments, and the chained linear method makes adjustments that are between these two extremes. Fourth, in developing the model based on a chained linear relationship approach, they generated a derivation of the Levine true-score method that does not explicitly rely on assumptions about true-score relationships and, thereby, avoids the awkward necessity pointed out by Kolen and Brennan (2004, pp. 117-118). Fifth, their results and those of others suggest that the weights used to specify the synthetic population in the parameter substitution methods do not make much difference in how the resulting equating relationships function. Sixth, they suggested that in comparing different linear equating methods in terms of the overall location of the line, the mean intercept is far more informative than the traditional "Y" intercept. All of the commentaries broadened the discussion in ways that the authors had not considered. They put the authors' results into a larger framework of equating, and in doing so raised a number of issues that they probably should have addressed, or at least acknowledged. (Contains 1 figure.)