Scale Shrinkage and the Estimation of Latent Distribution Parameters

Abstract

In this paper the phenomenon of scale shrinkage is examined. Specifically, emphasis is placed on the pattern of decreasing variances in IRT scale scores from fall to spring within a grade. It is concluded that certain situations exist in which scale shrinkage is predictable with unidimensional tests. It depends, to a large degree, on the match between item difficulties and the level of examinee ability. As the mismatch increases, so do distortions of scale because of systematic estimation errors (bias), measurement errors, and unobtainable ability estimates. These problems exist for all observed or estimated scores; however, it is shown in this paper that questions concerning the population distributions of true ability can potentially be addressed with empirical Bayes techniques.