Methods for Evaluating Empirical Bayes Point Estimates of Latent Trait Scores

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Abstract
Empirical Bayes point estimates of latent trait scores, derived under the assumptions of one of several test theory models, display a certain degree of instability unless the sample size is sufficiently large. A measure of this instability over repeated sampling is the distribution of the overall expected squared error loss which converges, both in probability and in the mean, to the minimum (Bayes) overall expected loss as sample size increases. An asymptotic distribution theory is developed, and the resulting large sample approximation is compared with results obtained from simulated data. Attention is also given to the effects of using a smoothing procedure.