In a situation where the population distribution of latent trait scores can be estimated, the ordinary maximum likelihood estimator of latent trait scores may be improved upon by taking the estimated population distribution into account. In this paper empirical Bayes estimators are compared with the liklihood estimator for three samples of 300…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…

Formulas are presented for decision reliability and for classification validity for mastery/nonmastery decisions based on criterion referenced tests. Two item parameters are used: the probability of a master answering an item correctly, and the probability of a nonmaster answering an item incorrectly. The theory explores the relationships of…