Correcting unconditional parameter estimates in the Rasch model for inconsistency

Abstract

Results of simulation studies indicate that the unconditional maximum likelihood method is commonly regarded as an appropriate substitute for the theoretically superior conditional method for estimating the parameters of the Rasch model. To this end, the unconditional estimates are "corrected" by a factor (K - 1)/K, where is the number of items. In this paper, the simulation study of Wright and Douglas (1977b), which seemed to corroborate this correction term, is critically discussed. It appears to contain a puzzling assumption, and to rest on inadequate logic. Accordingly, there is a need for new simulation studies on the validity of the correction term (K − 1)/K for unconditional maximum likelihood estimation in the Rasch model. Index terms: Item response theory, item parameter estimation; Item response theory, one-parameter logistic model; Maximum likelihood estimation, unconditional; One-parameter logistic model; Rasch model.