Improving likelihood-based estimates of the Rasch Model with ε-adjustments

Within the framework of the item response theory, the joint maximum likelihood (JML) estimation method does not provide finite latent ability estimates for respondents who obtain an extreme score (zero and/or perfect response patterns)– when a Rasch model (RM) is considered. To overcome this problem, computer programs usually produces finite measurements by estimating the abilities that correspond to the scores r and M – r where M is the maximum possible score, and r is an arbitrarily specified real number. In this paper a new method is proposed, based on the minimum Kullback-Leibler divergence estimation approach. As the sensitivity of this adjustment depends on an arbitrarily small positive number ε, we called it ε-adjustment method. The ε-adjustment warrants the existence of finite estimates for all the RM parameters, not only in the case of extreme score, but also for any other case of a “JML-anomalous” dataset. As a by-product, the new method is very effective in reducing the bias of the maximum likelihood estimates, and for this purpose it seems to work even better than other known bias-reducing methods.