A modified minimum divergence estimator: some preliminary results for the Rasch model

Since its introduction, the joint maximum likelihood (JML) has been widely used as an estimation method for Rasch measurement models. As is well known, when the JML method is used, all item and person parameters are regarded as unknowns to be estimated. In this paper we focus on some drawbacks of the JML for the Rasch model: viz. i) the occasional non-existence of estimates, and ii) the bias of item parameter estimates. We propose a new estimation method which is based on the Minimum Divergence Estimation approach and consists in appropriately modifying the empirical distribution function. We provide empirical evidence that this method can solve the problem of the non-existence of the estimates and, at the same time, can reduce the bias of item parameter estimates compared to those obtained with both traditional JML estimation and the (k-1)/k correction factor (where k is the number of items) commonly applied in JML software.