Consistency of Rasch model parameter estimation: A simulation study

It is shown in this paper that the unconditional or simultaneous maximum likelihood estimation procedure for the one-parameter logistic model gives rise to biased estimators. This bias cannot be removed by a correction factor (K - 1)/K (where K is the number of items), contrary to the contention of several authors. The bias is dependent not only on the number of items, but also on the distribution of the item parameters, which makes correcting for bias practically impossible. Furthermore, it is shown that the minimum chi-square estimation procedure, as introduced by Fischer, results in unbiased estimates. In addition, this method is computationally fast, so that it seems to be a good alternative for CML estimation when the latter method meets practical impediments. Index terms: Maximum likelihood estimation, conditional; Maximum likelihood estimation, unconditional; Minimum chi-square estimation; One-parameter logistic model; Rasch model