Consistency of Rasch model parameter estimation: A simulation study

It is shown in this paper that the unconditional orsimultaneous maximum likelihood estimation procedurefor the one-parameter logistic model gives rise tobiased estimators. This bias cannot be removed by acorrection factor (K - 1)/K (where K is the number ofitems), contrary to the contention of several authors.The bias is dependent not only on the number ofitems, but also on the distribution of the item parameters,which makes correcting for bias practically impossible.Furthermore, it is shown that the minimumchi-square estimation procedure, as introduced byFischer, results in unbiased estimates. In addition, thismethod is computationally fast, so that it seems to bea good alternative for CML estimation when the lattermethod meets practical impediments. Index terms:Maximum likelihood estimation, conditional; Maximumlikelihood estimation, unconditional; Minimumchi-square estimation; One-parameter logistic model;Rasch model.