Logit based parameter estimation in the Rasch model

The similarities between the logistic regression model and the Rasch model (used in psychometric item response theory) are used to derive several methods based on logits that produce parameter estimates for the Rasch model. A result from LeCam and Dzhaparidze is used by which an initial consistent estimate is transformed by one scoring method iteration into an estimate that has the same asymptotic efficiency as the (in this case conditional) maximum likelihood estimate of the item parameters. Indirect evidence about the bias of this CML estimator is produced by studying the (more easily derived) bias of the estimator based on the unweighted logits. Finally, some simple weighted least squares logit-based estimates are presented, and their performance is assessed. On the whole, the computationally simpler logit-based estimates give a fairly good approximation to the CML estimates.