Pairwise Parameter Estimation in Rasch Models

Rasch model item parameters can be estimated consistently with a pseudo-likelihood method based on comparing responses to pairs of items irrespective of other items. The pseudo-likelihood method is comparable to Fischer's (1974) Minchi method. A simulation study found that the pseudo-likelihood estimates and their (estimated) standard errors were comparable to conditional and marginal maximum likelihood estimates. The method is extended to estimate parameters of the linear logistic test model allowing the design matrix to vary between persons.