LAUSR

Rasch-type item response models are often estimated via a conditional maximum-likelihood approach. This article elaborates on the asymptotics of conditional maximum-likelihood estimates for an increasing number of items, important for modern data settings where a large number of items need to be scaled. Using approximations of the variance–covariance matrix based on Edgeworth expansions, the problem is studied theoretically as well as computationally. In a subsequent step, these results are used to split the large-scale estimation problem into smaller sub-problems involving blocks of items. These item blocks are estimated separately from each other and, finally, merged back into the full parameter vector (divide-and-conquer). By means of simulation studies, and in conjunction with the asymptotic results, it was found that block sizes in the range of 30–40 items approximate the full-scale estimators with a negligible loss in precision. It is also shown how varying block sizes affect the running time needed to fit the model.