Many applications of educational testing have a missing data aspect (MDA). This MDA is perhaps most pronounced in item banking, where each examinee responds to a different subtest of items from a large item pool and where both person and item parameter estimates are needed. The Rasch model is emphasized, and its non-parametric counterpart (the Mokken scale) is considered. The possibility of tailoring test items in combination with their estimation is discussed; however, most methods for the estimation of item parameters are inadequate under tailoring. Without special measures, only marginal maximum likelihood produces adequate item parameter estimates under item tailoring. Fischer's approximate minimum-chi-square method for estimation of item parameters for the Rasch model is discussed, which efficiently produces item parameters. (TJH)