Conditional pairwise person parameter estimates in Rasch models

Conditional pairwise estimates parameters in Rasch models separate inference on item parameters from inference on person parameters. Pairwise item parameter estimates are consistent when sample size approaches infinity, but adds an extra random error to estimation compared to conditional maximum likelihood estimates. Pairwise estimates of person parameters are easily calculated, but can rarely be assumed to be consistent since the number of items is often small and the properties of the estimates generally unknown. This note gives results from a study of conditional pairwise estimation of person parameters and suggests a modification of the estimate that takes care of some of the error.