A note on Tutz's pairwise separation estimator

The Rasch model has the desirable property that item parameter estimation can be separated from person parameter estimation. This implies that no assumptions about the ability distribution are required when estimating item difficulties. Pairwise estimation approaches in the Rasch model exploit this principle by estimating item difficulties solely from sample proportions of respondents who answer item i correctly and item j incorrectly. A recent contribution by Tutz introduced Tutz’s pairwise separation estimator (TPSE) for the more general class of homogeneous monotone (HM) models, extending the idea of pairwise estimation to this broader setting. The present article examines the asymptotic behavior of the TPSE within the Rasch model as a special case of the HM framework. It should be emphasized that both analytical derivations and a numerical illustration show that the TPSE yields asymptotically biased item parameter estimates, rendering the estimator inconsistent, even for a large number of items. Consequently, the TPSE cannot be recommended for empirical applications.