First, the paper illustrated the setting in which the bisquare estimator may not converge by an example. Then maximum-likelihood estimation of ability was reviewed and the rationale of the weighted likelihood approach used to robustify ability estimation was explained.
Then the research modified the robust estimation procedure by selecting Huber-type weights.
In the simulation study, three ability extimators-maximum-likelihood, bisquare, and Huber-were compared with the difficulties of the items ranged from -4.4 to +4.4 in steps of 0.2 and it was found that with the help of the weighted likelihood approach presented, robust ability estimates can be obtained that are considerably less biased and have smaller sampling variance.
Finally, the research pointed out that both robust estimators discussed would reduce estimation bias to a considerable extent, and Huber-type estimator should be used if response patterns having only a few correct responses occurred, since it seems to be free of convergence problems. However, if nonconvergence is not an issue, the essentially equivalent MSE of the robust estimators does not indicate a general preference for one of them. If reduce bias is preferred over reduced sampling variability, the bisquare estimate should be selected, or the Huber-type estimate should be preferred.
Generally, limited simulation studies were proposed in this study to exam the three ability estimators, and the conditions of different models were examined. However, there is no standard was proposed to exactly illustrate the bias and robustness of the models.