We understand that actually there are not any model can predict data absolutely. When the model assumption misspecificate the subject behavior, the parameter estimation will be biased. Fisher demonstrated the maximum likelihood estimator is unbiased statistic in 1935, but we need to modify it when model assumptions are violated. This study compare with three estimation methods, including ML, bisquare, and Huber Type estimator of ability. The bisquare and Huber estimator use weighting function to modify the ML. They both draw the lower weight when the subject responses are unexpected under his ability. Therefore, the aberrant responses will have less contribute to ability estimation. However, essentially the bisquare cannot be converged well.
This study simulate two kinds of aberrant response, guessing and transcription error. The modified methods of course were better than ML under those behaviors, and the robust estimator didn't lose many information under no guessing and transcription error. Further, the author recommended using them.
Question and Comment:
1) In function (7), bias and variance are simple trade-off, but How to see the bisquare is less biased than the Huber but the Huber has smaller variance than bisquare? Which table or which number presented this discussion?
2) In Table 3, I think Huber's effect was better than bisquare at sensation. However, the constant value of H=1 were a little arbitrary. I think it should have more reasonable explanation of H value.