The author proposed a modified estimation of latent trait to enhance the method. The only difference is between the bisquare and Huber function. The later can effectively avoid the non-convergence problem. The spirit of the two methods is to give a weight on the likelihood of suspected inconsistent response. They are all stochastic approach. Other function is available potentially. Seeing from figure 3, it is clear that the Huber function will still give weight on large value of r.
Simulation studies show that Huber-type mehod has slight higher bias than the bisqure method but lower than MLE. In terms of MSE, Huber-type has generally smaller sampling variability. Thus, Huber-type can be regarded as a compromise between the bisquare and maximum likelihood.
Q:
1. How robust it is? I think it is relative.
2. How much benefit we get if using modified method to estimate latent trait rather than alternative model? Robust estimation will never be right as well.
3. How to choose the incorrect response? If we know, we can just eliminate them without the need of robust estimation.
4. As many inconsistent response patterns were suspected, the robust method will be useless. When should we use it at safe?