This study compared three estimators for latent ability in item response models, with the presence of unexpected response patterns. The three estimators included the Maximum Likelihood Estimator, the Bisquare Ability Estimate, and the Huber Ability Estimate. Differences between these estimators is the weighting method, in which the MLE did not include weighting function, the BS used the bisquare weight function, and the HU employed the Huber-type weights.
MLE would give infinite estimation of ability if the response pattern is perfect (all correct or all incorrect), and would be biased if the response not perfectly map the model, so the weighting function is encouraged to be included. BS was useful in reducing the estimation bias, but it may face the problem of convergence in some cases, for example, when the correct response is sparse. HU was another alternative choice as the non-convergence is not an issue for it.
The simulation used the 1PL model as true model. Results showed the robust estimators would reduce the estimation bias, but no obvious preference for one of them. BS is more useful in reducing the bias, when HU more useful in reducing the sampling variability.
Q:
1. One error for the R code, the last second line “theta0 <- theta1theta1”, one more “theta1”.
2. What would be the performance of estimators if the item parameters are unknown.