Item response theory is use the response pattern to estimate ability, however, if the unexpected response (response disturbance) is existed, such as guessing, cheating, or carelessness, the ability estimation will biased. On strategy to handle unexpected responses is decrease their influence and give less weight on the maximum-likelihood function during the ability estimation, and called bisquare or biweight function. Although the bisquare weight function can reduce bias and improve measurement accuracy, but it will resulted in toward negative infinity when correct answers are sparse. This article proposed an alternative approach to robustify ability estimates and resolve the convergence problem (avoid to lead toward negative infinity when correct answers are sparse), and uses the weighting function is Huber weighting function.
Implemented a series of studies to illustrate the performances of the three estimators - maximum-likelihood, bisquare, and Huber under two types of response disturbances– random guessing and transcription errors. The results shown that, first, increasing the amount of disturbance yields increased bias. In terms of bias the Huber-type estimator can be considered a compromise between the bisquare and the maximum likelihood. Second, the bisquare is generally less biased than the Huber-type estimator, but the Huber-type estimator has generally smaller sampling variability compared to the bisquare estimator. Hence, this paper recommended that using the Huber-type estimator can resolve convergence problem and loss small precision compared to the bisquare estimator.
Comments & Questions:
1. The value of the tuning constant is arbitrary and how to set an appropriate level of tuning constant can be investigated in the future.