Asymptotic distribution of robust estimators of ability and applications

In item response theory (IRT), ability estimation can be seriously affected by abnormal responses occurring from e.g., cheating, inattention, lack of time, guessing, tiredness, stress… Those phenomena may influence the ability estimation process tremendously. One the one hand, person fit indices were developed as post-hoc approaches to identify abnormal responses patterns as a whole (e.g., Meijer & Sijtsma, 2001). On the other hand, getting uncontaminated ability estimates would also be a challenging issue.
Robust estimators were proposed in the IRT framework to lessen the impact of abnormal responses onto the estimation process (Mislevy & Bock, 1982; Schuster & Yuan, 2011; Wainer & Wright, 1980). Yet, these estimators are still rarely used in practice, mostly because very little is known about their statistical properties.
The purpose of this talk is to briefly present these robust ability estimators, and to derive their asymptotic distribution under mild regularity conditions. In particular, a simple formula for the asymptotic standard error (ASE) of these estimators is obtained (Magis, in press). Results of a simulation study that involves both presence and absence of cheating in the data generation process will be outlined.

References:
Magis, D. (in press). On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models. British Journal of Mathematical and Statistical Psychology.
Meijer, R., & Sijtsma, K. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25, 107-135. doi: 10.1177/01466210122031957
Mislevy, R. J., & Bock, R. D. (1982). Biweight estimates of latent ability. Educational and Psychological Measurement, 42, 725-737. doi: 10.1177/001316448204200302
Schuster, C., & Yuan, K.-H. (2011). Robust estimation of latent ability in item response models. Journal of Educational and Behavioral Statistics, 36, 720-735. doi: 10.3102/1076998610396890
Wainer, H., & Wright, B. D. (1980). Robust estimation of ability in the Rasch model. Psychometrika, 45, 373-391. doi: 10.1007/BF02293910