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Bayesian Extension of Biweight and Huber Weight for Robust Ability Estimation
Author(s) -
Maeda Hotaka,
Zhang Bo
Publication year - 2019
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12240
Subject(s) - bayesian probability , estimation , statistics , robust statistics , extension (predicate logic) , monte carlo method , bayes estimator , econometrics , computer science , mathematics , outlier , programming language , management , economics
When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods use the Bayesian prior distribution to compensate for information lost due to aberrant responses. They may also be more resistant to the detrimental effects of downweighting the nonaberrant responses. The effectiveness of BMAP and HMAP was evaluated through a Monte Carlo simulation. Results show that both methods, especially BMAP, are more effective than the original biweight and Huber weight in correcting mild forms of aberrant behavior.