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Bayesian Estimators, Robust Estimators: A Comparison and Some Asymptotic Results IRT

Author(s):
Jones, Douglas H.
Publication Year:
1984
Report Number:
RR-84-42, PSRTR-84-54
Source:
ETS Research Report
Document Type:
Report
Page Count:
16
Subject/Key Words:
Office of Naval Research, United States Air Force Human Resources Laboratory, Bayesian Statistics, Error of Measurement, Item Response Theory (IRT), Statistical Analysis

Abstract

Combinations of Bayes and resistant estimators of latent ability were studied in Wainer and Thissen (1984), who show that they have desirable performances for small to medium samples especially in the presence of contamination. While their study was based on computer simulations, this note provides the first order asymptotic theory, from which one may compute approximations to the standard errors of the estimators. A side issue concerns the "overshrinking phenomenon" which caused Wainer and Thissen to expand the scale of the estimators in order to increase their accuracy and to make them more comparable to the traditional estimators. This note derives a differential equation specifying a transform that may make Bayes/resistant estimators even more favorable. (16pp.)

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