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A Test-Length Correction to the Estimation of Extreme Proficiency Levels

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Title: A Test-Length Correction to the Estimation of Extreme Proficiency Levels
Language: English
Authors: Magis, David, Beland, Sebastien, Raiche, Gilles
Source: Applied Psychological Measurement. Mar 2011 35(2):91-109.
Availability: SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: http://sagepub.com
Peer Reviewed: Y
Physical Description: PDF
Page Count: 19
Publication Date: 2011
Document Type: Journal Articles
Reports - Research
Descriptors: Test Length, Computation, Item Response Theory, Maximum Likelihood Statistics, Bayesian Statistics, Statistical Bias, Ability
DOI: 10.1177/0146621610378289
ISSN: 0146-6216
Abstract: In this study, the estimation of extremely large or extremely small proficiency levels, given the item parameters of a logistic item response model, is investigated. On one hand, the estimation of proficiency levels by maximum likelihood (ML), despite being asymptotically unbiased, may yield infinite estimates. On the other hand, with an appropriate prior distribution, the Bayesian approach of maximum a posteriori (MAP) yields finite estimates, but it suffers from severe estimation bias at the extremes of the proficiency scale. As a first step, a simple correction to the MAP estimator is proposed to reduce this estimation bias. The correction factor is determined through a simulation study and depends only on the length of the test. In a second step, some additional simulations emphasize that the corrected estimator behaves like the ML estimator and outperforms the standard MAP method for extremely small or extremely large abilities. Although based on the Rasch model, the method could be adapted to other logistic item response models. (Contains 2 tables and 7 figures.)
Abstractor: As Provided
Number of References: 31
Entry Date: 2011
Accession Number: EJ916026
Database: ERIC
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  Data: A Test-Length Correction to the Estimation of Extreme Proficiency Levels
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  Data: In this study, the estimation of extremely large or extremely small proficiency levels, given the item parameters of a logistic item response model, is investigated. On one hand, the estimation of proficiency levels by maximum likelihood (ML), despite being asymptotically unbiased, may yield infinite estimates. On the other hand, with an appropriate prior distribution, the Bayesian approach of maximum a posteriori (MAP) yields finite estimates, but it suffers from severe estimation bias at the extremes of the proficiency scale. As a first step, a simple correction to the MAP estimator is proposed to reduce this estimation bias. The correction factor is determined through a simulation study and depends only on the length of the test. In a second step, some additional simulations emphasize that the corrected estimator behaves like the ML estimator and outperforms the standard MAP method for extremely small or extremely large abilities. Although based on the Rasch model, the method could be adapted to other logistic item response models. (Contains 2 tables and 7 figures.)
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