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: | |
| 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 |
| 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.) |
|---|---|
| ISSN: | 0146-6216 |
| DOI: | 10.1177/0146621610378289 |
