On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models.
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| Title: | On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models. |
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| Authors: | Magis, David |
| Source: | British Journal of Mathematical & Statistical Psychology. Nov2014, Vol. 67 Issue 3, p430-450. 21p. |
| Subjects: | Asymptotes, Error analysis in mathematics, Estimation theory, Model theory, Simulation methods & models, Maximum likelihood statistics |
| Abstract: | In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses on the estimation process. The computation of asymptotic (i.e., large-sample) standard errors ( ASE) for these robust estimators, however, has not yet been fully considered. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood ( ML) and the robust estimators, together with their estimated ASEs, are then compared in a simulation study by generating random guessing disturbances. It is concluded that both the estimators and their ASE perform similarly in the absence of random guessing, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in the presence of random guessing with large impact on the item response process. [ABSTRACT FROM AUTHOR] |
| Copyright of British Journal of Mathematical & Statistical Psychology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Psychology and Behavioral Sciences Collection |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: pbh DbLabel: Psychology and Behavioral Sciences Collection An: 98675811 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Magis%2C+David%22">Magis, David</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22British+Journal+of+Mathematical+%26+Statistical+Psychology%22">British Journal of Mathematical & Statistical Psychology</searchLink>. Nov2014, Vol. 67 Issue 3, p430-450. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Asymptotes%22">Asymptotes</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Model+theory%22">Model theory</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In item response theory, the classical estimators of ability are highly sensitive to response disturbances and can return strongly biased estimates of the true underlying ability level. Robust methods were introduced to lessen the impact of such aberrant responses on the estimation process. The computation of asymptotic (i.e., large-sample) standard errors ( ASE) for these robust estimators, however, has not yet been fully considered. This paper focuses on a broad class of robust ability estimators, defined by an appropriate selection of the weight function and the residual measure, for which the ASE is derived from the theory of estimating equations. The maximum likelihood ( ML) and the robust estimators, together with their estimated ASEs, are then compared in a simulation study by generating random guessing disturbances. It is concluded that both the estimators and their ASE perform similarly in the absence of random guessing, while the robust estimator and its estimated ASE are less biased and outperform their ML counterparts in the presence of random guessing with large impact on the item response process. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of British Journal of Mathematical & Statistical Psychology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/bmsp.12027 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 430 Subjects: – SubjectFull: Asymptotes Type: general – SubjectFull: Error analysis in mathematics Type: general – SubjectFull: Estimation theory Type: general – SubjectFull: Model theory Type: general – SubjectFull: Simulation methods & models Type: general – SubjectFull: Maximum likelihood statistics Type: general Titles: – TitleFull: On the asymptotic standard error of a class of robust estimators of ability in dichotomous item response models. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Magis, David IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2014 Type: published Y: 2014 Identifiers: – Type: issn-print Value: 00071102 Numbering: – Type: volume Value: 67 – Type: issue Value: 3 Titles: – TitleFull: British Journal of Mathematical & Statistical Psychology Type: main |
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