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Cited by 11Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Distribution Estimation and Applications

Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models

Magis, David·2016·Psychometrika
DOI 10.1007/s11336-015-9443-3
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Abstract

This paper focuses on the computation of asymptotic standard errors (ASE) of ability estimators with dichotomous item response models. A general framework is considered, and ability estimators are defined from a very restricted set of assumptions and formulas. This approach encompasses most standard methods such as maximum likelihood, weighted likelihood, maximum a posteriori, and robust estimators. A general formula for the ASE is derived from the theory of M-estimation. Well-known results are found back as particular cases for the maximum and robust estimators, while new ASE proposals for the weighted likelihood and maximum a posteriori estimators are presented. These new formulas are compared to traditional ones by means of a simulation study under Rasch modeling.

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  • Simulating 3600 examinees with true ability parameters drawn from a uniform distribution across 36 discrete ability levels from −3.5 to +3.5 provides a more stringent test of the CAT algorithm's robustness across the entire ability spectrum.

    “We simulated 3600 examinees with true ability parameters drawn from a uniform distribution, spanning 36 discrete ability levels from −3.5 to +3.5 at intervals of 0.2. Each ability level was replicated 100 times. This uniform sampling, as opposed to a normal distribution, provides a more stringent test of the CAT algorithm’s robustness across the entire ability spectrum15,29,33.”

    From Leveraging computerized adaptive testing for cost-effective evaluation of large language models in medical benchmarking (2026) · cites this paper as [33]

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Authors
Magis, D.
Affiliations
University of Liège (BE)
Corresponding author
Magis, David
Venue
Psychometrika
Publisher
Cambridge University Press (CUP)
Published
2016-03
Volume
81
Issue
1
Pages
184-200
ISSN
  • 0033-3123 (ISSN-L)
  • 1860-0980
DOI
10.1007/s11336-015-9443-3
OpenAlex
W2086007547
Cited by
9
References
41
Citations by year
2026: 1 · 2023: 1 · 2022: 1 · 2021: 2 · 2019: 2 · 2017: 1 · 2016: 1
FWCI
0.83
Type
journal article
Language
en
Open access
closed
Licence
Locations
  • Psychometrika (publishedVersion)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Lirias (submittedVersion)
  • ORBi (University of Liège) (submittedVersion)
Topics
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords
ability estimation, asymptotic standard errors, M-estimation, maximum likelihood estimation, weighted likelihood estimation, maximum a posteriori estimation, robust estimators, Rasch model
MeSH terms
Bayes Theorem, Computer Simulation, Humans, Psychometrics, Models, Statistical, Likelihood Functions

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