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Cited by 30Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceEducational Assessment and Pedagogy

Item Response Theory: A Statistical Framework for Educational and Psychological Measurement

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Chen, Yunxiao, Li, Xiaoou, Liu, Jingchen, Ying, Zhiliang·2025·Statistical Science
DOI 10.1214/23-sts896
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Abstract

Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation and prediction of individuals’ behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals’ test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning.

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  • Item Response Theory has been proposed for natural language processing and LLM evaluation, including methods that reconsider benchmark quality by analyzing item difficulty and model ability.

    “Item Response Theory has been proposed for natural language processing and LLM evaluation, including methods that reconsider benchmark quality by analyzing item difficulty and model ability [5, 6].”

    From Machine Psychometrics: A Mathematical Psychology of Artificial Intelligence (2026) · cites this paper as [5]

    The Abstract (p. 1) says IRT can validate a test scale, and §2.2 (p. 8) describes estimating test-taker ability from item responses. The cited paper does not describe proposals for NLP or LLM evaluation, or methods for reassessing LLM benchmark quality through item difficulty and model ability. (LLM, conf=0.83)

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Sorted by citations

Authors
Chen, Y., Li, X., Liu, J., & Ying, Z.
Affiliations
London School of Economics and Political Science (GB)
ORCID
Venue
Statistical Science
Publisher
Institute of Mathematical Statistics
Published
2025-05-01
Volume
40
Issue
2
Pages
167-194
ISSN
  • 0883-4237 (ISSN-L)
  • 2168-8745
DOI
10.1214/23-sts896
OpenAlex
W4411006456
Cited by
30
References
5
Citations by year
2026: 9 · 2025: 7 · 2024: 11 · 2023: 3
FWCI
12.31
Type
journal article
Language
en
Open access
Locations
  • Statistical Science (publishedVersion)
  • London School of Economics and Political Science Research Online (London School of Economics and Political Science) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • London School of Economics and Political Science Theses Online (London School of Economics and Political Science) (submittedVersion)
  • arXiv (Cornell University)
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
  • Social Sciences › Education › Educational Assessment and Pedagogy
Keywords
item response theory, psychometrics, latent factor models, test scoring, test linking, empirical Bayes, nonparametric statistics, matrix completion, regularized estimation, sequential analysis, statistical learning

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