Weighted Likelihood Estimation of Ability in Item Response Theory
Abstract
Applications of item response theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. A new method, weighted likelihood estimation (WLE), is derived, and proved to be less biased than maximum likelihood estimation (MLE) with the same asymptotic variance and normal distribution. WLE removes the first order bias term from MLE. Two Monte Carlo studies compare WLE with MLE and Bayesian modal estimation (BME) of ability in conventional tests and tailored tests, assuming the item parameters are known constants. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Multiple questionnaire items were used for each theoretical construct to create an index via a Rasch model to reduce measurement error.
“To reduce measurement error, multiple questionnaire items were used for each theoretical construct (e.g., SES) to create an index via a Rasch model (Warm, 1989).”
From Students’ Sense of Belonging at School in 41 Countries: Cross-Cultural Variability (2016) · cites this paper as Warm, 1989
Cites
Cox, D. R., & Hinkley, D. V. (1974) · doi:10.1007/978-1-4899-2887-0 · Cited by 3,089 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Fauth, B., Decristan, J., Decker, A.-T., Büttner, G., Hardy, I., Klieme, E., & Kunter, M. (2019) · Teaching and Teacher Education · doi:10.1016/j.tate.2019.102882 · Cited by 484 · see citing works
“Student parameters were estimated with weighted likelihood estimates (Warm, 1989).”
Method21st-Century Readers: Developing Literacy Skills in a Digital World
OECD (2021) · PISA · doi:10.1787/a83d84cb-en · Cited by 337 · see citing works
Chiu, M. M., & Klassen, R. M. (2010) · Learning and Instruction · doi:10.1016/j.learninstruc.2008.11.002 · Cited by 202 · see citing works
Students’ Sense of Belonging at School in 41 Countries: Cross-Cultural Variability
Chiu, M. M., Chow, B. W.-Y., McBride, C., & Mol, S. T. (2016) · Journal of Cross-Cultural Psychology · doi:10.1177/0022022115617031 · Cited by 180 · see citing works
Fütterer, T., Scherer, R., Scheiter, K., Stürmer, K., & Lachner, A. (2023) · Computers & Education · doi:10.1016/j.compedu.2023.104756 · Cited by 70 · see citing works
Capitalization on Item Calibration Error in Adaptive Testing
van der Linden, W. J., & Glas, C. A. W. (2000) · Applied Measurement in Education · doi:10.1207/s15324818ame1301_2 · Cited by 63 · see citing works
Gnambs, T., Stasielowicz, L., Wolter, I., & Appel, M. (2020) · Psychology of Popular Media · doi:10.1037/ppm0000204 · Cited by 35 · see citing works
Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models
Magis, D. (2016) · Psychometrika · doi:10.1007/s11336-015-9443-3 · Cited by 9 · see citing works
- Authors
- Warm, T. A.
- Affiliations
- Federal Aviation Administration (US)
- Corresponding author
- Warm, Thomas A.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1989-09
- Volume
- 54
- Issue
- 3
- Pages
- 427-450
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2022276698
- Cited by
- 1,216
- References
- 1
- Citations by year
- 2026: 56 · 2025: 62 · 2024: 86 · 2023: 59 · 2022: 71 · 2021: 86 · 2020: 88 · 2019: 79 · 2018: 53 · 2017: 61 · 2016: 53 · 2015: 39 · 2014: 99 · 2013: 37 · 2012: 34
- FWCI
- 0.61
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychometrika (publishedVersion)
- RePEc: Research Papers in Economics (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
- Social Sciences › Education › Educational Assessment and Pedagogy
- Keywords
- weighted likelihood estimation, item response theory, ability estimation, bias mitigation, maximum likelihood estimation, parameter invariance, asymptotic normality
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
