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The bit scale: a metric score scale for unidimensional item response theory models
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-7573-0671
Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Statistics.ORCID iD: 0000-0001-5549-8262
2026 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 91, no 1, p. 30-46Article in journal (Refereed) Published
Abstract [en]

In Item Response Theory (IRT), the conventional latent trait scale (θ) is inherently arbitrary, lacking a fixed unit or origin and often tied to specific population distributional assumptions (e.g., standard normal). This limits the direct comparability and interpretability of scores across different tests, populations, or model estimation methods. This paper introduces the “bit scale,” a novel metric transformation for unidimensional IRT scores derived from fundamental principles of information theory, specifically surprisal and entropy. Bit scores are anchored to the properties of the test items rather than the test-taker population. This item-based anchoring ensures the scale’s invariance to population assumptions and provides a consistent metric for comparing latent trait levels. We illustrate the utility of the bit scale through empirical examples: demonstrating consistent scoring when fitting models with different θ scale assumptions, and using anchor items to directly link scores from different test administrations. A simulation study confirms the desirable statistical properties (low bias, accurate standard errors) of Maximum Likelihood estimated bit scores and their robustness to extreme scores. The bit scale offers a theoretically grounded, interpretable, and comparable metric for reporting and analyzing IRT-based assessment results. Software implementations in R (bitscale) and Python (IRTorch) are available and practical implications are discussed.

Place, publisher, year, edition, pages
Cambridge University Press, 2026. Vol. 91, no 1, p. 30-46
Keywords [en]
bit scale, bit scores, information, rescaling, scale transformation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-248215DOI: 10.1017/psy.2025.10071ISI: 001658889300001PubMedID: 41367367Scopus ID: 2-s2.0-105025666005OAI: oai:DiVA.org:umu-248215DiVA, id: diva2:2026602
Funder
Marianne and Marcus Wallenberg Foundation, 2019-0129Swedish Research Council, 2022-02046Available from: 2026-01-09 Created: 2026-01-09 Last updated: 2026-05-21Bibliographically approved

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Wallmark, JoakimWiberg, Marie

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