{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T11:04:17Z","timestamp":1790766257574,"version":"4.1.0"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G050826N"],"award-info":[{"award-number":["G050826N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Psychometrika"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Psychometric models use latent variables to quantify psychological traits, but statistical and substantive inferences based on these variables may depend on how the latent scale is parametrized. Consequently, the same fitted model can yield qualitatively different conclusions under different parametrizations. Building on Ramsay\u2019s (1996,\n                    <jats:italic>Behaviormetrika<\/jats:italic>\n                    , 23, 3\u201316) geometric perspective, we reinterpret this problem using differential geometry. While Ramsay defined ability via an arc length in Euclidean space, psychometric models can be seen instead as a curved statistical manifold with the Fisher\u2013Rao metric. This allows for a parametrization-invariant definition of ability, which we term geodesic ability. We illustrate this concept for unidimensional item response theory models, including the Rasch and 3PL models, and compare it to Ramsay\u2019s arc-length approach.\n                  <\/jats:p>","DOI":"10.1017\/psy.2026.10144","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:32:10Z","timestamp":1790764330000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Geodesic Ability in Unidimensional IRT Models: A Geometric Perspective on Parametrization Invariance"],"prefix":"10.1017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1775-7654","authenticated-orcid":false,"given":"Francis","family":"Tuerlinckx","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05f950310","id-type":"ROR","asserted-by":"publisher"}],"name":"KU Leuven"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hern\u00e1n","family":"Robledo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04teye511","id-type":"ROR","asserted-by":"publisher"}],"name":"Pontificia Universidad Cat\u00f3lica de Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"S0033312326101446_r18","volume-title":"Applications of item response theory to practical testing problems","author":"Lord","year":"1980"},{"key":"S0033312326101446_r12","doi-asserted-by":"publisher","DOI":"10.1111\/insr.12053"},{"key":"S0033312326101446_r11","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1028905934"},{"key":"S0033312326101446_r1","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55978-8"},{"key":"S0033312326101446_r24","doi-asserted-by":"publisher","DOI":"10.3102\/1076998616680841"},{"key":"S0033312326101446_r22","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.170283897"},{"key":"S0033312326101446_r26","doi-asserted-by":"publisher","DOI":"10.3102\/10769986027003291"},{"key":"S0033312326101446_r15","volume-title":"Geometrical foundations of asymptotic inference","author":"Kass","year":"2011"},{"key":"S0033312326101446_r8","doi-asserted-by":"publisher","DOI":"10.1007\/s11336-018-9642-9"},{"key":"S0033312326101446_r10","first-page":"376","article-title":"Applications and extensions of metric stability analysis","volume":"5","author":"Feuerstahler","year":"2023","journal-title":"The Psychiatrist"},{"key":"S0033312326101446_r9","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2020.1809980"},{"key":"S0033312326101446_r6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-07779-6"},{"key":"S0033312326101446_r21","doi-asserted-by":"publisher","DOI":"10.1007\/s41884-024-00143-2"},{"key":"S0033312326101446_r16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9982-5"},{"key":"S0033312326101446_r20","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1035844977"},{"key":"S0033312326101446_r23","doi-asserted-by":"publisher","DOI":"10.2333\/bhmk.23.3"},{"key":"S0033312326101446_r13","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1982.tb01205.x"},{"key":"S0033312326101446_r17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02291567"},{"key":"S0033312326101446_r19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2017.05.006"},{"key":"S0033312326101446_r7","unstructured":"Caticha, A . (2022). Entropic physics: Probability, entropy, and the foundations of physics (version of July 26, 2022). https:\/\/www.arielcaticha.com\/my-book-entropic-physics"},{"key":"S0033312326101446_r28","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7161(06)26022-X"},{"key":"S0033312326101446_r5","doi-asserted-by":"publisher","DOI":"10.1201\/9780429275326"},{"key":"S0033312326101446_r3","doi-asserted-by":"publisher","DOI":"10.1162\/edfp.2009.4.4.351"},{"key":"S0033312326101446_r2","first-page":"345","article-title":"Rao\u2019s distance measure","volume":"43","author":"Atkinson","year":"1981","journal-title":"Sankhy\u0101: The Indian Journal of Statistics, Series A"},{"key":"S0033312326101446_r14","article-title":"The geometry of asymptotic inference","volume":"188\u2013219","author":"Kass","year":"1989","journal-title":"Statistical Science"},{"key":"S0033312326101446_r29","volume-title":"An introduction to manifolds","author":"Tu","year":"2010"},{"key":"S0033312326101446_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmp.2019.04.002"},{"key":"S0033312326101446_r4","volume-title":"An introduction to differentiable manifolds and Riemannian geometry","author":"Boothby","year":"1986"},{"key":"S0033312326101446_r25","first-page":"81","article-title":"Information and the accuracy attainable in the estimation of statistical parameters","volume":"37","author":"Rao","year":"1945","journal-title":"Bulletin of Calcutta Mathematical Society"}],"container-title":["Psychometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0033312326101446","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T10:32:14Z","timestamp":1790764334000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0033312326101446\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,30]]},"references-count":29,"alternative-id":["S0033312326101446"],"URL":"https:\/\/doi.org\/10.1017\/psy.2026.10144","relation":{},"ISSN":["0033-3123","1860-0980"],"issn-type":[{"value":"0033-3123","type":"print"},{"value":"1860-0980","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,30]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. Published by Cambridge University Press on behalf of Psychometric Society","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}