{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T11:52:50Z","timestamp":1791978770254,"version":"4.4.0"},"reference-count":72,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T00:00:00Z","timestamp":1791936000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T00:00:00Z","timestamp":1791936000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["VI.Vidi.201.009"],"award-info":[{"award-number":["VI.Vidi.201.009"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["bpspsychub.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Brit J Math &amp;amp; Statis"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Generalizability theory (GT) provides a variety of intraclass correlation coefficients (ICCs) to quantify reliability across different conditions of measurement\u2014for example, scale and interrater reliability quantify generalization across items and raters, respectively. In a multilevel modelling (MLM) context, an ICC is often used to quantify the proportion of a subject\u2010level variable's variance that is attributable to cluster\u2010level differences (e.g., between schools or neighbourhoods). When data from cluster members are their ratings of a group\u2010level characteristic, the ICC is an inter\u2010rater reliability coefficient, interpreted as the degree to which observations of a cluster generalize across members of that cluster. Structural equation modelling (SEM) is becoming a popular framework for modelling GT, and the \u2018omega\u2019 indices of composite reliability\u2014which are functions of SEM parameters\u2014are special cases of GT (i.e., how measurements of a construct generalize across indicators). The merger of MLM and SEM (i.e., ML\u2010SEM) provides a unique opportunity to explore how well measurements of cluster\u2010level constructs generalize across multiple measurement conditions (indicators, cluster members, or both). A taxonomy of ICCs is explicated to appropriately quantify reliability across aspects of a procedure for measuring cluster\u2010level constructs, adding value to the limited ICCs currently considered in ML\u2010SEM applications.<\/jats:p>","DOI":"10.1111\/bmsp.70074","type":"journal-article","created":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T11:42:26Z","timestamp":1791978146000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A taxonomy of reliability indices for cluster\u2010level constructs measured by multiple individual\u2010level indicators"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5111-6773","authenticated-orcid":false,"given":"Terrence D.","family":"Jorgensen","sequence":"first","affiliation":[{"name":"University of Amsterdam  Amsterdam The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2223-5594","authenticated-orcid":false,"given":"Suzanne","family":"Jak","sequence":"additional","affiliation":[{"name":"University of Amsterdam  Amsterdam The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,14]]},"reference":[{"key":"e_1_2_15_2_1","doi-asserted-by":"publisher","DOI":"10.2466\/pr0.1966.19.1.3"},{"key":"e_1_2_15_3_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v067.i01"},{"key":"e_1_2_15_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289328"},{"key":"e_1_2_15_5_1","doi-asserted-by":"publisher","DOI":"10.1207\/S15328007SEM0704_5"},{"key":"e_1_2_15_6_1","first-page":"349","volume-title":"Multilevel theory, research, and methods in organizations","author":"Bliese P. D.","year":"2000"},{"key":"e_1_2_15_7_1","doi-asserted-by":"crossref","DOI":"10.1002\/9781118619179","volume-title":"Structural equations with latent variables","author":"Bollen K. A.","year":"1989"},{"key":"e_1_2_15_8_1","doi-asserted-by":"publisher","DOI":"10.3102\/10769986027004335"},{"key":"e_1_2_15_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/job.1960"},{"key":"e_1_2_15_10_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3456-0","volume-title":"Generalizability theory","author":"Brennan R. L.","year":"2001"},{"key":"e_1_2_15_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/08957347.2011.532417"},{"key":"e_1_2_15_12_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094428116656239"},{"key":"e_1_2_15_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11336\u2010021\u201009801\u20101"},{"key":"e_1_2_15_14_1","doi-asserted-by":"publisher","DOI":"10.1177\/0013164415612255"},{"key":"e_1_2_15_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02310555"},{"key":"e_1_2_15_16_1","volume-title":"The dependability of behavioral measurements: Theory of generalizability for scores and profiles","author":"Cronbach L. J.","year":"1972"},{"key":"e_1_2_15_17_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044\u20108317.1963.tb00206.x"},{"key":"e_1_2_15_18_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0032138"},{"key":"e_1_2_15_19_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15327906mbr3102_3"},{"key":"e_1_2_15_20_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082\u2010989X.11.4.323"},{"key":"e_1_2_15_21_1","volume-title":"Handbook of inter\u2010rater reliability, volume 2: Analysis of quantitative ratings","author":"Gwet K. L.","year":"2021"},{"key":"e_1_2_15_22_1","doi-asserted-by":"publisher","DOI":"10.2307\/270785"},{"key":"e_1_2_15_23_1","volume-title":"Multilevel analysis: Techniques and applications","author":"Hox J. J.","year":"2018"},{"key":"e_1_2_15_24_1","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2017.01640"},{"key":"e_1_2_15_25_1","doi-asserted-by":"publisher","DOI":"10.1177\/25152459231182319"},{"key":"e_1_2_15_26_1","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2013.769392"},{"key":"e_1_2_15_27_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-47946-0","volume-title":"Linear and generalized linear mixed models and their applications","author":"Jiang J.","year":"2007"},{"key":"e_1_2_15_28_1","doi-asserted-by":"publisher","DOI":"10.1027\/1614\u20102241\/a000149"},{"key":"e_1_2_15_29_1","doi-asserted-by":"publisher","DOI":"10.1177\/00131644211033899"},{"key":"e_1_2_15_30_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02291393"},{"key":"e_1_2_15_31_1","doi-asserted-by":"publisher","DOI":"10.3390\/psych3020011"},{"key":"e_1_2_15_32_1","doi-asserted-by":"crossref","unstructured":"Jorgensen T. D. Pornprasertmanit S. Schoemann A. M. &Rosseel Y.(2026).semTools: Useful tools for structural equation modeling [Computer software manual]. (R package version 0.5\u20109).https:\/\/doi.org\/10.32614\/CRAN.package.semTools","DOI":"10.32614\/CRAN.package.semTools"},{"key":"e_1_2_15_33_1","doi-asserted-by":"publisher","DOI":"10.1177\/00131644211020112"},{"key":"e_1_2_15_34_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000287"},{"key":"e_1_2_15_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02295278"},{"key":"e_1_2_15_36_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000738"},{"key":"e_1_2_15_37_1","volume-title":"Statistical theories of mental test scores","author":"Lord F. M.","year":"1968"},{"key":"e_1_2_15_38_1","doi-asserted-by":"publisher","DOI":"10.1080\/10705519609540045"},{"key":"e_1_2_15_39_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082\u2010989x.11.4.344"},{"key":"e_1_2_15_40_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044\u20108317.1970.tb00432.x"},{"key":"e_1_2_15_41_1","volume-title":"Test theory: A unified treatment","author":"McDonald R. P.","year":"1999"},{"key":"e_1_2_15_42_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082\u2010989X.1.1.30"},{"key":"e_1_2_15_43_1","volume-title":"Linear mixed models for longitudinal data","author":"Molenberghs G.","year":"1997"},{"key":"e_1_2_15_44_1","unstructured":"Mullis I. V. S. Martin M. O. Foy P. Kelly D. L. &Fishbein B.(2020).TIMSS 2019: International results in mathematics and science. (Tech. Rep.). Lynch School of Education and Human Development Boston College and International Association for the Evaluation of Educational Achievement (IEA).https:\/\/www.iea.nl\/sites\/default\/files\/2021\u201001\/TIMSS%202019\u2010International\u2010Results\u2010in\u2010Mathematics\u2010and\u2010Science.pdf"},{"key":"e_1_2_15_45_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000132"},{"key":"e_1_2_15_46_1","doi-asserted-by":"publisher","DOI":"10.1080\/19312458.2012.679848"},{"key":"e_1_2_15_47_1","doi-asserted-by":"publisher","DOI":"10.1037\/0021\u20109010.93.5.959"},{"key":"e_1_2_15_48_1","unstructured":"R Core Team. (2026).R: A language and environment for statistical computing. (version 4.6.1) [Computer software manual]. Vienna Austria.https:\/\/www.R\u2010project.org."},{"key":"e_1_2_15_49_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15327574ijt0601_5"},{"key":"e_1_2_15_50_1","doi-asserted-by":"crossref","DOI":"10.4324\/9780203841624","volume-title":"Introduction to psychometric theory","author":"Raykov T.","year":"2011"},{"key":"e_1_2_15_51_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v048.i02"},{"key":"e_1_2_15_52_1","doi-asserted-by":"crossref","unstructured":"Rosseel Y. Jorgensen T. D. &De Wilde L.(2026).lavaan: Latent variable analysis [Computer software manual]. (R package version 0.7\u20102).https:\/\/doi.org\/10.32614\/CRAN.package.lavaan","DOI":"10.32614\/CRAN.package.lavaan"},{"key":"e_1_2_15_53_1","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2014.931800"},{"key":"e_1_2_15_54_1","volume-title":"Generalizability theory: A primer","author":"Shavelson R. J.","year":"1991"},{"key":"e_1_2_15_55_1","doi-asserted-by":"publisher","DOI":"10.1037\/0033\u20102909.86.2.420"},{"key":"e_1_2_15_56_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11336\u2010008\u20109101\u20100"},{"key":"e_1_2_15_57_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11336\u2010021\u201009789\u20108"},{"key":"e_1_2_15_58_1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780195152968.001.0001","volume-title":"Applied longitudinal data analysis: Modeling change and event occurrence","author":"Singer J. D.","year":"2003"},{"key":"e_1_2_15_59_1","volume-title":"Multilevel analysis: An introduction to basic and advanced multilevel modeling","author":"Snijders T. A. B.","year":"2012"},{"key":"e_1_2_15_60_1","doi-asserted-by":"publisher","DOI":"10.1177\/2515245919855039"},{"key":"e_1_2_15_61_1","doi-asserted-by":"publisher","DOI":"10.3102\/1076998616646200"},{"key":"e_1_2_15_62_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000391"},{"key":"e_1_2_15_63_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000516"},{"key":"e_1_2_15_64_1","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2025.2507745"},{"key":"e_1_2_15_65_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006\u2010341X.2005.031040.x"},{"key":"e_1_2_15_66_1","doi-asserted-by":"publisher","DOI":"10.1080\/08957347.2023.2274573"},{"key":"e_1_2_15_67_1","doi-asserted-by":"publisher","DOI":"10.1037\/pas0001170"},{"key":"e_1_2_15_68_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000107"},{"key":"e_1_2_15_69_1","doi-asserted-by":"publisher","DOI":"10.1080\/00223891.2020.1808474"},{"key":"e_1_2_15_70_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v087.c01"},{"key":"e_1_2_15_71_1","unstructured":"Ye W. Scherer R. &Bl\u00f6meke S.(2022).SEAS in TIMSS 2019. (Project available from the Open Science Framework (OSF)).https:\/\/doi.org\/10.17605\/OSF.IO\/YB9HV"},{"key":"e_1_2_15_72_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40536\u2010024\u201000207\u2010w"},{"key":"e_1_2_15_73_1","doi-asserted-by":"publisher","DOI":"10.1177\/0146621605278814"}],"container-title":["British Journal of Mathematical and Statistical Psychology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/bmsp.70074","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/bmsp.70074","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/bmsp.70074","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T11:42:33Z","timestamp":1791978153000},"score":1,"resource":{"primary":{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/10.1111\/bmsp.70074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,14]]},"references-count":72,"alternative-id":["10.1111\/bmsp.70074"],"URL":"https:\/\/doi.org\/10.1111\/bmsp.70074","archive":["Portico"],"relation":{},"ISSN":["0007-1102","2044-8317"],"issn-type":[{"value":"0007-1102","type":"print"},{"value":"2044-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,14]]},"assertion":[{"value":"2025-05-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"bmsp.70074"}}