{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T09:51:36Z","timestamp":1791280296047,"version":"4.1.0"},"reference-count":54,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005416","name":"Norges Forskningsr\u00e5d","doi-asserted-by":"publisher","award":["33160"],"award-info":[{"award-number":["33160"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Psychometrika"],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Time-varying coefficient modeling (TVCM), which represents regression coefficients as smooth functions of continuous time, provides a flexible framework for uncovering complex patterns of change in levels and associations in intensive longitudinal data. However, conventional TVCM remains limited to investigating directional effects across individuals. By introducing a TVCM formulation of the multivariate normal distribution, the present study extends TVCM to explore change in undirected associations (couplings) and variability, thereby broadening its utility for psychological research. We discuss three versions of this approach: an aggregate-level model and two hierarchical versions capturing interindividual differences in unfolding change, either via person-specific intercepts accounting for onset differences or through fully person-specific coefficient functions smoothed via partial pooling. To illustrate the proposed developments, we apply them to six weeks of intensive longitudinal data from 16 anxiety patients undergoing therapy and examine unfolding changes in the level and volatility of nervousness and threat monitoring, their coupling, as well as between-person heterogeneity in each of these. We further show how inspecting first-order derivatives of the coefficient functions supports identifying periods of stability and change. Finally, we discuss extensions incorporating person-level characteristics to explain heterogeneity in patterns of change and predict outcomes.<\/jats:p>","DOI":"10.1017\/psy.2026.10125","type":"journal-article","created":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T05:13:51Z","timestamp":1783401231000},"page":"1498-1523","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Capturing Heterogeneity in Levels, Variability, and Couplings across Persons and Time with a Hierarchical Time-Varying Coefficient Formulation of the Multivariate Normal"],"prefix":"10.1017","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9267-8542","authenticated-orcid":false,"given":"Esther","family":"Ulitzsch","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01xtthb56","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oslo"},{"id":[{"id":"https:\/\/ror.org\/01xtthb56","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oslo"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steffen","family":"Nestler","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00pd74e08","id-type":"ROR","asserted-by":"publisher"}],"name":"University of M\u00fcnster"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sverre Urnes","family":"Johnson","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01xtthb56","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oslo"},{"id":[{"id":"https:\/\/ror.org\/03vek6s52","id-type":"ROR","asserted-by":"publisher"}],"name":"Harvard University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Therese Ruud","family":"Snuggerud","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01xtthb56","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oslo"},{"id":[{"id":"https:\/\/ror.org\/026nfkh32","id-type":"ROR","asserted-by":"publisher"}],"name":"Modum Bad Psychiatric Hospital"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Oliver","family":"L\u00fcdtke","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/008n8dd57","id-type":"ROR","asserted-by":"publisher"}],"name":"Leibniz Institute for Science and Mathematics Education"},{"name":"Centre for International Student Assessment"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,7,7]]},"reference":[{"key":"S0033312326101252_r10","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-clinpsy-081423-022947"},{"key":"S0033312326101252_r18","doi-asserted-by":"publisher","DOI":"10.1037\/met0000034"},{"key":"S0033312326101252_r44","doi-asserted-by":"publisher","DOI":"10.1111\/add.16284"},{"key":"S0033312326101252_r31","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2022.2103703"},{"key":"S0033312326101252_r13","doi-asserted-by":"publisher","DOI":"10.1177\/2167702620901744"},{"key":"S0033312326101252_r24","doi-asserted-by":"publisher","DOI":"10.1037\/met0000536"},{"key":"S0033312326101252_r6","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177011136"},{"key":"S0033312326101252_r52","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010404"},{"key":"S0033312326101252_r34","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2024.2398034"},{"key":"S0033312326101252_r19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-70944-0"},{"key":"S0033312326101252_r41","doi-asserted-by":"publisher","DOI":"10.1016\/j.janxdis.2026.103136"},{"key":"S0033312326101252_r15","volume-title":"Bayesian statistics for the social sciences","author":"Kaplan","year":"2023"},{"key":"S0033312326101252_r9","unstructured":"Guo, J. , Gabry, J. , & Goodrich, B. (2018). RStan: R interface to Stan. [R package version 2.18.2]. https:\/\/CRAN.R-project.org\/package=rstan"},{"key":"S0033312326101252_r29","doi-asserted-by":"publisher","DOI":"10.1111\/jopy.12351"},{"key":"S0033312326101252_r40","doi-asserted-by":"publisher","DOI":"10.1080\/16506073.2025.2509168"},{"key":"S0033312326101252_r26","doi-asserted-by":"publisher","DOI":"10.2196\/11845"},{"key":"S0033312326101252_r28","doi-asserted-by":"publisher","DOI":"10.1037\/met0000481"},{"key":"S0033312326101252_r51","doi-asserted-by":"publisher","DOI":"10.2196\/69297"},{"key":"S0033312326101252_r54","doi-asserted-by":"publisher","DOI":"10.1177\/10731911211067538"},{"key":"S0033312326101252_r36","doi-asserted-by":"publisher","DOI":"10.5334\/jopd.83"},{"key":"S0033312326101252_r5","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0111080"},{"key":"S0033312326101252_r3","doi-asserted-by":"publisher","DOI":"10.1016\/j.addbeh.2019.106192"},{"key":"S0033312326101252_r30","doi-asserted-by":"publisher","DOI":"10.1159\/000507993"},{"key":"S0033312326101252_r49","doi-asserted-by":"publisher","DOI":"10.4324\/9780429273872-6"},{"key":"S0033312326101252_r33","volume-title":"R: A language and environment for statistical computing","year":"2017"},{"key":"S0033312326101252_r22","doi-asserted-by":"publisher","DOI":"10.1037\/met0000663"},{"key":"S0033312326101252_r14","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.4.809"},{"key":"S0033312326101252_r20","doi-asserted-by":"publisher","DOI":"10.1093\/ntr\/ntt128"},{"key":"S0033312326101252_r8","doi-asserted-by":"publisher","DOI":"10.1007\/s10608-023-10453-x"},{"key":"S0033312326101252_r45","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000523"},{"key":"S0033312326101252_r23","doi-asserted-by":"publisher","DOI":"10.1037\/met0000250"},{"key":"S0033312326101252_r1","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2017.1406803"},{"key":"S0033312326101252_r35","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755453"},{"key":"S0033312326101252_r43","unstructured":"Stan Development Team (2017). Stan modeling language: User\u2019s guide and reference manual (Version No. 2.17.0). https:\/\/github.com\/stan-dev\/stan\/releases\/download\/v2.17.1\/stan-reference-2.17.1.pdf"},{"key":"S0033312326101252_r47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpsychires.2021.02.012"},{"key":"S0033312326101252_r2","doi-asserted-by":"publisher","DOI":"10.1037\/met0000085"},{"key":"S0033312326101252_r17","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2022.2130331"},{"key":"S0033312326101252_r4","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1038425655"},{"key":"S0033312326101252_r50","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-016-9696-4"},{"key":"S0033312326101252_r48","article-title":"A graph-theory based similarity metric enables comparison of sub-population psychometric networks","author":"Ulitzsch","year":"2023","journal-title":"Psychological Methods"},{"key":"S0033312326101252_r11","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2020.1743630"},{"key":"S0033312326101252_r37","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2017.06.039"},{"key":"S0033312326101252_r32","doi-asserted-by":"publisher","DOI":"10.1111\/add.16308"},{"key":"S0033312326101252_r53","doi-asserted-by":"publisher","DOI":"10.1037\/a0034430"},{"key":"S0033312326101252_r25","doi-asserted-by":"publisher","DOI":"10.1080\/10705511.2021.1915788"},{"key":"S0033312326101252_r7","first-page":"163","volume-title":"Handbook of Markov chain Monte Carlo","author":"Gelman","year":"2011"},{"key":"S0033312326101252_r12","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1993.tb01939.x"},{"key":"S0033312326101252_r39","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780195152968.001.0001"},{"key":"S0033312326101252_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpsychires.2016.01.011"},{"key":"S0033312326101252_r42","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2025.2507297"},{"key":"S0033312326101252_r16","volume-title":"Semiparametric regression for the social sciences","author":"Keele","year":"2008"},{"key":"S0033312326101252_r21","article-title":"Intensive longitudinal methods: Toward a psychological science of daily life","volume":"77","author":"Laurenceau","year":"2025","journal-title":"Annual Review of Psychology"},{"key":"S0033312326101252_r46","doi-asserted-by":"publisher","DOI":"10.1037\/a0025814"},{"key":"S0033312326101252_r38","doi-asserted-by":"publisher","DOI":"10.1007\/s11121-011-0264-z"}],"container-title":["Psychometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0033312326101252","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T08:59:10Z","timestamp":1791277150000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0033312326101252\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,7]]},"references-count":54,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["S0033312326101252"],"URL":"https:\/\/doi.org\/10.1017\/psy.2026.10125","relation":{},"ISSN":["0033-3123","1860-0980"],"issn-type":[{"value":"0033-3123","type":"print"},{"value":"1860-0980","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,7]]},"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"}]}}