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<article article-type="research-article" dtd-version="1.1" xml:lang="en" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="publisher-id">ASM</journal-id><journal-id journal-id-type="nlm-ta">Assessment</journal-id><journal-title-group><journal-title>Assessment</journal-title></journal-title-group><issn pub-type="ppub">1073-1911</issn><issn pub-type="epub">1552-3489</issn><publisher><publisher-name>SAGE Publications</publisher-name><publisher-loc>Sage CA: Los Angeles, CA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.1177/10731911231182687</article-id><article-id pub-id-type="publisher-id">10.1177_10731911231182687</article-id><article-categories><subj-group subj-group-type="heading"><subject>Original Research Articles</subject></subj-group></article-categories><title-group><article-title>Measurement Invariance in Longitudinal Bifactor Models: Review and Application Based on the <italic>p</italic> Factor</article-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5470-3770</contrib-id><name><surname>Neufeld</surname><given-names>Sharon A. S.</given-names></name><xref ref-type="aff" rid="aff1-10731911231182687">1</xref><xref ref-type="corresp" rid="corresp1-10731911231182687"/></contrib><contrib contrib-type="author"><name><surname>St Clair</surname><given-names>Michelle</given-names></name><xref ref-type="aff" rid="aff2-10731911231182687">2</xref></contrib><contrib contrib-type="author"><name><surname>Brodbeck</surname><given-names>Jeannette</given-names></name><xref ref-type="aff" rid="aff3-10731911231182687">3</xref></contrib><contrib contrib-type="author"><name><surname>Wilkinson</surname><given-names>Paul O.</given-names></name><xref ref-type="aff" rid="aff1-10731911231182687">1</xref></contrib><contrib contrib-type="author"><name><surname>Goodyer</surname><given-names>Ian M.</given-names></name><xref ref-type="aff" rid="aff1-10731911231182687">1</xref></contrib><contrib contrib-type="author"><name><surname>Jones</surname><given-names>Peter B.</given-names></name><xref ref-type="aff" rid="aff1-10731911231182687">1</xref></contrib></contrib-group><aff id="aff1-10731911231182687"><label>1</label>University of Cambridge, UK</aff><aff id="aff2-10731911231182687"><label>2</label>University of Bath, UK</aff><aff id="aff3-10731911231182687"><label>3</label>University of Bern, Switzerland</aff><author-notes><corresp id="corresp1-10731911231182687">Sharon A. S. Neufeld, Department of Psychiatry, University of Cambridge, Douglas House, 18b Trumpington Road, Cambridge CB2 8AH, UK. Email: <email>sasn2@medschl.cam.ac.uk</email></corresp></author-notes><pub-date pub-type="epub"><day>22</day><month>6</month><year>2023</year></pub-date><volume>31</volume><issue>4</issue><fpage>774</fpage><lpage>793</lpage><permissions><copyright-statement>© The Author(s) 2023</copyright-statement><copyright-year>2023</copyright-year><copyright-holder content-type="sage">SAGE Publications</copyright-holder><license><ali:license_ref start_date="2023-06-22" xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This article is distributed under the terms of the Creative Commons Attribution 4.0 License (<ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link>) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (<ext-link ext-link-type="uri" xlink:href="https://us.sagepub.com/en-us/nam/open-access-at-sage">https://us.sagepub.com/en-us/nam/open-access-at-sage</ext-link>).</license-p></license></permissions><abstract><p>Bifactor models are increasingly being utilized to study latent constructs such as psychopathology and cognition, which change over the lifespan. Although longitudinal measurement invariance (MI) testing helps ensure valid interpretation of change in a construct over time, this is rarely and inconsistently performed in bifactor models. Our review of MI simulation literature revealed that only one study assessed MI in bifactor models under limited conditions. Recommendations for how to assess MI in bifactor models are suggested based on existing simulation studies of related models. Estimator choice and influence of missing data on MI are also discussed. An empirical example based on a model of the general psychopathology factor (<italic>p</italic>) elucidates our recommendations, with the present model of <italic>p</italic> being the first to exhibit residual MI across gender and time. Thus, changes in the ordered-categorical indicators can be attributed to changes in the latent factors. However, further work is needed to clarify MI guidelines for bifactor models, including considering the impact of model complexity and number of indicators. Nonetheless, using the guidelines justified herein to establish MI allows findings from bifactor models to be more confidently interpreted, increasing their comparability and utility.</p></abstract><kwd-group><kwd>longitudinal bifactor modeling</kwd><kwd>measurement invariance</kwd><kwd>review</kwd><kwd>simulation studies</kwd><kwd><italic>p</italic> factor (general psychopathology)</kwd></kwd-group><funding-group specific-use="FundRef"><award-group id="award1-10731911231182687"><funding-source id="funding1-10731911231182687"><institution-wrap><institution>Wellcome Trust Institutional Strategic Support Fund</institution><institution-id/></institution-wrap></funding-source><award-id rid="funding1-10731911231182687">204845/Z/16/Z</award-id></award-group><award-group id="award2-10731911231182687"><funding-source id="funding2-10731911231182687"><institution-wrap><institution>Cundill Centre for Child and Youth Depression at the Centre for Addiction and Mental Health</institution><institution-id/></institution-wrap></funding-source></award-group><award-group id="award3-10731911231182687"><funding-source id="funding3-10731911231182687"><institution-wrap><institution>NIHR Collaboration for Leadership in Applied Health Research &amp; Care East of England</institution><institution-id/></institution-wrap></funding-source></award-group><award-group id="award4-10731911231182687"><funding-source id="funding4-10731911231182687"><institution-wrap><institution>NIHR Cambridge Biomedical Research Centre</institution><institution-id institution-id-type="FundRef">https://doi.org/10.13039/501100018956</institution-id></institution-wrap></funding-source><award-id rid="funding4-10731911231182687">BRC-1215-20014</award-id></award-group><award-group id="award5-10731911231182687"><funding-source id="funding5-10731911231182687"><institution-wrap><institution>Wellcome Trust Cambridge-UCL Mental Health and Neurosciences Network</institution><institution-id/></institution-wrap></funding-source><award-id rid="funding5-10731911231182687">095844/Z/11/Z</award-id></award-group></funding-group><custom-meta-group><custom-meta><meta-name>typesetter</meta-name><meta-value>ts1</meta-value></custom-meta></custom-meta-group></article-meta></front></article>