{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T06:47:59Z","timestamp":1790232479104,"version":"4.1.0"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2014,4,18]],"date-time":"2014-04-18T00:00:00Z","timestamp":1397779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["11271347"],"award-info":[{"award-number":["11271347"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["11171321"],"award-info":[{"award-number":["11171321"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010346","name":"University of Colorado Denver","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010346","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In longitudinal studies, it is of fundamental importance to understand the dynamics in the mean function, variance function and correlations of the repeated or clustered measurements. For modelling the covariance structure, Cholesky-type decomposition-based approaches have been demonstrated to be effective. However, parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored, and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure. We propose a novel joint mean\u2013variance correlation modelling approach for longitudinal studies. By applying hyperspherical co-ordinates, we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness, and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization. The modelling framework proposed is parsimonious, interpretable and flexible for analysing longitudinal data. Extensive data examples and simulations support the effectiveness of the approach proposed.<\/jats:p>","DOI":"10.1111\/rssb.12065","type":"journal-article","created":{"date-parts":[[2014,4,19]],"date-time":"2014-04-19T06:12:41Z","timestamp":1397887961000},"page":"219-238","source":"Crossref","is-referenced-by-count":81,"title":["A Joint Modelling Approach for Longitudinal Studies"],"prefix":"10.1093","volume":"77","author":[{"given":"Weiping","family":"Zhang","sequence":"first","affiliation":[{"name":"University of Science and Technology of China , Hefei , People's Rebublic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chenlei","family":"Leng","sequence":"additional","affiliation":[{"name":"University of Warwick , Coventry , UK"},{"name":"National University of Singapore , Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng Yong","family":"Tang","sequence":"additional","affiliation":[{"name":"University of Colorado Denver , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2014,4,18]]},"reference":[{"key":"2023022002192076000_rssb12065-cit-0001","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/BF02607055","article-title":"Regularization in statistics (with discussion)","volume":"15","author":"Bickel","year":"2006","journal-title":"Test"},{"key":"2023022002192076000_rssb12065-cit-0002","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1111\/j.0006-341X.2003.00089.x","article-title":"Random effects selection in linear mixed models","volume":"59","author":"Chen","year":"2003","journal-title":"Biometrics"},{"key":"2023022002192076000_rssb12065-cit-0003","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1080\/01621459.1996.10476677","article-title":"The matrix-logarithm covariance model","volume":"91","author":"Chiu","year":"1996","journal-title":"J. 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