{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T17:21:58Z","timestamp":1787505718509,"version":"build-2736575974"},"reference-count":28,"publisher":"Wiley","issue":"18-19","license":[{"start":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T00:00:00Z","timestamp":1785801600000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100012325","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["21BTJ044"],"award-info":[{"award-number":["21BTJ044"]}],"id":[{"id":"10.13039\/501100012325","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12371267"],"award-info":[{"award-number":["12371267"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>With population aging, Alzheimer's disease has gained increasing attention. Advances in medical technology and longitudinal studies such as the Alzheimer's Disease Neuroimaging Initiative (ADNI) have generated diverse follow\u2010up data, which can be viewed as multilevel multisource functional data for understanding disease progression. In this paper, we propose a new estimation method for the multilevel multisource functional principal components. This method first applies the multilevel functional principal component analysis on the univariate multilevel functional data, then obtains the estimation of the principal components of the multilevel multisource functional principal component model based on the relationship between the univariate and the multisource principal component models, thus realizing the multisource\u2010component\u2010based two\u2010stage estimation of the generalized multilevel multisource functional regression model. We also further consider Bayesian estimation based on the two\u2010stage estimation. Numerical simulations and empirical analyses show that both the proposed multisource\u2010component\u2010based two\u2010stage estimation and Bayesian estimation methods work well. Compared to the multisource\u2010component\u2010based two\u2010stage estimation methods, the classification performance of Bayesian estimation is significantly improved.<\/jats:p>","DOI":"10.1002\/sim.70688","type":"journal-article","created":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T10:53:26Z","timestamp":1785840806000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generalized Multilevel Multisource Functional Regression With an Application to Alzheimer's Disease"],"prefix":"10.1002","volume":"45","author":[{"given":"Xiuli","family":"Du","sequence":"first","affiliation":[{"name":"College of Mathematical Sciences Ministry of Education Key Laboratory of NSLSCS Nanjing Normal University  Nanjing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guorong","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Medical Engineering and Affiliated Zhuhai People's Hospital Beijing Institute of Technology  Zhuhai China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yenan","family":"Ren","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences Ministry of Education Key Laboratory of NSLSCS Nanjing Normal University  Nanjing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziting","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences Ministry of Education Key Laboratory of NSLSCS Nanjing Normal University  Nanjing China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9562-4515","authenticated-orcid":false,"given":"Hui","family":"Mi","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences Ministry of Education Key Laboratory of NSLSCS Nanjing Normal University  Nanjing China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,4]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2011.03.011"},{"issue":"4","key":"e_1_2_11_3_1","first-page":"1571","article-title":"Multivariate Functional Principal Component Analysis: A Normalization Approach","volume":"24","author":"Chiou J. 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