{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:36:28Z","timestamp":1760146588869,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,16]],"date-time":"2024-11-16T00:00:00Z","timestamp":1731715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Project on Graduate Education and Teaching Reform of Hebei Province, China","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}]},{"name":"Open Fund Project of the Marine Ecological Restoration and Smart Ocean Engineering Research Center of Hebei Province","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}]},{"name":"Technical Service Project of the Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}]},{"name":"Technical Service Project of Hebei Baodi Construction Engineering Co., Ltd.","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}]},{"name":"Natural Science Foundation of Hebei Province, China","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"],"award-info":[{"award-number":["YJG2024133","HBMESO2321","KJ2022-021","KJ2024-012","A2020501007","N2123015"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Poisson regression is a statistical method specifically designed for analyzing count data. Considering the case where the functional and vector-valued covariates exhibit a linear relationship with the log-transformed Poisson mean, while the covariates in complex domains act as nonlinear random effects, an intrinsic functional partially linear Poisson regression model is proposed. This model flexibly integrates predictors from different spaces, including functional covariates, vector-valued covariates, and other non-Euclidean covariates taking values in complex domains. A truncation scheme is applied to approximate the functional covariates, and the random effects related to non-Euclidean covariates are modeled based on the reproducing kernel method. A quasi-Newton iterative algorithm is employed to optimize the parameters of the proposed model. Furthermore, to capture the intrinsic geometric structure of the covariates in complex domains, the heat kernel is employed as the kernel function, estimated via Brownian motion simulations. Both simulation studies and real data analysis demonstrate that the proposed method offers significant advantages over the classical Poisson regression model.<\/jats:p>","DOI":"10.3390\/axioms13110795","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T11:58:07Z","timestamp":1732017487000},"page":"795","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Intrinsic Functional Partially Linear Poisson Regression Model for Count Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-8878-7173","authenticated-orcid":false,"given":"Jiaqi","family":"Xu","sequence":"first","affiliation":[{"name":"Sydney Smart Technology College, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Lu","sequence":"additional","affiliation":[{"name":"Sydney Smart Technology College, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanshen","family":"Su","sequence":"additional","affiliation":[{"name":"Sydney Smart Technology College, Northeastern University, Shenyang 110004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1024-3201","authenticated-orcid":false,"given":"Tao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunfei","family":"Qi","sequence":"additional","affiliation":[{"name":"Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wu","family":"Xie","sequence":"additional","affiliation":[{"name":"Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Getaneh, F.B., Belete, A.G., Ayres, A., Ayalew, T., Muche, A., and Derseh, L. 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