{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T03:11:33Z","timestamp":1768619493314,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T00:00:00Z","timestamp":1724716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009546","name":"Yujie Talent Project of North China University of Technology","doi-asserted-by":"publisher","award":["107051360024XN153"],"award-info":[{"award-number":["107051360024XN153"]}],"id":[{"id":"10.13039\/501100009546","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a generalized partially functional linear model with interaction terms. It is suitable for cases where the response variable is scalar, and the predictor variables include a mix of functional and scalar types, while considering the correlations among functional predictor variables. The model uses principal component analysis for dimensionality reduction, employs maximum likelihood estimation to obtain parameter values, proves the asymptotic properties of the estimates, and validates the model\u2019s accuracy through data simulation experiments. Finally, the proposed model was applied to investigate the influence of air quality, climate factors, and medical and social indicators, along with their interactions, on cancer incidence, which is a binary response.<\/jats:p>","DOI":"10.3390\/axioms13090583","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T06:19:01Z","timestamp":1724739541000},"page":"583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Partially Functional Linear Model with Interaction between Functional Predictors"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9553-2581","authenticated-orcid":false,"given":"Weiwei","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Science, North China University of Technology, Beijing 100144, China"}]},{"given":"Kejing","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Science, North China University of Technology, Beijing 100144, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3442-1722","authenticated-orcid":false,"given":"Haiyan","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Leeds, Leeds LS2 9JT, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ramsay, J.O., and Silverman, B.W. 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