Intrinsic Functional Partially Linear Poisson Regression Model for Count Data
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 effec...
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MDPI AG
2024-11-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/11/795 |
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| author | Jiaqi Xu Yu Lu Yuanshen Su Tao Liu Yunfei Qi Wu Xie |
| author_facet | Jiaqi Xu Yu Lu Yuanshen Su Tao Liu Yunfei Qi Wu Xie |
| author_sort | Jiaqi Xu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c4d9c05e5fd64ceca976bae61cbbb7b1 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c4d9c05e5fd64ceca976bae61cbbb7b12024-11-26T17:50:56ZengMDPI AGAxioms2075-16802024-11-01131179510.3390/axioms13110795Intrinsic Functional Partially Linear Poisson Regression Model for Count DataJiaqi Xu0Yu Lu1Yuanshen Su2Tao Liu3Yunfei Qi4Wu Xie5Sydney Smart Technology College, Northeastern University, Shenyang 110004, ChinaSydney Smart Technology College, Northeastern University, Shenyang 110004, ChinaSydney Smart Technology College, Northeastern University, Shenyang 110004, ChinaSchool of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, ChinaEighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, ChinaEighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration (Hebei Center of Marine Geological Resources Survey), Qinhuangdao 066000, ChinaPoisson 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.https://www.mdpi.com/2075-1680/13/11/795Poisson regressionKarhunen–Loève expansionrandom effectsheat kernelquasi-Newton algorithm |
| spellingShingle | Jiaqi Xu Yu Lu Yuanshen Su Tao Liu Yunfei Qi Wu Xie Intrinsic Functional Partially Linear Poisson Regression Model for Count Data Axioms Poisson regression Karhunen–Loève expansion random effects heat kernel quasi-Newton algorithm |
| title | Intrinsic Functional Partially Linear Poisson Regression Model for Count Data |
| title_full | Intrinsic Functional Partially Linear Poisson Regression Model for Count Data |
| title_fullStr | Intrinsic Functional Partially Linear Poisson Regression Model for Count Data |
| title_full_unstemmed | Intrinsic Functional Partially Linear Poisson Regression Model for Count Data |
| title_short | Intrinsic Functional Partially Linear Poisson Regression Model for Count Data |
| title_sort | intrinsic functional partially linear poisson regression model for count data |
| topic | Poisson regression Karhunen–Loève expansion random effects heat kernel quasi-Newton algorithm |
| url | https://www.mdpi.com/2075-1680/13/11/795 |
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