Spatially varying coefficient models using reduced-rank thin-plate splines
Spatially varying coefficient (SVC) regression models are concerned about regression for spatial data, where regression coefficients may vary in space. This paper proposes a new approach for SVC modeling by representing regression coefficients using a class of multiresolution spline basis functions...
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| Published in | Spatial statistics Vol. 51; p. 100654 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.10.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2211-6753 2211-6753 |
| DOI | 10.1016/j.spasta.2022.100654 |
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| Abstract | Spatially varying coefficient (SVC) regression models are concerned about regression for spatial data, where regression coefficients may vary in space. This paper proposes a new approach for SVC modeling by representing regression coefficients using a class of multiresolution spline basis functions in a generalized-linear model framework. The proposed method provides flexible and parsimonious representations for regression coefficients. It enables commonly used (generalized) linear-regression packages for estimation, testing, and constructing confidence levels. We develop a fast estimation algorithm that simultaneously performs variable selection, detects spatial heterogeneity for each variable, and determines its complexity. We provide numerical examples and an application to a real estate dataset to demonstrate the proposed method’s effectiveness. |
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| AbstractList | Spatially varying coefficient (SVC) regression models are concerned about regression for spatial data, where regression coefficients may vary in space. This paper proposes a new approach for SVC modeling by representing regression coefficients using a class of multiresolution spline basis functions in a generalized-linear model framework. The proposed method provides flexible and parsimonious representations for regression coefficients. It enables commonly used (generalized) linear-regression packages for estimation, testing, and constructing confidence levels. We develop a fast estimation algorithm that simultaneously performs variable selection, detects spatial heterogeneity for each variable, and determines its complexity. We provide numerical examples and an application to a real estate dataset to demonstrate the proposed method’s effectiveness. |
| ArticleNumber | 100654 |
| Author | Fan, Yu-Ting Huang, Hsin-Cheng |
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| Cites_doi | 10.1175/MWR2904.1 10.1111/j.1467-9868.2005.00532.x 10.1080/10485252.2020.1759596 10.1080/00401706.2017.1345701 10.1016/j.spasta.2016.12.001 10.1111/1467-9868.00374 10.1016/j.spasta.2019.02.003 10.1080/00401706.2017.1317290 10.1016/j.spasta.2020.100470 10.1111/biom.13077 10.1007/s10109-006-0028-7 10.1214/13-AOS1201 10.1214/aos/1176344136 10.1002/env.2485 10.1002/env.599 10.1198/016214503000170 |
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| Keywords | Multiresolution spline basis function Generalized linear model Model selection Log-normal regression Cross-validation Geographically weighted regression |
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| Title | Spatially varying coefficient models using reduced-rank thin-plate splines |
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