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題名 GWTools：地理加權迴歸擴展方法與工具之R套件
GWTools: A Collection of Methods and Tools for Geographically Weighted Regression Extensions in R
作者 張倢琳
Chang, Chieh-Lin
貢獻者 陳怡如<br>吳漢銘
Chen, Yi-Ju<br>Wu, Han-Ming
張倢琳
Chang, Chieh-Lin
關鍵詞 地理加權迴歸
R套件開發
地理加權廣義線性模型
地理加權分量迴歸
地理加權有序邏輯斯迴歸
地理加權多變量迴歸
Geographically Weighted Regression
R package development
GWGLM
GWQR
GWOLR
GWMMR
日期 2025
上傳時間 1-Sep-2025 14:48:40 (UTC+8)
摘要 地理加權迴歸（Geographically Weighted Regression, GWR)為一種常用於探討空間異質性之統計分析方法，近年已廣泛應用於都市規劃、環境分析等領域。然而，現有套件多數侷限於傳統 GWR 架構，對於多樣資料型態（如順序型、分量型、多變量資料）的支援仍不完善，亦缺乏統一具模組化的設計架構。 本研究開發一套具整合性與使用彈性的 R 套件 -- GWTools，整合多種地理加權迴歸擴展模型，包括地理加權廣義線性模型（GWGLM）、二階段地理加權廣義線性模型（TSGWML）、地理加權有序邏輯斯迴歸模型（GWOLR）、地理加權分量迴歸模型（GWQR）與地理加權多變量迴歸模型（GWMMR），提供這些技術建模之帶寬選擇、估計程序與空間異質性檢定函數，並支援平行運算與彈性參數設定。 本研究亦透過東京死亡率資料（Tokyo）、美國喬治亞州嬰兒死亡率資料（Infant） 與美國波士頓房價資料（Boston）等實際資料與模擬範例展示模型應用流程，說明各模型於不同資料結構下使用流程。整體而言，GWTools 為一套功能完整、架構清晰且操作彈性高的地理加權模型 R 套件，可作為未來空間建模應用與方法發展之基礎。
Geographically Weighted Regression (GWR) is a widely used statistical method for analyzing spatial heterogeneity and has been increasingly applied in fields such as urban planning and environmental analysis. However, most existing packages are limited to the traditional GWR framework, lacking support for diverse data types (e.g., ordinal, quantile, and multivariate data) and a consistent and component-based structure. This study proposes an integrated and extensible R package -- GWTools, which integrates various GWR-based model extensions, including Geographically Weighted Generalized Linear Model (GWGLM), Two-Stage Geographically Weighted Maximum Likelihood Models (TSGWML), Geographically Weighted Ordinal Logistic Regression (GWOLR), Geographically Weighted Quantile Regression (GWQR), and Geographically Weighted Multivariate Multiple Regression (GWMMR). The package provides consistent interfaces for bandwidth selection, model estimation, and spatial heterogeneity testing, while supporting parallel computing and flexible parameter settings. We also demonstrate the practical implementation of these models through real and simulated datasets, including the Tokyo, Infant and Boston datasets. These examples help explain how different models in the package can be applied to various data types and response structures. Overall, GWTools is a complete, well-structured, and flexible R package for geographically weighted modeling, and it can serve as a useful tool for future spatial analysis and method development.
參考文獻 [1] Atkinson, P. M., German, S. E., Sear, D. A., and Clark., M. J. (2003). Exploring the relations between riverbank erosion and geomorphological controls using geographi-cally weighted logistic regression. Geographical Analysis, 35(1):58–82. [2] Bo, H., Wu, B., and Barry, M. (2010). Geographically and temporally weighted re-gression for modeling spatio-temporal variation in house prices. International Journal of Geographical Information Science, 24(3):383–401. [3] Brunsdon, C., Fotheringham, S., and Chariton, M. (1998). Geographically weighted regression-modelling spatial non-stationarity. The Statisticia, 47(3):431–443. [4] Brunsdon, C., Fotheringham, S., and Charlton, M. (2007). Geographically weighted discriminant analysis. Geographical Analysis, 39(4). [5] Chen, Y.-J., Deng, W.-S., Yang, T.-C., and Matthews, S. A. (2012). Geographically weighted quantile regression (gwqr): An application to u.s. mortality data. Geograph-ical Analysis, 44:134–150. [6] Chen, Y.-J., Park, K., Sun, F., and Yang, T.-C. (2022a). Assessing covid-19 risk with temporal indices and geographically weighted ordinal logistic regression in us counties. PLOS ONE, 17(4). [7] Chen, Y.-J. and Yang, T.-C. (2012). Sas macro programs for geographically weighted generalized linear modeling with spatial point data: Applications to health research. Computer Methods and Programs in Biomedicine, 107:262–273. [8] Chen, Y.-J. and Yang, T.-C. (2022). Spatial and statistical heterogeneities in popula-tion science using geographically weighted quantile regression. Journal of Population Studies, 65:43–84. [9] Chen, Y.-J., Yang, T.-C., and Jian, H.-L. (2022b). Geographically weighted regression modeling for multiple outcomes. Annals of the American Association of Geographers. DOI: 10.1080/24694452.2021.1985955. [10] da Silva, A. R. and de Oliveira Lima, A. (2017). Geographically weighted beta regression. Spatial Statistics, 21(1). [11] da Silva, A. R. and de Sousa, M. D. R. (2023). Geographically weighted zero-inflated negative binomial regression: A general case for count data. Spatial Statistics, 58:100790. [12] da Silva, A. R. and Rodrigues, T. C. V. (2014). Geographically weighted negative binomial regression—incorporating overdispersion. Statistics and Computing, 24:769–783. [13] Dokmanić, I., Parhizkar, R., Ranieri, J., and Vetterli, M. (2015). Euclidean distance matrices: Essential theory, algorithms and applications. arXiv preprint arXiv:1502.07541. [14] Dong, G., Nakaya, T., and Brunsdon, C. (2018). Geographically weighted regression models for ordinal categorical response variables: An application to geo-referenced life satisfaction data. Computers, Environment and Urban Systems, 70:35–42. [15] Fotheringham, A. S., Brunsdon, C., and Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley. [16] Fotheringham, A. S., Yang, W., and Kang, W. (2017). Multiscale geographically weighted regression (mgwr). Annals of the American Association of Geographers, 107(6):1247–1265. [17] Geraci, M. (2016). Qtools: A collection of models and tools for quantile inference. The R Journal, 8(2):117–138. [18] Gollini, I., Lu, B., Charlton, M., Brunsdon, C., and Harris, P. (2015). Gwmodel: An r package for exploring spatial heterogeneity using geographically weighted models. Journal of Statistical Software, 63(17). [19] Harris, P., Brunsdon, C., and Charlton, M. (2011). Geographically weighted princi-pal components analysis. International Journal of Geographical Information Science, 25(10):1717–1736. [20] Harris, P., Fotheringham, A. S., and Juggins, S. (2010). Robust geographically weighted regression: A technique for quantifying spatial relationships between fresh-water acidification critical loads and catchment attributes. Annals of the American Association of Geographers, 100(2):286–306. [21] Kalogirou, S. (2008). Testing geographically weighted multicollinearity diagnostics. In Proceedings of the 10th AGILE International Conference on Geographic Informa-tion Science. [22] Kalogirou, S. (2016). Destination choice of athenians: An application of geographi-cally weighted versions of standard and zero inflated poisson spatial interaction models. Geographical Analysis, 48:191–230. [23] Li, D. and Mei, C. (2018). A two-stage estimation method with bootstrap inference for semi-parametric geographically weighted generalized linear models. International Journal of Geographical Information Science, 32(9):1860–1883. [24] Liu, X., Liu, X., Zhang, R., Luo, D., Xu, G., and Chen, X. (2022). Securely com-puting the manhattan distance under the malicious model and its applications. Applied Sciences, 12. [25] Morioka, N., Tomio, J., Seto, T., Yumoto, Y., Ogata, Y., and Kobayashi, Y. (2018). Association between local-level resources for home care and home deaths: A nation-wide spatial analysis in japan. PLOS ONE, 13(8). [26] Murakami, D., Tsutsumida, N., Yoshida, T., Nakaya, T., and Lu, B. (2021). Scalable gwr: A linear-time algorithm for large-scale geographically weighted regression with polynomial kernels. Annals of the American Association of Geographers, 111(2):459–480. [27] Nakaya, T. (2015). Geographically Weighted Generalised Linear Modelling. Pages 201–220. [28] Nakaya, T., Fotheringham, A. S., Brunsdon, C., and Charlton, M. (2005). Geo-graphically weighted poisson regression for disease association mapping. Statistics in Medicine, 24(17):2695–2717. [29] Nakaya, T., Fotheringham, A. S., Charlton, M., and Brunsdon, C. (2009). Semipara-metric geographically weighted generalised linear modelling in gwr 4.0. [30] Tomal, M. and Helbich, M. (2022). A spatial autoregressive geographically weighted quantile regression to explore housing rent determinants in amsterdam and warsaw. EPB: Urban Analytics and City Science, 0(0):1–21. [31] Yu, K. and Jones, M. (1997). A comparison of local constant and local linear regres-sion quantile estimators. Computational Statistics & Data Analysis, 25:159–166.
描述 碩士
國立政治大學
統計學系
112354002
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0112354002
資料類型 thesis
dc.contributor.advisor 陳怡如<br>吳漢銘zh_TW
dc.contributor.advisor Chen, Yi-Ju<br>Wu, Han-Mingen_US
dc.contributor.author (Authors) 張倢琳zh_TW
dc.contributor.author (Authors) Chang, Chieh-Linen_US
dc.creator (作者) 張倢琳zh_TW
dc.creator (作者) Chang, Chieh-Linen_US
dc.date (日期) 2025en_US
dc.date.accessioned 1-Sep-2025 14:48:40 (UTC+8)-
dc.date.available 1-Sep-2025 14:48:40 (UTC+8)-
dc.date.issued (上傳時間) 1-Sep-2025 14:48:40 (UTC+8)-
dc.identifier (Other Identifiers) G0112354002en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/159035-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 112354002zh_TW
dc.description.abstract (摘要) 地理加權迴歸（Geographically Weighted Regression, GWR)為一種常用於探討空間異質性之統計分析方法，近年已廣泛應用於都市規劃、環境分析等領域。然而，現有套件多數侷限於傳統 GWR 架構，對於多樣資料型態（如順序型、分量型、多變量資料）的支援仍不完善，亦缺乏統一具模組化的設計架構。 本研究開發一套具整合性與使用彈性的 R 套件 -- GWTools，整合多種地理加權迴歸擴展模型，包括地理加權廣義線性模型（GWGLM）、二階段地理加權廣義線性模型（TSGWML）、地理加權有序邏輯斯迴歸模型（GWOLR）、地理加權分量迴歸模型（GWQR）與地理加權多變量迴歸模型（GWMMR），提供這些技術建模之帶寬選擇、估計程序與空間異質性檢定函數，並支援平行運算與彈性參數設定。 本研究亦透過東京死亡率資料（Tokyo）、美國喬治亞州嬰兒死亡率資料（Infant） 與美國波士頓房價資料（Boston）等實際資料與模擬範例展示模型應用流程，說明各模型於不同資料結構下使用流程。整體而言，GWTools 為一套功能完整、架構清晰且操作彈性高的地理加權模型 R 套件，可作為未來空間建模應用與方法發展之基礎。zh_TW
dc.description.abstract (摘要) Geographically Weighted Regression (GWR) is a widely used statistical method for analyzing spatial heterogeneity and has been increasingly applied in fields such as urban planning and environmental analysis. However, most existing packages are limited to the traditional GWR framework, lacking support for diverse data types (e.g., ordinal, quantile, and multivariate data) and a consistent and component-based structure. This study proposes an integrated and extensible R package -- GWTools, which integrates various GWR-based model extensions, including Geographically Weighted Generalized Linear Model (GWGLM), Two-Stage Geographically Weighted Maximum Likelihood Models (TSGWML), Geographically Weighted Ordinal Logistic Regression (GWOLR), Geographically Weighted Quantile Regression (GWQR), and Geographically Weighted Multivariate Multiple Regression (GWMMR). The package provides consistent interfaces for bandwidth selection, model estimation, and spatial heterogeneity testing, while supporting parallel computing and flexible parameter settings. We also demonstrate the practical implementation of these models through real and simulated datasets, including the Tokyo, Infant and Boston datasets. These examples help explain how different models in the package can be applied to various data types and response structures. Overall, GWTools is a complete, well-structured, and flexible R package for geographically weighted modeling, and it can serve as a useful tool for future spatial analysis and method development.en_US
dc.description.tableofcontents 摘要 i Abstract ii 第一章 緒論 p1 1.1 研究背景與動機 p1 1.2 研究目的 p4 1.3 論文架構 p5 第二章 文獻探討 p7 2.1 地理加權迴歸 p7 2.1.1 參數估計 p8 2.1.2 核函數與帶寬 p9 2.1.3 蒙地卡羅空間異質性檢定方法 p11 2.1.4 拔靴法空間異質性檢定方法 p11 2.2 地理加權迴歸擴展方法 p12 第三章 套件設計與架構 p17 3.1 目前套件現況 p17 3.2 套件架構設計 p21 3.3 核心參數設計 p23 3.3.1 距離矩陣 p24 3.3.2 核函數與帶寬 p24 3.3.3 運算優化設計 p25 3.4 各模型函數介紹 p25 3.5 各模型主要函數語法格式與參數說明 p26 3.6 資料集介紹 p31 3.7 資料格式與輸入設計 p32 第四章 GWGLM 與 TSGWML 模型之套件應用 p33 4.1 模型介紹 p33 4.1.1 地理加權廣義線性模型（GWGLM） p33 4.1.2 二階段地理加權廣義線性模型（TSGWML） p34 4.2 GWGLM 模型實作範例 p36 4.2.1 Tokyo 資料– 計數型反應變數 p36 4.2.2 Infant 資料– 二元型資料 p43 4.3 TSGWML 模型實作範例 p49 第五章 GWOLR 模型之套件應用 p54 5.1 地理加權有序邏輯斯迴歸模型 (GWOLR) 模型介紹 p54 5.2 GWOLR 模型實作範例 p55 第六章 GWQR 模型之套件應用 p59 6.1 地理加權分量迴歸模型 (GWQR) 模型介紹 p59 6.2 GWQR 模型實作範例 p60 第七章 GWMMR 模型之套件應用 p65 7.1 地理加權多變量迴歸 (GWMMR) 模型介紹 p65 7.2 GWMMR 模型實作範例 p67 第八章 結論 p72 8.1 總結與討論 p72 8.2 未來研究 p75 第九章 軟體細節 p77 參考文獻 p78zh_TW
dc.format.extent 6379413 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0112354002en_US
dc.subject (關鍵詞) 地理加權迴歸zh_TW
dc.subject (關鍵詞) R套件開發zh_TW
dc.subject (關鍵詞) 地理加權廣義線性模型zh_TW
dc.subject (關鍵詞) 地理加權分量迴歸zh_TW
dc.subject (關鍵詞) 地理加權有序邏輯斯迴歸zh_TW
dc.subject (關鍵詞) 地理加權多變量迴歸zh_TW
dc.subject (關鍵詞) Geographically Weighted Regressionen_US
dc.subject (關鍵詞) R package developmenten_US
dc.subject (關鍵詞) GWGLMen_US
dc.subject (關鍵詞) GWQRen_US
dc.subject (關鍵詞) GWOLRen_US
dc.subject (關鍵詞) GWMMRen_US
dc.title (題名) GWTools：地理加權迴歸擴展方法與工具之R套件zh_TW
dc.title (題名) GWTools: A Collection of Methods and Tools for Geographically Weighted Regression Extensions in Ren_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Atkinson, P. M., German, S. E., Sear, D. A., and Clark., M. J. (2003). Exploring the relations between riverbank erosion and geomorphological controls using geographi-cally weighted logistic regression. Geographical Analysis, 35(1):58–82. [2] Bo, H., Wu, B., and Barry, M. (2010). Geographically and temporally weighted re-gression for modeling spatio-temporal variation in house prices. International Journal of Geographical Information Science, 24(3):383–401. [3] Brunsdon, C., Fotheringham, S., and Chariton, M. (1998). Geographically weighted regression-modelling spatial non-stationarity. The Statisticia, 47(3):431–443. [4] Brunsdon, C., Fotheringham, S., and Charlton, M. (2007). Geographically weighted discriminant analysis. Geographical Analysis, 39(4). [5] Chen, Y.-J., Deng, W.-S., Yang, T.-C., and Matthews, S. A. (2012). Geographically weighted quantile regression (gwqr): An application to u.s. mortality data. Geograph-ical Analysis, 44:134–150. [6] Chen, Y.-J., Park, K., Sun, F., and Yang, T.-C. (2022a). Assessing covid-19 risk with temporal indices and geographically weighted ordinal logistic regression in us counties. PLOS ONE, 17(4). [7] Chen, Y.-J. and Yang, T.-C. (2012). Sas macro programs for geographically weighted generalized linear modeling with spatial point data: Applications to health research. Computer Methods and Programs in Biomedicine, 107:262–273. [8] Chen, Y.-J. and Yang, T.-C. (2022). Spatial and statistical heterogeneities in popula-tion science using geographically weighted quantile regression. Journal of Population Studies, 65:43–84. [9] Chen, Y.-J., Yang, T.-C., and Jian, H.-L. (2022b). Geographically weighted regression modeling for multiple outcomes. Annals of the American Association of Geographers. DOI: 10.1080/24694452.2021.1985955. [10] da Silva, A. R. and de Oliveira Lima, A. (2017). Geographically weighted beta regression. Spatial Statistics, 21(1). [11] da Silva, A. R. and de Sousa, M. D. R. (2023). Geographically weighted zero-inflated negative binomial regression: A general case for count data. Spatial Statistics, 58:100790. [12] da Silva, A. R. and Rodrigues, T. C. V. (2014). Geographically weighted negative binomial regression—incorporating overdispersion. Statistics and Computing, 24:769–783. [13] Dokmanić, I., Parhizkar, R., Ranieri, J., and Vetterli, M. (2015). Euclidean distance matrices: Essential theory, algorithms and applications. arXiv preprint arXiv:1502.07541. [14] Dong, G., Nakaya, T., and Brunsdon, C. (2018). Geographically weighted regression models for ordinal categorical response variables: An application to geo-referenced life satisfaction data. Computers, Environment and Urban Systems, 70:35–42. [15] Fotheringham, A. S., Brunsdon, C., and Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley. [16] Fotheringham, A. S., Yang, W., and Kang, W. (2017). Multiscale geographically weighted regression (mgwr). Annals of the American Association of Geographers, 107(6):1247–1265. [17] Geraci, M. (2016). Qtools: A collection of models and tools for quantile inference. The R Journal, 8(2):117–138. [18] Gollini, I., Lu, B., Charlton, M., Brunsdon, C., and Harris, P. (2015). Gwmodel: An r package for exploring spatial heterogeneity using geographically weighted models. Journal of Statistical Software, 63(17). [19] Harris, P., Brunsdon, C., and Charlton, M. (2011). Geographically weighted princi-pal components analysis. International Journal of Geographical Information Science, 25(10):1717–1736. [20] Harris, P., Fotheringham, A. S., and Juggins, S. (2010). Robust geographically weighted regression: A technique for quantifying spatial relationships between fresh-water acidification critical loads and catchment attributes. Annals of the American Association of Geographers, 100(2):286–306. [21] Kalogirou, S. (2008). Testing geographically weighted multicollinearity diagnostics. In Proceedings of the 10th AGILE International Conference on Geographic Informa-tion Science. [22] Kalogirou, S. (2016). Destination choice of athenians: An application of geographi-cally weighted versions of standard and zero inflated poisson spatial interaction models. Geographical Analysis, 48:191–230. [23] Li, D. and Mei, C. (2018). A two-stage estimation method with bootstrap inference for semi-parametric geographically weighted generalized linear models. International Journal of Geographical Information Science, 32(9):1860–1883. [24] Liu, X., Liu, X., Zhang, R., Luo, D., Xu, G., and Chen, X. (2022). Securely com-puting the manhattan distance under the malicious model and its applications. Applied Sciences, 12. [25] Morioka, N., Tomio, J., Seto, T., Yumoto, Y., Ogata, Y., and Kobayashi, Y. (2018). Association between local-level resources for home care and home deaths: A nation-wide spatial analysis in japan. PLOS ONE, 13(8). [26] Murakami, D., Tsutsumida, N., Yoshida, T., Nakaya, T., and Lu, B. (2021). Scalable gwr: A linear-time algorithm for large-scale geographically weighted regression with polynomial kernels. Annals of the American Association of Geographers, 111(2):459–480. [27] Nakaya, T. (2015). Geographically Weighted Generalised Linear Modelling. Pages 201–220. [28] Nakaya, T., Fotheringham, A. S., Brunsdon, C., and Charlton, M. (2005). Geo-graphically weighted poisson regression for disease association mapping. Statistics in Medicine, 24(17):2695–2717. [29] Nakaya, T., Fotheringham, A. S., Charlton, M., and Brunsdon, C. (2009). Semipara-metric geographically weighted generalised linear modelling in gwr 4.0. [30] Tomal, M. and Helbich, M. (2022). A spatial autoregressive geographically weighted quantile regression to explore housing rent determinants in amsterdam and warsaw. EPB: Urban Analytics and City Science, 0(0):1–21. [31] Yu, K. and Jones, M. (1997). A comparison of local constant and local linear regres-sion quantile estimators. Computational Statistics & Data Analysis, 25:159–166.zh_TW