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題名 地理加權迴歸模型估計方法之比較
A Study of Estimation Methods for Geographically Weighted Regression作者 郭柔芸
Kuo, Rou-Yun貢獻者 楊曉文<br>余清祥
Yang, Sheau-Wen<br>Yue, Ching-Syang
郭柔芸
Kuo, Rou-Yun關鍵詞 空間分析
地理加權迴歸
探索性資料分析
環寬
電腦模擬
Spatial analysis
Geographically weighted regression
Exploratory data analysis
Bandwidth
Computer simulation日期 2022 上傳時間 2-Sep-2022 14:45:20 (UTC+8) 摘要 隨著資料蒐集普及化，有效率呈現龐雜資訊的需求愈發殷切，其中資料視覺化(Data Visualization)更是探索性資料分析(Exploratory Data Analysis)的核心，協助人們以目視判斷關鍵資訊。以空間資料而言，地理加權迴歸(Geographically Weighted Regression, GWR)取代傳統迴歸模型，以解除樣本間獨立和同質變異下的限制，可用於描述解釋變數和目標變數間的局部關係。但GWR的估計結果有時卻不盡理想，近年有不少研究從環寬(bandwidth)的選擇上出發，希冀可改善估計值不平滑等之問題，修正方法包括多尺度地理加權迴歸模型(Multiscale GWR, MGWR)和條件地理加權迴歸(Conditional GWR, CGWR)，但少有研究比較GWR及其修正模型的適用情況。本文以電腦模擬比較GWR、MGWR、CGWR三個模型。實驗空間為1010的格子點，僅考慮簡單線性迴歸，亦即y(u,v)=β_0 (u,v)+β_1 (u,v)×x(u,v)，參數曲面β_0 (u,v)和β_1 (u,v)為線性曲面、二次曲面。本文比較目標變數、參數曲面估計值的誤差，作為三種模型的比較依據，說明GWR的限制及可能問題，測試修正方法是否有效。電腦模擬的結果顯示GWR在目標變數的估計結果尚稱準確，但係數曲面的估計結果相當不理想，而CGWR無論是係數曲面的形狀、或是係數MSE (Mean Squared Error)誤差都比較穩定，MGWR在複雜參數曲面下較不穩定。實證分析的結果顯示，MGWR在目標變數有較穩定的估計表現，而三個模型在係數曲面結果不盡相同。
With the rapidly growing of data size and complexity, the need to efficiently present useful information becomes more essential. Data Visualization, the core of Exploratory Data Analysis, can help people to detect key information in data analysis. Taking the analysis of spatial data as an example, Geographically Weighted Regression (GWR) can be treated as an extension of traditional regression models. It can remove the constraints of independent and homogeneous variation among samples, and especially visually describe the local relationship between explanatory variables and target variables. However, the estimation of GWR can be unsatisfactory and produce distorted relationship. In recent years, many studies tried to modify GWR in order to improve the estimation results and adjusting the estimation bandwidth is one of them. Multiscale geographically weighted regression models (MGWR) and Conditional Geographically Weighted Regression (CGWR) are two methods of adjusting bandwidth, but few studies compare the estimation results of GWR and its modified models (e.g., MGWR and CGWR).In this paper, we use simulation and empirical data to evaluate GWR, MGWR and CGWR. The simulation is based on a region of 1010 lattice points, assuming the data satisfied the simple linear regression model y(u,v)=β_0 (u,v)+β_1 (u,v)×x(u,v), where the parametric surface β_0 (u,v) and β_1 (u,v) are linear surfaces and quadratic surfaces. We consider MSE (Mean squared error) as a measure for comparing the estimation results of target variable and parameters. Also, there are two data sets considered in empirical data analysis. In the simulation study, we found that the estimation results of GWR in the target variable is still accurate, but the estimates of parameters can be misleading. On the other hand, the estimation results of CGWR are relatively stable in terms of the shape of the coefficient surface and the MSE, while those of MGWR are less stable under quadratic surfaces. In the empirical analysis, MGWR has a relatively stable estimation results on the target variable, while the three models show different estimation results on the parameters.參考文獻 一、 中文部分王劲峰(2006)。《空间分析》，北京：科学出版社，1-20。余清祥、梁穎誼、郭柔芸(2022)。「地理加權迴歸在視覺化之探討」，to appear in《中國統計學報》。林家興(2019)。「應用地理加權迴歸於不動產價格評估之比較研究」，國立政治大學地政學系碩士論文。凃明蕙（2020）。「臺灣居民健康與壽命之空間分析」，國立政治大學統計學系碩士論文。陳君厚（2003）。「全矩陣式資料視覺化與資訊探索」。《數位典藏與數位學習聯合目錄》，15(3)，68-72。陳章瑞（2013）。「以地理加權迴歸模型之空間分析探討都市公園之寧適效益」，《造園景觀學報》，199(1)，17-46。黃郁文. (2020)。「應用地理加權邏吉斯迴歸於台灣南部登革熱資料之分析」，淡江大學統計學系碩士論文。張文菘、陳嘉惠、張國楨 (2017)。「應用空間統計於桃園地區土地利用變遷因素分析」，《 地理研究》，67，137-161。盧賓賓、葛詠、秦昆、鄭江華(2020)。「地理加權回歸分析技術綜述」，《武漢大學學報》，45(9)，1356-1366。二、 英文部分Atkinson, P. M., German, S. E., Sear, D. A., & Clark, M. J. (2003). “Exploring the relations between riverbank erosion and geomorphological controls using geographically weighted logistic regression” Geographical Analysis, 35(1), 58–82.Brunsdon, C., Fotheringham, A.S., and Charlton, M.E. (1996). “Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity”, Geographical analysis, 28(4), 281–298.Brunsdon, C., Fotheringham, A.S., and Charlton, M.E. (1998). “Geographically Weighted Regression-Modelling Spatial Non-stationarity”, Statistician, 47, 431–443.Brunsdon, C., Fotheringham, A.S., and Charlton, M. (1999). “Some Notes on Parametric Significance Tests for Geographically Weighted Regression”, Journal of Regional Science, 39(3), 497–524. doi:10.1111/0022-4146.00146Fotheringham, A.S., Brunsdon, C., and Charlton, M. (2003). “Geographically Weighted Regression The Analysis of Spatially Varying Relationships”, 44–47.Fotheringham, A.S., Charlton, M., and Brunsdon, C. (1997). “Two Techniques for Exploring Nonstationarity in Geographical data”, Geographical Systems, 4(1): 59–82.Fotheringham, A.S., Crespo, R., & Yao, J. (2015). “Geographical and temporal weighted regression (GTWR).” Geographical Analysis, 47(4), 431–452.Fotheringham, A.S., Yang, W., & Kang, W. (2017). “Multiscale Geographically Weighted Regression (MGWR)”, Annals of the American Association of Geographers, 107(6), 1247–1265.Huang, B., Wu, B., & Barry, M. (2010). “Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices.” International journal of geographical information science, 24(3), 383–401.Lansley, G., & Cheshire, J. (2016). “An Introduction to Spatial Data Analysis and Visualisation in R”, CDRC Learning Resources, 86–97.Leong, Y.-Y. and Yue, J.C. (2017). “A Modification to Geographically Weighted Regression ”, International Journal of Health Geographics, 16(1).Lu, B., Brunsdon, C., Charlton, M. (2019) “A Response to “A Comment on Geographically Weighted Regression with Parameter-Specific Distance Metrics” International Journal of Geographical Information Science, 33(7), 1300–1312Lu, B., Brunsdon, C., Charlton, M., and Harris, P. (2017). “Geographically Weighted Regression with Parameter-Specific Distance Metrics”, International Journal of Geographical Information Science, 31(5), 982–998.Lu, B., Charlton, M., Brunsdon, C., & Harris, P. (2016). “The Minkowski approach for choosing the distance metric in geographically weighted regression.” International Journal of Geographical Information Science, 30(2), 351–368.Lu, B., Charlton, M., Harris, P., & Fotheringham, A. S. (2014). “Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data.” International Journal of Geographical Information Science, 28(4), 660–681.Nakaya, T., Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2005) “ Geographically weighted Poisson regression for disease association mapping.” Statistics in medicine, 24(17), 2695–2717.Oshan, T.M., Li, Z., Kang, W., Wolf, L.J., and Fotheringham, A.S. (2019) “Mgwr: A Python Implementation of Multiscale Geographically Weighted Regression for Investigating Process Spatial Heterogeneity and Scale” ISPRS International Journal of Geo-Information, 8(6), 269.Oshan, T., Wolf, L. J., Fotheringham, A. S., Kang, W., Li, Z., and Yu, H. (2019) “ A Comment on Geographically Weighted Regression with Parameter-Specific Distance Metrics” International Journal of Geographical Information Science, 33(7), 1289–1299.Sadiku, M., Shadare, A. E., Musa, S. M., Akujuobi, C. M., & Perry, R. (2016). “Data visualization” International Journal of Engineering Research And Advanced Technology (IJERAT), 2(12), 11–16.Silverman, B.W. (1985), “Spline Aspects of Spline Smoothing Approaches to Nonparametric Regression Curve Fitting”, Journal of the Royal Statistical Society, Series B 47: 1–52.Telea, A.C. (2014), Data Visualization: Principles and Practice, CRC Press 1–10.Tomal, M. (2020), “Modelling Housing Rents Using Spatial Autoregressive Geographically Weighted Regression: A Case Study in Cracow,” ISPRS International Journal of Geo-Information, 9(6), 346. 描述 碩士
國立政治大學
統計學系
109354007資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354007 資料類型 thesis dc.contributor.advisor 楊曉文<br>余清祥 zh_TW dc.contributor.advisor Yang, Sheau-Wen<br>Yue, Ching-Syang en_US dc.contributor.author (Authors) 郭柔芸 zh_TW dc.contributor.author (Authors) Kuo, Rou-Yun en_US dc.creator (作者) 郭柔芸 zh_TW dc.creator (作者) Kuo, Rou-Yun en_US dc.date (日期) 2022 en_US dc.date.accessioned 2-Sep-2022 14:45:20 (UTC+8) - dc.date.available 2-Sep-2022 14:45:20 (UTC+8) - dc.date.issued (上傳時間) 2-Sep-2022 14:45:20 (UTC+8) - dc.identifier (Other Identifiers) G0109354007 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141545 - 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) 109354007 zh_TW dc.description.abstract (摘要) 隨著資料蒐集普及化，有效率呈現龐雜資訊的需求愈發殷切，其中資料視覺化(Data Visualization)更是探索性資料分析(Exploratory Data Analysis)的核心，協助人們以目視判斷關鍵資訊。以空間資料而言，地理加權迴歸(Geographically Weighted Regression, GWR)取代傳統迴歸模型，以解除樣本間獨立和同質變異下的限制，可用於描述解釋變數和目標變數間的局部關係。但GWR的估計結果有時卻不盡理想，近年有不少研究從環寬(bandwidth)的選擇上出發，希冀可改善估計值不平滑等之問題，修正方法包括多尺度地理加權迴歸模型(Multiscale GWR, MGWR)和條件地理加權迴歸(Conditional GWR, CGWR)，但少有研究比較GWR及其修正模型的適用情況。本文以電腦模擬比較GWR、MGWR、CGWR三個模型。實驗空間為1010的格子點，僅考慮簡單線性迴歸，亦即y(u,v)=β_0 (u,v)+β_1 (u,v)×x(u,v)，參數曲面β_0 (u,v)和β_1 (u,v)為線性曲面、二次曲面。本文比較目標變數、參數曲面估計值的誤差，作為三種模型的比較依據，說明GWR的限制及可能問題，測試修正方法是否有效。電腦模擬的結果顯示GWR在目標變數的估計結果尚稱準確，但係數曲面的估計結果相當不理想，而CGWR無論是係數曲面的形狀、或是係數MSE (Mean Squared Error)誤差都比較穩定，MGWR在複雜參數曲面下較不穩定。實證分析的結果顯示，MGWR在目標變數有較穩定的估計表現，而三個模型在係數曲面結果不盡相同。 zh_TW dc.description.abstract (摘要) With the rapidly growing of data size and complexity, the need to efficiently present useful information becomes more essential. Data Visualization, the core of Exploratory Data Analysis, can help people to detect key information in data analysis. Taking the analysis of spatial data as an example, Geographically Weighted Regression (GWR) can be treated as an extension of traditional regression models. It can remove the constraints of independent and homogeneous variation among samples, and especially visually describe the local relationship between explanatory variables and target variables. However, the estimation of GWR can be unsatisfactory and produce distorted relationship. In recent years, many studies tried to modify GWR in order to improve the estimation results and adjusting the estimation bandwidth is one of them. Multiscale geographically weighted regression models (MGWR) and Conditional Geographically Weighted Regression (CGWR) are two methods of adjusting bandwidth, but few studies compare the estimation results of GWR and its modified models (e.g., MGWR and CGWR).In this paper, we use simulation and empirical data to evaluate GWR, MGWR and CGWR. The simulation is based on a region of 1010 lattice points, assuming the data satisfied the simple linear regression model y(u,v)=β_0 (u,v)+β_1 (u,v)×x(u,v), where the parametric surface β_0 (u,v) and β_1 (u,v) are linear surfaces and quadratic surfaces. We consider MSE (Mean squared error) as a measure for comparing the estimation results of target variable and parameters. Also, there are two data sets considered in empirical data analysis. In the simulation study, we found that the estimation results of GWR in the target variable is still accurate, but the estimates of parameters can be misleading. On the other hand, the estimation results of CGWR are relatively stable in terms of the shape of the coefficient surface and the MSE, while those of MGWR are less stable under quadratic surfaces. In the empirical analysis, MGWR has a relatively stable estimation results on the target variable, while the three models show different estimation results on the parameters. en_US dc.description.tableofcontents 第一章 緒論 1第一節 研究動機 1第二節 研究目的 3第二章 文獻回顧與研究方法 4第一節 文獻回顧 4第二節 研究方法 6第三章 模擬研究 12第一節 模擬設定 12第二節 自變數x1~U(0.5-d,0.5+d)模擬結果 21第三節 自變數x1~U(0,d)模擬結果 32第四章 實證應用 43第一節 實證模擬 43第二節 台灣健保資料 50第三節 Boston房價資料 54第五章 結論與建議 60第一節 結論 60第二節 研究限制與建議 61參考文獻 63附錄：參數區面的估計結果 66附錄一、模擬設定1-a 目標變數期望值估計曲面 66附錄二、模擬設定1-b 目標變數期望值估計曲面 67附錄三、模擬設定2-a 目標變數期望值估計曲面 68附錄四、模擬設定2-b 目標變數期望值估計曲面 69 zh_TW dc.format.extent 10912850 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354007 en_US dc.subject (關鍵詞) 空間分析 zh_TW dc.subject (關鍵詞) 地理加權迴歸 zh_TW dc.subject (關鍵詞) 探索性資料分析 zh_TW dc.subject (關鍵詞) 環寬 zh_TW dc.subject (關鍵詞) 電腦模擬 zh_TW dc.subject (關鍵詞) Spatial analysis en_US dc.subject (關鍵詞) Geographically weighted regression en_US dc.subject (關鍵詞) Exploratory data analysis en_US dc.subject (關鍵詞) Bandwidth en_US dc.subject (關鍵詞) Computer simulation en_US dc.title (題名) 地理加權迴歸模型估計方法之比較 zh_TW dc.title (題名) A Study of Estimation Methods for Geographically Weighted Regression en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、 中文部分王劲峰(2006)。《空间分析》，北京：科学出版社，1-20。余清祥、梁穎誼、郭柔芸(2022)。「地理加權迴歸在視覺化之探討」，to appear in《中國統計學報》。林家興(2019)。「應用地理加權迴歸於不動產價格評估之比較研究」，國立政治大學地政學系碩士論文。凃明蕙（2020）。「臺灣居民健康與壽命之空間分析」，國立政治大學統計學系碩士論文。陳君厚（2003）。「全矩陣式資料視覺化與資訊探索」。《數位典藏與數位學習聯合目錄》，15(3)，68-72。陳章瑞（2013）。「以地理加權迴歸模型之空間分析探討都市公園之寧適效益」，《造園景觀學報》，199(1)，17-46。黃郁文. (2020)。「應用地理加權邏吉斯迴歸於台灣南部登革熱資料之分析」，淡江大學統計學系碩士論文。張文菘、陳嘉惠、張國楨 (2017)。「應用空間統計於桃園地區土地利用變遷因素分析」，《 地理研究》，67，137-161。盧賓賓、葛詠、秦昆、鄭江華(2020)。「地理加權回歸分析技術綜述」，《武漢大學學報》，45(9)，1356-1366。二、 英文部分Atkinson, P. M., German, S. E., Sear, D. A., & Clark, M. J. (2003). “Exploring the relations between riverbank erosion and geomorphological controls using geographically weighted logistic regression” Geographical Analysis, 35(1), 58–82.Brunsdon, C., Fotheringham, A.S., and Charlton, M.E. (1996). “Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity”, Geographical analysis, 28(4), 281–298.Brunsdon, C., Fotheringham, A.S., and Charlton, M.E. (1998). “Geographically Weighted Regression-Modelling Spatial Non-stationarity”, Statistician, 47, 431–443.Brunsdon, C., Fotheringham, A.S., and Charlton, M. (1999). “Some Notes on Parametric Significance Tests for Geographically Weighted Regression”, Journal of Regional Science, 39(3), 497–524. doi:10.1111/0022-4146.00146Fotheringham, A.S., Brunsdon, C., and Charlton, M. (2003). “Geographically Weighted Regression The Analysis of Spatially Varying Relationships”, 44–47.Fotheringham, A.S., Charlton, M., and Brunsdon, C. (1997). “Two Techniques for Exploring Nonstationarity in Geographical data”, Geographical Systems, 4(1): 59–82.Fotheringham, A.S., Crespo, R., & Yao, J. (2015). “Geographical and temporal weighted regression (GTWR).” Geographical Analysis, 47(4), 431–452.Fotheringham, A.S., Yang, W., & Kang, W. (2017). “Multiscale Geographically Weighted Regression (MGWR)”, Annals of the American Association of Geographers, 107(6), 1247–1265.Huang, B., Wu, B., & Barry, M. (2010). “Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices.” International journal of geographical information science, 24(3), 383–401.Lansley, G., & Cheshire, J. (2016). “An Introduction to Spatial Data Analysis and Visualisation in R”, CDRC Learning Resources, 86–97.Leong, Y.-Y. and Yue, J.C. (2017). “A Modification to Geographically Weighted Regression ”, International Journal of Health Geographics, 16(1).Lu, B., Brunsdon, C., Charlton, M. (2019) “A Response to “A Comment on Geographically Weighted Regression with Parameter-Specific Distance Metrics” International Journal of Geographical Information Science, 33(7), 1300–1312Lu, B., Brunsdon, C., Charlton, M., and Harris, P. (2017). “Geographically Weighted Regression with Parameter-Specific Distance Metrics”, International Journal of Geographical Information Science, 31(5), 982–998.Lu, B., Charlton, M., Brunsdon, C., & Harris, P. (2016). “The Minkowski approach for choosing the distance metric in geographically weighted regression.” International Journal of Geographical Information Science, 30(2), 351–368.Lu, B., Charlton, M., Harris, P., & Fotheringham, A. S. (2014). “Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data.” International Journal of Geographical Information Science, 28(4), 660–681.Nakaya, T., Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2005) “ Geographically weighted Poisson regression for disease association mapping.” Statistics in medicine, 24(17), 2695–2717.Oshan, T.M., Li, Z., Kang, W., Wolf, L.J., and Fotheringham, A.S. (2019) “Mgwr: A Python Implementation of Multiscale Geographically Weighted Regression for Investigating Process Spatial Heterogeneity and Scale” ISPRS International Journal of Geo-Information, 8(6), 269.Oshan, T., Wolf, L. J., Fotheringham, A. S., Kang, W., Li, Z., and Yu, H. (2019) “ A Comment on Geographically Weighted Regression with Parameter-Specific Distance Metrics” International Journal of Geographical Information Science, 33(7), 1289–1299.Sadiku, M., Shadare, A. E., Musa, S. M., Akujuobi, C. M., & Perry, R. (2016). “Data visualization” International Journal of Engineering Research And Advanced Technology (IJERAT), 2(12), 11–16.Silverman, B.W. (1985), “Spline Aspects of Spline Smoothing Approaches to Nonparametric Regression Curve Fitting”, Journal of the Royal Statistical Society, Series B 47: 1–52.Telea, A.C. (2014), Data Visualization: Principles and Practice, CRC Press 1–10.Tomal, M. (2020), “Modelling Housing Rents Using Spatial Autoregressive Geographically Weighted Regression: A Case Study in Cracow,” ISPRS International Journal of Geo-Information, 9(6), 346. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202201195 en_US
