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| Title: | 半參數地理加權貝它迴歸模型之建立與應用
Semi-Parametric Geographically Weighted Beta Regression : Development and Application |
| Authors: | 韓昕頻
Han, Sin-Pin |
| Contributors: | 陳怡如
Chen, Yi-Ju
韓昕頻
Han, Sin-Pin |
| Keywords: | 地理加權迴歸
Beta迴歸
半參數迴歸
拔靴法
空間分析
Geographically weighted regression
Beta regression
Semiparametric regression
Bootstrap
Spatial analysis |
| Date: | 2024 |
| Issue Date: | 2024-09-04 14:55:45 (UTC+8) |
| Abstract: | 根據過往文獻，空間分析的一個重要方向在於探討空間異質性，這種異質性指的是反應變數與解釋變數之間的關係會因地理位置的不同而有所不同。在眾多技術中，地理加權迴歸（Geographically Weighted Regression; GWR）因其計算方法直觀且易於解釋，已成為分析空間異質性時廣泛使用的工具之一。近年來，許多學者對GWR進行了擴展和改進。其中，Silva與Lima於2017年結合Beta迴歸與GWR，提出了地理加權Beta迴歸（Geographically Weighted Beta Regression; GWBR），用於探討反應變數為連續型比例資料之空間異質性。然而，該方法假設所有變數與反應變數之間的關係均會隨空間位置而改變，但此一假設在實際應用中可能並不適用，因為部分變數的迴歸關係可能不會隨空間位置變動。因此，本研究旨在進一步擴展GWBR模型，提出半參數地理加權Beta迴歸模型（semi-parametric GWBR; semi-GWBR），將變數分為全域性與局部性兩類，其中全域性變數對反應變數的影響不隨空間位置改變，而局部性變數則會隨空間位置變動。本研究採用兩階段方法估計semi-GWBR模型的參數，並利用拔靴法計算標準誤，以進行變數的統計推論。此外，本研究還進行了模擬實驗，以評估semi-GWBR模型的估計效果和表現。結果顯示，semi-GWBR模型能夠提供穩定的估計。最後，本研究以2020年6月至2022年6月臺北市各村里大坪數房屋的成交比例作為實證分析資料，將數據分為疫情前後兩個時期，運用semi-GWBR探討疫情前後對臺北市大坪數房屋成交比例的影響因素。研究結果顯示，在此資料的空間異質性分析中，同時存在全域性與局部性變數，且部分變數對大坪數房屋成交比例的影響在疫情前後有所變化；而相比於傳統的Beta迴歸和GWR模型，semi-GWBR模型的表現更為優異。
Based on previous studies, a key focus in spatial analysis is the exploration of spatial heterogeneity, which refers to how the relationships between a response variable and explanatory variables vary across locations. Among various methods, Geographically Weighted Regression (GWR) has become one of the most widely used tools for analyzing such relationship heterogeneity due to its intuitive computation and ease of interpretation. In recent years, many researchers have extended and improved GWR. In particular, Silva and Lima proposed Geographically Weighted Beta Regression (GWBR), which combines Beta regression with GWR to examine spatial heterogeneity in regression relationships for proportion outcomes in unit interval. However, this method assumes that the relationships between all explanatory variables and the response variable are spatially varying, which may not always be appropriate in real-world applications because some variables may have stable relationships that do not change with location. Therefore, this study aims to extend the GWBR model by introducing a semi-parametric GWBR (semi-GWBR) model. In this model, explanatory variables are classified into global and local categories: the effect of global explanatory variables on the response variable remains constant across space, while the effect of local explanatory variables varies spatially. We use bootstrap methods to estimate standard errors for statistical inference of semi-GWBR parameters. Finally, we apply the model to empirical housing market data from Taipei City to analyze the proportion of large house transactions in different geographical units from June 2020 to June 2022. We divide the data into pre-COVID 19 and post-COVID 19 periods to investigate the factors influencing the proportion of large house transactions in Taipei before and after the pandemic. The results reveal the presence of both global and local factors, with some variables showing different effects after the pandemic. Moreover, the semi-GWBR model outperforms the traditional Beta regression and the GWR model in the current context. |
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| Description: | 碩士
國立政治大學
統計學系
111354007 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111354007 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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