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| Title: | 地理加權迴歸模型估計方法之比較
A Study of Estimation Methods for Geographically Weighted Regression |
| Authors: | 郭柔芸
Kuo, Rou-Yun |
| Contributors: | 楊曉文
余清祥
Yang, Sheau-Wen
Yue, Ching-Syang
郭柔芸
Kuo, Rou-Yun |
| Keywords: | 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 |
| Date: | 2022 |
| Issue Date: | 2022-09-02 14:45:20 (UTC+8) |
| Abstract: | 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. |
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| Description: | 碩士
國立政治大學
統計學系
109354007 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109354007 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202201195 |
| Appears in Collections: | [統計學系] 學位論文
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