運用分量回歸與地理加權發展區域空間分量迴歸方法
學年 98
學期 1
出版（發表）日期 2010-01-01
作品名稱 運用分量回歸與地理加權發展區域空間分量迴歸方法
作品名稱（其他語言） A New Local Spatial Quantile Regression Approach by Fusing Geographical Weighting with Quantile Regression
著者 陳怡如; 鄧文舜
單位 淡江大學統計學系
描述 計畫編號：NSC99-2118-M032-009 研究期間：201008~201107 研究經費：377,000
委託單位 行政院國家科學委員會
摘要 近年來，在公衛及流行病學的領域中，利用空間(或地理)位置的變化作為衛生及健康之預測越來越明顯。隨著地理資訊系統技術的進步，以及空間性公衛及流行病學資料的大量激增，相關領域研究人員，也需要更多更有效率的空間性分析工具 (spatial analysis tools)。然而，目前可用的空間統計分析工具，大多無法處理空間性的非定態分析 (spatial non-stationarity)。另一方面，分量迴歸 (qunatile regression) 可估計反應變數之百分數 (quantile) 的預測，故近年來亦備受注意並已廣泛運用於公衛與流行病學領域。當空間分析與分量迴歸逐漸被廣泛使用之此時，兩者卻未能有效地結合並應用於上述的空間性公衛及流性病學研究。 在流行病學及公衛領域中，不同區域有不同的地理及人文背景，會導致若干解釋變數對反應變數或反應變數的分量有不同的影響。因此，建構一個能因應地理位置變動而變動的空間性分量迴歸分析模型(spatial quantile regretssion)才能有效的解讀資料的意義。由於目前極少有文獻探討上述空間性的分量迴歸分析，再加上多數研究也侷限在空間性的定態分析 (spatial stationarity) (亦即, 迴歸係數無法隨地理位置變化而變化)。本計劃將結合無母數方法，利用局部平滑技巧，把局部加權 (locally weighing scheme) 的方法，應用到分量迴歸模型，使得迴歸係數可以顧及地理人文特性，隨地理位置變化而改變分析方式，讓分析工具更有彈性。由於目前學界或統計軟體業者未提供空間性分量迴歸所需的軟體，因此本計劃預計將撰寫出應用程式，並進行新模型的實證及模擬研究。 Recent years have witnessed an increasing interest in exploring the geographically varying health outcomes in public health and epidemiology. Coupled with the advancement in geographical information system and the proliferation of spatial data, health researchers have demanded advanced spatial analysis tools. However, most of the readily available spatial analysis tools only are incapable of handling spatial non-stationarity. Furthermore, qunatile regression is an emerging modeling technique that permits estimating various conditional quantile functions and has drawn much attention of health researchers. While both spatial analysis and quantile regression are getting widely used, they seem to be two unconnected lines of knowledge inquiry. If interest lies in estimating low or high quantiles of outcome distribution and determining its relationships with a set of regional characteristics, a spatial regression modeling technique which allows for estimating various conditional quantile functions shall be recommended. Very recently few articles have made a first step towards spatial quantile-based analysis. Unfortunately, these proposed techniques are mainly undertaken with the assumption of spatial stationarity. This proposal endeavors to tackle this weakness by introducing a locally (or equivalently geographically varying) weighing scheme into the quantile regression setup, such that the resultant coefficient estimates can be geographically varying. In other words, via this project, we expect to create a novel local spatial quantile regression tool to fill the gap in literature and serve the scientific communities. Necessary program or algorithm for calculating the desired estimates of the proposed model will be provided. We will also illustrate the new approach using some real data sets (from published books or articles) or simulated data.
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