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研究生:梁穎誼
研究生(外文):Leong , Yin Yee
論文名稱:以部分法修正地理加權迴歸
論文名稱(外文):A conditional modification to geographically weighted regression
指導教授:余清祥余清祥引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:99
語文別:英文
論文頁數:40
中文關鍵詞:地理加權迴歸廣義加法模型交叉驗證法Jacobi疊代法電腦模擬MAUP問題
外文關鍵詞:Geographically weighted regressionGeneralized additive modelCross validationJacobi iterationComputer simulationModifiable areal unit problem
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在二十世紀九十年代,學者提出地理加權迴歸(Geographically Weighted Regression;簡稱GWR)。GWR是一個企圖解決空間非穩定性的方法。此方法最大的特性,是模型中的迴歸係數可以依空間的不同而改變,這也意味著不同的地理位置可以有不同的迴歸係數。在係數的估計上,每個觀察值都擁有一個固定環寬,而估計值可以由環寬範圍內的觀察值取得。然而,若變數之間的特性不同,固定環寬的設定可能會產生不可靠的估計值。
為了解決這個問題,本文章提出CGWR(Conditional-based GWR)的方法嘗試修正估計值,允許各迴歸變數有不同的環寬。在估計的程序中,CGWR運用疊代法與交叉驗證法得出最終的估計值。本文驗證了CGWR的收斂性,也同時透過電腦模擬比較GWR, CGWR與local linear法(Wang and Mei, 2008)的表現。研究發現,當迴歸係數之間存有正相關時,CGWR比其他兩個方法來的優異。最後,本文使用CGWR分析台灣高齡老人失能資料,驗證CGWR的效果。

Geographically weighted regression (GWR), first proposed in the 1990s, is a modelling technique used to deal with spatial non-stationarity. The main characteristic of GWR is that it allows regression coefficients to vary across space, and so the values of the parameters can vary depending on locations. The parameters for each location can be estimated by observations within a fixed range (or bandwidth). However, if the parameters differ considerably, the fixed bandwidth may produce unreliable or even unstable estimates.
To deal with the estimation of greatly varying parameter values, we propose Conditional-based GWR (CGWR), where a different bandwidth is selected for each independent variable. The bandwidths for the independent variables are derived via an iteration algorithm using cross-validation. In addition to showing the convergence of the algorithm, we also use computer simulation to compare the proposed method with the basic GWR and a local linear method (Wang and Mei, 2008). We found that the CGWR outperforms the other two methods if the parameters are positively correlated. In addition, we use elderly disability data from Taiwan to demonstrate the proposed method.

Index
1. Introduction
2. GWR and its extension
2.1 GWR
2.2 Local linear method
2.3 Drawbacks
3. Methodology
3.1 Generalized Addictive Model
3.2 Jacobi Iteration
3.3 Proposed CGWR
4. Simulation Study
4.1 Simulation Setting
4.2 Single type surfaces
4.3 Mixed type surfaces
4.4 Random effect model
5 Empirical Study
6. Discussion and Concluding Remarks

Bivand R, Danlin Y, 2010, R manual for package “spgwr”,
http://cran.r-project.org/web/packages/spgwr/spgwr.pdf (2010/08/01)
Bivand R, R. Brunstad R, 2005, Further Explorations of Interactions between Agricultural Policy and Regional Growth in Western Europe. Approaches to Nonstationarity in Spatial Econometrics,
http://www.feweb.vu.nl/ersa2005/final_papers/671.pdf (2010/09/30)
Brunsdon C, Fotheringham A S, Charlton M, 1998, “Geographically weighted regression: modelling spatial nonstationarity” The Statistician 47, 431 – 443
Brunsdon C, Fotheringham A S, Charlton M, 1999, “Some notes on parametric significance tests for geographically weighted regression” Journal of Regional Science 39, 497 – 524
Brunsdon C, Fotheringham A S, Charlton M, 2002, Geographically Weighted Regression: the analysis of spatially varying relationships (John Wiley & Sons)
Cleveland W S, Grosse E, Shyu W M, 1991, “ Local regression models” Statistical Models in S (Chambers, J. M. and Hastie,T. J., eds), 309–376. (Wadsworth & Brooks, Pacific Grove.)
Cressie N, 1993, Statistics for spatial data (John Wiley & Sons)
Fan J Q, Zhang W Y, 2008, “ Statistical methods with varying coefficient models” Statistics and its interface 1, 179 – 195
Farber S, Páez A, 2007, “A systematic investigation of cross-validation in GWR model estimation: empirical analysis and Monte Carlo simulations” Journal of Geographical Systems 9, 371 – 396
Haining R, 2003, Spatial data analysis, Theory and practice (Cambridge University Press)
Hastie T J, Tibshirani R J, 1990, Generalized additive models, (Chapman and Hall, London, New York)
Hu Y W, Yue J C, 2002, “Spatial Analysis of Taiwan Elderly Disability” Technical Report, Department of Statistics, National Chengchi University, Taipei, Taiwan R.O.C.
Leung Y, Mei C L, Zhang W X, 2000, “Statistical tests for spatial nonstationarity based on the geographically weighted regression model” Environment and Planning A 32, 9 – 32
Manoranjan V S, Olmos G M, 1997, “A Two-Step Jacobi-Type Iterative Method” Computers Math. Application 34, 1, 1 – 9
Shi H J, Zhang L J, Liu J G, 2006, “A new spatial-attribute weighting function for geographically weighted regression” Canadian Journal of Forest Research 36, 4 996 – 1005
Wang N, Mei C L, Yan X D, 2008, “Local linear estimation of spatially varying coefficient models: an improvement on the geographically weighted regression technique” Environment and Planning A 40, 986 – 1005
Wu C O, Chiang C T, 2000, “Kernel smoothing on varying coefficient models with longitudinal dependent variable” Statistica Sinica 10, 433 – 456

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