由於地理資訊系統技術的進步, 以及其空間資料的取得容易, 使得空間計量經濟(Spatial Econometrics) 方法已廣泛的應用於各領域。其中, Nakaya et al.(2005, 2009)提出的地理加權廣義線性迴歸模式(Geographically Weighted Generalized Linear Regression model, GWGLM) 分析方法主要應用於研究空間異質性(Spatial Nonstationarity)的問題, 其模式的建立根據資料類型的差異, 有邏輯斯(Logistic) 、卜瓦松(Poisson)與常態(Normal) 三種選擇。隨著此地理加權廣義線性迴歸方法的備受重視, 研究人員期望使用一有效率、方便且快速的軟體或程式來執行空間異值性分析的需求亦與日遽增。近年來, 已有部分套裝軟體(GWR 軟體) 或程式(R package 、Stata 模組) 應運而生; 當這些工具被廣泛使用之此時, 卻未有相關SAS 統計程式的設計與開發, 直至Chen and Yang 於2012年提出一SAS 巨集程式(Sas Macro) 才有效的將其應用於地理加權廣義線性迴歸。為了提高資料分析的彈性與實用性, 本研究有別於Chen and Yang(2012) , 所提出的巨集程式, 利用SAS IML 軟體設計一套完整的使用者介面, 並將其應用於實際資料, 與以上提到的現行分析工具做比較。此介面除了可做到現有工具所提供之主要功能外, 亦額外增加了部分新功能或選擇, 以彌補現有分析技巧上的缺點與不足,進而使其他領域研究者(如社科人員、地理分析人員) 在分析空間資料時更加方便。此外, 本研究的提出也進一步拓展了SAS 的應用範圍, 讓後續有興趣的開發者, 能根據所提供的程式碼進行的推廣與改進。

Due to the rapid development of techniques on Geographic Information System (GIS) and with the geographical database being accessible easily, spatial statistical analysis tools have been widely applied in empirical studies of various
disciplines. Of them, the Geographically Weighted Generalized Linear Model (GWGLM) introduced by Nataya et al. (2005, 2009) is mainly designed to explore
spatial nonstationarity of the data. The GWGLM fits ”local” regression models where the response variable could go beyond continuous measures and the error terms are allowed to follow nonnormal distributions such as binomial and poisson. As the GWGLM has received increasing attention in recent years, researchers demand user-friendly analysis programs to analyze georeferenced data.Such inquiries have generated several specialized software programs (e.g. GWR 4.0, packages in R, modules in Stata); none of them, however, can be integrated natively into SAS environment. Very recently, Chen and Yang (2012) proposed
a macro program to fill the gap. Their work are among the first to fuse strength of SAS into the GWGLM framework.
The objective of this study is to expand the work of Chen and Yang using the new SAS/IML (or SAS/IML Studio) programming software. We not only design and develop effective user interfaces to conduct GWGLM but also distinguish our work with great flexibilities in the modeling process and data analysis.We illustrate the capability of SAS/IML by applying the proposed programs to
several empirical datasets, and then demonstrate the advantages by comparing the GWGLM results with those obtained from other existing software programs.It is concluded that this software program provides researchers a relatively new,yet powerful and flexible, computational environment to investigate spatial nonstationarity in empirical studies. The programs can be also easily modified or restructured by SAS users for the purpose of developing advanced analysis tools related to GWGLM.

目錄
第一章緒論.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.1 研究背景.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.2 研究動機與目的.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 2
1.3 研究架構.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 3
第二章文獻探討.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4
2.1 地理加權迴歸.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4
2.1.1 空間異質性. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 地理加權迴歸之建模問題. . . . . . . . . . . . . . . . . 9
2.2 地理加權廣義線性模式.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10
2.3 半參數地理加權廣義估計方式.. .. .. .. .. .. .. .. .. .. .. .. .. .. 14
2.4 現行可執行GWR/GWGLM/S-GWGLM 分析的軟體/程式.. .. 16
第三章研究方法.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 21
3.1 地理加權廣義區域線性估計法.. .. .. .. .. .. .. .. .. .. .. .. .. .. 21
3.2 廣義線性模型拔靴法.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 22
3.3 地理加權廣義線性模式之拔靴法.. .. .. .. .. .. .. .. .. .. .. .. .. 25
3.4 SAS / IML Studio 於GWR/GWGLM/S-GWGLM 之應用.. 27
3.4.1 SAS / IML Studio 軟體介紹. . . . . . . . . . . . . . . 27
3.4.2 地理加權廣義線性模式的介面操作. . . . . . . . . . . . . 28
3.4.3 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
第四章實例探討.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 44
4.1 地理加權迴歸分析.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 44
4.2 地理加權卜瓦松迴歸分析.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 49
4.3 地理加權羅吉斯迴歸分析.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 53
4.4 半參數地理加權廣義線性模式之比較.. .. .. .. .. .. .. .. .. .. .. .. 58
4.4.1 半參數地理加權迴歸模式. . . . . . . . . . . . . . . . . 58
4.4.2 半參數地理加權卜瓦松線性模式之比較. . . . . . . . . . 62
4.4.3 半參數地理加權羅吉斯線性模式之比較. . . . . . . . . . 67
第五章結論與討論.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 71
5.1 結論與討論.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 71
5.2 討論及未來研究.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 72
參考文獻.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 73

圖目錄
2.1 固定核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 適應核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 資料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 模式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 核函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6 輸出. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.7 執行. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.8 流程圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.9 匯入資料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.10 說明檔. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.11 轉檔檔案步驟. . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.12 匯入資料. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.13 變數選擇與模式設定. . . . . . . . . . . . . . . . . . . . . . . . 34
3.14 資料變數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.15 模式選擇. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.16 核函數與帶寬選擇. . . . . . . . . . . . . . . . . . . . . . . . . 36
3.17 變數選擇與模式設定. . . . . . . . . . . . . . . . . . . . . . . . 37
3.18 分析方法與檔案輸出. . . . . . . . . . . . . . . . . . . . . . . . 37
3.19 估計方法與進階選項. . . . . . . . . . . . . . . . . . . . . . . . 37
3.20 檔案輸出. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.21 清除變數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.22 分析方法與檔案輸出. . . . . . . . . . . . . . . . . . . . . . . . 39
3.23 功能選單. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.24 GWR分析之SAS / IML Studio 介面操作設定. . . . . . . . . . 46
4.25 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 47
4.26 GWR4.0軟體輸出文字檔. . . . . . . . . . . . . . . . . . . . . 47
4.27 GWPR分析之SAS / IML Studio 介面操作設定. . . . . . . . . 50
4.28 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 51
4.29 GWR4.0軟體輸出文字檔. . . . . . . . . . . . . . . . . . . . . 53
4.30 GWLR分析之SAS / IML Studio 介面操作設定. . . . . . . . . 55
4.31 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 56
4.32 S-GWR分析之SAS / IML Studio 介面操作設定. . . . . . . . 59
4.33 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 60
4.34 GWR4.0軟體輸出文字檔. . . . . . . . . . . . . . . . . . . . . 60
4.35 S-GWPR分析之SAS / IML Studio 介面操作設定. . . . . . . . 63
4.36 GWR4.0軟體輸出文字檔. . . . . . . . . . . . . . . . . . . . . 64
4.37 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 64
4.38 S-GWLR分析之SAS / IML Studio 介面操作設定. . . . . . . . 67
4.39 SAS / IML Studio 軟體輸出檔. . . . . . . . . . . . . . . . . . 68

表目錄
3.1 SAS / IML Studio 介面函數. . . . . . . . . . . . . . . . . . . 28
3.2 各軟體使用地理加權迴歸模式比較表. . . . . . . . . . . . . . . . 40
3.3 各軟體之地理加權模式比較表. . . . . . . . . . . . . . . . . . . 43
4.4 地理加權迴歸模式之參數估計. . . . . . . . . . . . . . . . . . . 48
4.5 地理加權卜瓦松線性模式之參數估計. . . . . . . . . . . . . . . . 52
4.6 地理加權羅吉斯線性模式之參數估計. . . . . . . . . . . . . . . . 57
4.7 半參數地理加權迴歸模式. . . . . . . . . . . . . . . . . . . . . . 61
4.8 半參數地理加權迴歸卜瓦松模式之參數估計. . . . . . . . . . . . 66
4.9 半參數地理加權羅吉斯線性模式之參數估計. . . . . . . . . . . . 70

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