|摘要: ||近年來，空間非平穩性(spatial non-stationarity)與迴歸其依變量百分數預測之議題被廣泛討論。前者之分析方法以地理加權迴歸法(geographically weighted regression, GWR)，而後者以分量迴歸法(quantile regression, QR)最為被使用。當此兩種方法被廣泛使用之此時，兩者卻未能有效地結合並應用於各個領域。鑑於此，我們在99年度國科會計劃中(NSC 99-2118-M-032-009)，提出了地理加權分量迴歸方法(geographically weighted quantile regression , GWQR)。此方法不僅可估計各條件分量函數，同時也可探討空間非平穩性。然而，地理加權分量迴歸法仍存在改善空間；當各地區間存在一定程度的相關，此法並未考慮所謂的空間相依性。因此，本計劃將延續目前地理加權分量迴歸(GWQR)的研究，主要目的在建立一更具彈性之模式，以改善所述之缺點。本計畫預計將空間落遲依變數(spatially-lagged dependent variable)納入地理加權分量迴歸模型中，以提出一套能同時處理空間相關性與異質性的新地理加權分量回歸法。我們將以程式模擬來評估新方法的效能並用實際資料呈現新方法的應用。新方法的績效及空間相關性對模型的影響也將一併納入探討。
Recent years have witnessed developments in exploring spatial non-stationarity and modeling the entire distribution of the regressand. Currently, the former is mainly addressed by geographically weighted regression (GWR) and quantile regression (QR) is developed to handle the latter. While both of them are widely used, little attention, however, has been paid to combining these analytical techniques. To fill this methodological gap in literature, a very recent study (Chen et al., 2010) supported by Taiwan National Science Council (NSC 99-2118-M-032-009) grants is conducted. In this study, we have developed the geographically weighted quantile regression (GWQR) which combines both GWR and QR methods. The GWQR is a new approach which not only permits estimating various conditional quantile functions but also allows for exploring spatial non-stationarity. However, it has a limitation that does not account for spatial dependence between locations. There is, to the best of our knowledge, lack of a spatial local quantile regression modeling technique which addresses spatial dependence and heterogeneity simultaneously. This proposal is a follow-up study of GWQR. We attempts to include a spatial dependence component into GWQR by integrating the feature of spatial lag model into the modeling process. A GWQR with spatially-lagged dependent variable will be developed in this study. Necessary program or algorithm for calculating the desired estimates of the proposed model will be provided. We will illustrate the new approach using some real data sets (from published books, articles, websites) or simulated data. Further issues regarding the inference procedure, assessment of spatial dependence effect as well as the model performance will be also discussed in this proposal.