空間異質性檢測方法的比較與應用

空間異質性(Spatial Inhomogeneity)是空間統計中的重要議題。空間異質性的檢定可分為三種類型：總體檢定(Global test)、局部檢定(Local test)、焦點檢定(Focused test)，總體檢定可用於檢定全區域的資料是否為空間同質，局部檢定多用於偵測高風險地區（或稱為群聚，Cluster），焦點檢定可用於確認特定地區周圍是否有較高的發生率。本文選擇常見的三種異質性檢定：Moran’s I（總體檢定）、SaTScan（局部檢定）以及Tango Score Test（焦點檢定），透過模擬及實證分析評估這些方法在不同空間特性之下，像是存在空間自相關(Spatial Autocorrelation)及群聚時的偵測效果，以提供實務分析的參考。本文電腦模擬的實驗區間為二度空間，大小為5×5、7×7、9×9、…、21×21的格子點，檢測各方法在空間同質、空間自相關、群聚的效果。研究發現三種方法在空間同質性的結果大致相同，Moran’s I對於空間自相關的最為敏感，而對於群聚存在則以SaTScan效果最佳，Tango Score Test次之。模擬結果亦發現，在風力影響之下會導致Tango Score Test以及SaTScan的偵測能力（偽陰性，False Negative）大幅度下降，但Moran’s I的偽陽性（False Positive）偏高，使用時需特別注意。本文也將這些方法套用至臺灣鄉鎮市區歷年前三大死因（惡性腫瘤、心臟疾病、肺炎），發現主要死因的死亡率具有空間異質性，熱區大多落在東南部山區，且位置並未隨時間有明顯改變，可能與醫療資源分配不均有關；肺炎死亡率在資源充足的西半部逐年上升，推測與都市化的空氣品質惡化有關。

關鍵字

空間異質性；群聚偵測；空間自相關；電腦模擬；檢定力

並列摘要

Judging spatial heterogeneity has always been an important topic in spatial statistics. There are three types of tests for checking spatial heterogeneity: Global test, Local test and Focused test. Global test can be used to test whether the data are spatially homogeneous; Local test is usually used to detect the location of high-risk areas (i.e., clusters); Focused test can be used to confirm whether there are high incident rates around a specific area. In this study, we select three common heterogeneity tests: Moran’s I (Global test), SaTScan (Local test) and Tango Score Test (Focused test), and evaluate these methods can detect spatial autocorrelation and/or clusters via simulation and empirical analysis. The simulation study is performed on a two-dimensional space, with lattice data of size 5×5, 7×7, 9×9, …, 21×21, under the assumption that the data satisfying spatial homogeneity, spatial autocorrelation and clustering. The empirical data considered are the township-level overall and major cause mortality rates in Taiwan. We found that these methods have similar results in checking spatial homogeneity. Moran’s I is the most sensitive test to spatial autocorrelation, and SaTScan is the best for testing the existence of clusters, followed by Tango Score Test. On the other hand, the simulation results show that under the influence of wind, the testing powers of Tango Score Test and SaTScan will be greatly reduced, while the False Positive rates of Moran’s I are misleadingly high. Thus, the spatial methods need to be used carefully under the influenced of wind. We also apply these methods to the mortality rates of top three major death causes (cancer, heart disease and pneumonia) in Taiwan. It seem they change steadily, or the difference of mortality rates between two consecutive years satisfying spatially heterogeneity, and most clusters of mortality rates are located in the southeastern mountain areas.