土地使用變遷之空間自迴歸分析─以新店安坑地區為例

Abstract

由於空間特性的資料並非獨立，而是相互影響，因而使得於模型的殘差（error term）特性不符合模型的基本假設。因而近年來研究於以空間相鄰權重為基礎的空間自相關量測與空間迴歸模型的應用上日漸增加。 由於在空間資料型態上多採用網格的方式，故在量測空間自相關時，皆假設各個網格之間是獨立的。然而，在土地使用開發時，其真實的開發情況並不符合獨立的性質。因此，本研究即針對真實發展情形來調整網格的定義，並比較假設獨立的網格與調整網格定義後所衡量出來的空間自相關情形有何異同。 於空間相鄰權重的概念中，除了考量距離此一因素外，也認為各網格屬性的不同也會影響空間相鄰權重，故本研究參考重力模型（gravity model）的概念，將空間相鄰權重加入屬性的概念，並比較各個模型之間的配適度以及估計能力，來得知何種模型對於土地使用變遷的估計能力較佳。 本研究成果發現，在比較假設獨立的網格與調整網格定義後所衡量出來的空間自相關方面，網格定義的不同會影響到空間自相關量測的最終結果。在各模型估計能力的比較上，在此實例地區的應用上，當模型於空間相鄰權重內的中心網格屬性置入建物覆蓋率且周邊網格屬性置入坡度時，能獲得較其他模型較佳的估計能力，且將空間影響加入模型中皆可有效提高模型配適度。

Land use change models often involve substantial amounts of data with spatial characteristics. The problem is that these methods assume the data to be statistically independent and identically distributed (iid). But, spatial data have the tendency to be dependent, and the error term in a regression model tends to be spatially correlated. Therefore, models that explicitly deal with spatial autocorrelation are widely available and applicable. Spatial data are usually organized as polygons or grid cells. Through spatial autocorrelation analysis, the relationship between cells is always assumed to be independent. However, considering the real development situation, it does not obey the presumption of independent. As a result, a purpose of the study is to compare the results of spatial autocorrelation with the different definitions of cells. In the aspect of spatial weights, assuming that cells with the same distance, the different quantity may also result in different values of spatial weight. This paper use the concept of gravity model to acknowledge that cells are related to each other not only by the distance between them but also the quantity, namely ratio of coverage of land uses in each cell, and further compare the goodness-of-fit and evaluation between every model. The result is also compared with those of conventional regression model and data mining to find out which type of model has the best evaluation power. The results show that the definition of cell has an impact on the results of spatial autocorrelation. Comparing the evaluation of every model, models that deal explicitly with spatial effects are better than conventional regression models in the goodness-of-fit. The comparative analysis shows that the model which considering built-up area coverage and surrounding slope has advantages over the other models for our specific application. This finding shows that spatial proximity is essential in obtaining a better fit.