土地利用变化的多尺度空间自相关分析——以内蒙古翁牛特旗为例

用传统统计学方法模拟和解释土地利用变化的前提条件是研究分析的数据在统计上必须独立且均匀分布。但是空间数据相互之间通常具有依赖性 (即空间自相关),某一变量的值随着测定距离的缩小而变得更相似或更为不同。由于经典线性回归方法未能抓住数据的空间自相关特征,而空间自相关包含一些有用的信息,为了克服这一缺点,利用Moran的I系数自相关图来描述研究区土地利用变化的空间自相关,并且建立了不仅考虑回归而且又考虑空间自相关的混合回归-空间自相关回归模型 (即空间滞后模型)。研究得到：① 研究区土地利用变化模型中不但自变量之间而且因变量之间存在空间正自相关,这表明土地利用变化数据的空间自相关很强;② Moran的I系数随着尺度的变粗而减小,这是由于数据平均时的滤波特性和Moran的I系数对距离的非线性特征造成的;③ 经典线性回归模型的残差也表现出正相关,这表明标准的多元线性回归模型未能考虑土地利用数据所存在的空间依赖性;④ 混合回归-空间自相关回归模型 (即空间滞后模型) 的残差未存在空间自相关,并且有更好的拟合度;⑤ 相对于经典线性回归模型,混合回归-空间自相关回归模型 (即空间滞后模型) 对于存在空间自相关性的数据来说有着统计上的合理性,而经典线性回归模型未能考虑这些因素。

Spatial Autocorrelation Analysis of Multi-scale Land-use Changes: A Case Study in Ongniud Banner, Inner Mongolia

A prerequisite in using conventional statistical methods, like regression models in land-use changes model, is that the data analyzed with these methods should be statistically independent and identically distributed. But spatial data, like land-use data, have a tendency to be dependent (spatial autocorrelation), which means that when using spatial models, a part of the variance may be explained by neighbouring values. In other words, values over distance may be more similar or less similar than expected for randomly associated pairs of observations. This indicates that standard multiple regression models cannot capture all the spatial autocorrelative characteristics in the data. Spatial dependency contains useful information but the appropriate methods have to be used to deal with it. To overcome this defect, correlograms of the Moran's I are used to describe the spatial autocorrelation for data of Ongniud Banner. And in this paper, mixed regressive-spatial autoregressive models (spatial lag models), which incorporate both regression and spatial autocorrelation, were constructed. The following results were obtained:(1) Positive spatial autocorrelation was detected not only between dependent variables but also between independent variables, indicating that the occurrence of spatial autocorrelation was highly dependent on the aggregation scale.(2) The Moran's I decreased with the increase of the aggregation levels, a result of the non-linear smoothing character between Moran's I and distance.(3) The residuals of the standard regression model also showed positive autocorrelation,indicating that the standard multiple linear regression model failed to consider all the spatial dependencies in the land use data.(4) The mixed regressive-spatial autoregressive models (spatial lag models) yielded residuals without spatial autocorrelation but with a better goodness-of-fit.(5) The mixed regressive-spatial autoregressive model was statistically sound in the presence of spatially dependent data, in contrast with the standard linear model.