论文标题
用于估计Moran指数的反向空间自回旋模型的推导
Derivation of an Inverse Spatial Autoregressive Model for Estimating Moran's Index
论文作者
论文摘要
基于标准化尺寸变量和全球归一化的重量矩阵，可以将诸如Moran指数之类的空间自相关度量（例如Moran指数）表示。一个基于内部产品，另一个基于尺寸变量的外产物。内部产品方程实际上是一个空间自相关模型。但是，Moran指数内部产品方程的理论基础尚不清楚。本文致力于揭示Moran指数内部产品方程的前因和后果。该方法是数学推导和经验分析。主要结果如下。首先，内部产品方程是从简单的空间自回归模型得出的，因此阐明了Moran索引和空间自动回归系数之间的关系。其次，事实证明，最小二乘回归是估计空间自回旋系数的有效方法之一。第三，可以从三个角度识别空间自回旋系数的值范围。可以得出结论，空间自相关模型实际上是一种反向空间自回归模型，而Moran的索引和空间自回归模型可以通过内部产品和外部产品方程集成到同一框架中。这项工作可能有助于理解空间自相关测量和空间自回旋建模之间的连接和差异。
Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer product of the size variable. The inner product equation is actually a spatial autocorrelation model. However, the theoretical basis of the inner product equation for Moran's index is not clear. This paper is devoted to revealing the antecedents and consequences of the inner product equation of Moran's index. The method is mathematical derivation and empirical analysis. The main results are as follows. First, the inner product equation is derived from a simple spatial autoregressive model, and thus the relation between Moran's index and spatial autoregressive coefficient is clarified. Second, the least squares regression is proved to be one of effective approaches for estimating spatial autoregressive coefficient. Third, the value ranges of the spatial autoregressive coefficient can be identified from three angles of view. A conclusion can be drawn that a spatial autocorrelation model is actually an inverse spatial autoregressive model, and Moran's index and spatial autoregressive models can be integrated into the same framework through inner product and outer product equations. This work may be helpful for understanding the connections and differences between spatial autocorrelation measurements and spatial autoregressive modeling.
