论文标题
基于标准化变量的空间回归模型的系数分解
Coefficient Decomposition of Spatial Regressive Models Based on Standardized Variables
论文作者
论文摘要
空间自相关分析是空间自回归建模的基础。但是，空间相关系数与空间回归模型之间的关系尚未得到充分阐明。该论文致力于探索空间回归系数的深层结构。通过数学推理，一对规范空间回归系数的公式来自基于标准化变量的通用空间回归模型。空间自身和滞后回归系数还原为一系列统计参数和测量值，包括常规回归系数，Pearson相关系数，Moran的索引，空间互相关系数以及预测残差的方差。该公式显示空间相关系数与空间回归系数之间的固有关系。新发现如下：空间自回归系数主要取决于自变量的Moran索引，而空间滞后系数主要取决于自变量和因变量的互相关系数。北京，天津和中国河北地区的城市系统的观察数据被用来验证新得出的公式，结果令人满意。新的公式及其变体从空间相关的角度了解空间回归模型有助于理解空间回归模型，并且可用于协助空间回归模型。
Spatial autocorrelation analysis is the basis for spatial autoregressive modeling. However, the relationships between spatial correlation coefficients and spatial regression models are not yet well clarified. The paper is devoted to explore the deep structure of spatial regression coefficients. By means of mathematical reasoning, a pair of formulae of canonical spatial regression coefficients are derived from a general spatial regression model based on standardized variables. The spatial auto- and lag-regression coefficients are reduced to a series of statistic parameters and measurements, including conventional regressive coefficient, Pearson correlation coefficient, Moran's indexes, spatial cross-correlation coefficients, and the variance of prediction residuals. The formulae show determinate inherent relationships between spatial correlation coefficients and spatial regression coefficients. New finding is as below: the spatial autoregressive coefficient mainly depends on the Moran's index of the independent variable, while the spatial lag-regressive coefficient chiefly depends on the cross-correlation coefficient of independent variable and dependent variable. The observational data of an urban system in Beijing, Tianjin, and Hebei region of China were employed to verify the newly derived formulae, and the results are satisfying. The new formulae and their variates are helpful for understand spatial regression models from the perspective of spatial correlation and can be used to assist spatial regression modeling.
