空间滞后–混合地理加权回归模型中的数据分区及参数估计

Data Partition and Parameter Estimation in Spatial Lag-Mixed Geographical Weighted Regression Model

摘要: 空间滞后模型和地理加权回归模型均为经典的地统计学模型，分别用于处理带有空间自相关性或异质性的数据，但是在处理同时带有空间自相关性和异质性的数据时拟合效果较差。为了同时考虑数据的自相关性和异质性，提升模型的拟合效果，本文在空间滞后模型和地理加权回归模型的基础上做出改进。首先针对空间数据的异质性，使用改进的k均值聚类方法对空间数据进行分区处理。其次，在分区内部引入空间的自相关性，给出空间滞后–混合地理加权回归模型，并提出了基于莫兰指数与权重矩阵的关系进行估计的莫兰指数优化法。通过在真实数据集上的实验研究，证明了本文方法相比传统方法具有更好的拟合效果。

Abstract: Both the spatial lag model and the geographically weighted regression model are classically geostatistical models, which are used to deal with data with spatial autocorrelation or heterogeneity respectively, but the fitting effect is poor when dealing with data with both spatial autocorrelation and heterogeneity. In order to consider the autocorrelation and heterogeneity of the data at the same time and improve the fitting effect of the model, this paper makes improvements on the basis of the spatial lag model and the geographically weighted regression model. Firstly, according to the heterogeneity of spatial data, the improved k-means clustering method is used to partition the spatial data. Secondly, the spatial autocorrelation is introduced into the interior of the zone, and the spatial lag-mixed geographically weighted regression model is given, and the Moran’s I optimization method based on the relationship between Moran’s I and weighted matrix is proposed. Through experimental research on real data sets, it is proved that this method has better fitting effect than traditional methods.