基于时空窗口改进的时空加权回归分析——以湖北省黄石市住房价格为例

针对地理加权回归(GWR)模型不能有效处理样本数据空间自相关性这一问题,构造局部时空窗口统计量,尝试改进时空加权回归(GTWR)模型。定义多时空窗口的概念,给出其选取、计算和验证方法;计算时空窗口包含的各样本点的被解释变量平均值,与样本拟合点的被解释变量值的比值,作为新的解释变量,构建改进的时空加权回归(IGTWR)模型。以土地稀缺、多中心、资源型城市——湖北省黄石市为例,收集2007~2012年商品住宅成交价格1.93万个数据和398个楼栋样本点,选取小区等级、绿化率、楼栋总层数、容积率、距区域中心距离和销售年份6个解释变量,分别利用常规线性回归(OLS)、GWR、GTWR和IGTWR方法进行回归分析。模型结果表明：计算Moran’s I指数和分析时间序列的自相关性,能确定时空窗口的大小和数量的选取;IGTWR模型和各变量的回归统计均通过0.05的显著性水平检验,有关解释变量的系数估计值在空间分布上能合理解释;GWR拟合结果优于OLS,GTWR优于GWR,而IGTWR拟合精度最好。与GTWR模型分析相比, IGTWR模型R²从0.877提升到0.919,而AICc、残差方(RSS)和均方差(MSE)分别从6 226、49 996 201和354.427下降到6 206、32 327 472和284.969。案例研究表明：IGTWR能够表达一定时空范围的时空自相关特征,减小了估计误差,提高了回归拟合精度。

An Improved Spatiotemporally Weighted Regression Analysis Based on Spatiotemporal Windows: A Case Study of Housing Price of Huangshi City,Hubei Province

Geographically weighted regression (GWR) is a useful technique for exploring spatial nonstationarity by calibrating a regression model which allows different relationships to exist at different points in space. However, spatial autocorrelation can invalidate the model assumption and sometimes may result in residual dependency. This article aims to improve the spatiotemporal weighted regression (GTWR) by introducing additional variables based on spatiotemporal windows. The size parameters for defining spatiotemporal windows are estimated by spatial and temporal statistics of all the sample data. The new window variables are calculated by averaging the explained variables which are located in its spatio-temporal window. The new variables are added in GTWR as an improved regression (IGTWR) model. Huangshi City, a resource-dependent, land-scarce and multi-center city in Hubei Province, is selected as the study area. 19 300 commercial housing units and 398 buildings in 2007-2012 are collected as sample data. Based on general and spatial statistics, the number of building floors, the plot ratio, the greening ratio, the level of property management, the distance to region center, and the year of sale are selected as explanatory variables. The sample data are analyzed by four regression models respectively: ordinary linear regression (OLS), GWR, GTWR and IGTWR. The optimum size and number of spatiotemporal window are estimated by the Moran's I index and the correlation coefficients between temporal sequences. Modeling results indicate that both the IGTWR model and its variables pass the statistical test at the significant level 0.05. The spatial distribution of the variable coefficients can be explained reasonably. The comparison of all modeling results shows that GWR is better than OLS, GTWR is better than GWR, and IGTWR is better than GTWR, in terms of the measure of goodness of fit (R²), the Akaike information criterion (AICc) , the residual sum of squares (RSS) and the mean squared error(MSE). In the case study, compared with GTWR, the R², AICc, RSS and MSE from IGTWR are improved from 0.877 to 0.919, 6 226 to 6 206, 49 996 201 to 32 327 472 and 354.427 to 284.969 respectively. The case study indicates that the IGTWR model is effective for temporal and spatial analysis of urban housing price. By introducing window based indicators in GTWR model as new variables, the IGTWR model may estimate the impact of spatial and temporal autocorrelation between geographic data, and thus is able to reduce the model error and increase the model accuracy.