顾及空间分异性的回归模型研究

发布时间：2018-10-09 20:56

【摘要】：由于地理实体广泛的存在着空间相关性和空间异质性,而传统的回归模型是全局性的、假设地理实体间不存在相关性和空间异质性,因此导致其拟合精度较低。本文以住宅价格为例,利用探索式空间数据分析方法分析住宅价格数据的空间自相关性和空间异质性,探讨其时空演变特征。针对传统的空间自回归模型存在的问题,首先尝试并实验了以距离权重矩阵代替空间邻接矩阵的空间自回归模型,从而为空间自回归模型权重的选择提供了一个新的方向,然后提出了兼顾空间相关性和异质性的地理加权自回归模型,并在此基础上,将时间因素纳入到模型中,在住宅价格数据回归模型中引入了时空地理加权回归模型,从而解决了空间实体的空间异质性和时间特性。主要的研究内容及成果为:(1)针对地理实体普遍存在的空间自相关性和空间异质性,本文采用全局莫兰指数来衡量自相关的程度,利用局部莫兰指数探究局部数据的自相关性模式;然后利用半变异函数检验地理实体的空间异质性。(2)本文分别以基于距离倒数和高斯核函数的空间权重矩阵为例进行试验,研究距离权重矩阵代替空间邻接矩阵的可能性,基于距离倒数空间权重矩阵的自回归模型和基于高斯权重矩阵的自回归模型相对于传统的空间自回归模型其拟合精度分别提高了0.08和0.11。(3)提出了兼顾空间自相关性和空间异质性的地理加权自回归模型,在传统的地理加权模型的基础上,增加自回归项。主要内容包括模型的两步最小二乘估计,CV值法选取最优空间带宽,其拟合精度相对于传统的空间自回归模型和地理加权回归模型提高了0.16和0.07。(4)在地理加权回归模型的基础上中增加时间因素,从而构建了时空地理加权回归模型。主要过程有时空核函数的建立和时空因子的选取,并对实验结果进行了方差分析、回归系数分析和拟合优度分析。试验结果表明:时空地理加权回归模型在残差平方和、均方误差、拟合优度等方面具有最佳的表现。
[Abstract]:Because geographical entities have spatial correlation and spatial heterogeneity widely, but the traditional regression model is global, it is assumed that there is no correlation and spatial heterogeneity among geographical entities, so the fitting accuracy is low. Taking housing price as an example, this paper analyzes the spatial autocorrelation and spatial heterogeneity of housing price data by means of exploratory spatial data analysis, and discusses its space-time evolution characteristics. Aiming at the problems existing in the traditional spatial autoregressive model, the spatial autoregressive model with the distance weight matrix instead of the spatial adjacent matrix is tried and experimented, which provides a new direction for the weight selection of the spatial autoregressive model. Then, a geo-weighted autoregressive model which takes spatial correlation and heterogeneity into account is put forward. On the basis of this, time factor is brought into the model, and space-time geo-weighted regression model is introduced into the regression model of housing price data. Thus, the spatial heterogeneity and temporal characteristics of spatial entities are solved. The main research contents and results are as follows: (1) aiming at the spatial autocorrelation and spatial heterogeneity of geographical entities, this paper uses the global Moran index to measure the degree of autocorrelation. The autocorrelation model of local data is explored by using local Moran index, and then the spatial heterogeneity of geographical entities is tested by semi-variable function. (2) the spatial weight matrix based on distance reciprocal and Gao Si kernel function is taken as an example in this paper. The possibility of distance weight matrix replacing spatial adjacent matrix is studied. Compared with the traditional spatial autoregressive model, the autoregressive model based on the reciprocal spatial weight matrix of distance and the autoregressive model based on Gao Si weight matrix improve the fitting accuracy by 0.08 and 0.11 respectively. (3) the spatial autocorrelation is proposed. And spatial heterogeneity, a geo-weighted autoregressive model, The autoregressive term is added on the basis of the traditional geographical weighted model. The main contents include the two-step least square estimation of the model and the selection of optimal spatial bandwidth by CV method. Compared with the traditional spatial autoregressive model and geo-weighted regression model, the fitting accuracy is improved by 0.16 and 0.07. (4) the time factor is added to the geo-weighted regression model, and the spatio-temporal geo-weighted regression model is constructed. The main processes are the establishment of space-time kernel function and the selection of space-time factors. The analysis of variance, regression coefficient and goodness of fit of experimental results are carried out. The experimental results show that the space-time geographical weighted regression model has the best performance in terms of sum of square of residuals, mean square error and goodness of fit.
【学位授予单位】：山东农业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P208

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