广义空间变系数自回归模型的研究与应用

发布时间：2018-01-23 03:16

本文关键词： 地理加权广义线性模型地理加权泊松回归模型局部线性地理加权泊松回归模型广义空间变系数自回归模型空间变系数泊松自回归模型　出处：《新疆大学》2017年硕士论文　论文类型：学位论文

【摘要】：线性回归模型主要适用于因变量为连续型随机变量的情形;GLM可以处理因变量为离散型和连续型的随机变量;GWR方法假定回归系数是观测点地理位置的函数,解决了空间研究对象的空间非平稳性问题.所以对于经典的GLM而言,GWGLM能探测到包括离散型变量在内的空间变量在空间分布上的非平稳性,可以更深入了解空间研究对象的空间异质性的结构和影响因素.由于边界效应的存在会使得系数函数在边界区域的估计失真,从而导致不真实的分析结果,且局部多项式拟合方法具有自动更正边界效应的优点,所以本文借鉴局部线性GWR方法,将GWGLM中的系数函数局部展开为空间地理位置坐标的线性函数,称之为局部线性地理加权广义线性模型.并对泊松回归模型进行具体的分析,称为局部线性地理加权泊松回归模型.通过数值模拟试验考察其精确性,通过绘制曲面图、计算偏差平方的平均值与地理加权泊松回归模型的相应结果进行比较,以说明局部线性地理加权泊松回归模型模型在减小回归系数函数估计的边界效应和偏差方面的优良性.并将这两种模型同时用于实证分析2012年全国31个省的宏观因素,包括经济水平、交通、社会保障、卫生水平,对艾滋病发病数影响的空间变化特征,通过拟合优度检验进一步说明局部线性地理加权泊松回归模型优于地理加权泊松回归模型.因为空间数据具有空间相关性和空间异质性,只有同时考虑这两种性质才能更好地表示数据的空间关系.但是对于具有空间依赖性的离散型空间数据,变系数广义线性模型并不能进行很好的分析.所以本文将数据的空间自回归过程引入到变系数广义线性模型中,提出广义空间变系数自回归模型,用来处理包括离散型在内的具有空间依赖性和空间异质性的空间数据的问题.并针对泊松回归模型进行具体的描述及分析,称为空间变系数泊松自回归模型.同样通过数值模拟试验考察空间变系数泊松自回归模型的精确性.同时将这两种模型应用于上述实证分析,通过拟合优度检验说明空间变系数泊松自回归模型更适用于此类空间数据的分析.
[Abstract]:The linear regression model is mainly suitable for the case where the dependent variable is a continuous random variable. GLM can deal with discrete and continuous random variables. The GWR method assumes that the regression coefficient is a function of the geographical position of the observation point, which solves the spatial nonstationarity problem of the spatial research object, so for the classical GLM. GWGLM can detect the nonstationarity of spatial variables including discrete variables. The structure of spatial heterogeneity and the influencing factors of spatial heterogeneity can be further understood. Because of the existence of boundary effect, the estimation of coefficient function in the boundary region will be distorted, resulting in untrue analysis results. And the local polynomial fitting method has the advantage of automatic correction of the boundary effect, so this paper draws lessons from the local linear GWR method. The coefficient function in GWGLM is locally expanded into a linear function of spatial geographical coordinates, which is called the locally linear geo-weighted generalized linear model, and the Poisson regression model is analyzed in detail. Called locally linear geographical weighted Poisson regression model, the accuracy of the model is investigated by numerical simulation, and the surface graph is drawn. The mean value of the square of the calculation deviation is compared with the corresponding results of the geo-weighted Poisson regression model. In order to illustrate the superiority of local linear geographical weighted Poisson regression model in reducing the boundary effect and deviation of regression coefficient function estimation, the two models are used to analyze 31 regression models in China in 2012. The macro factors of the province. Including the economic level, transportation, social security, health level, the number of AIDS incidence of the impact of spatial changes. Through the goodness of fit test, it is further proved that the local linear geographical weighted Poisson regression model is superior to the geographical weighted Poisson regression model, because the spatial data have spatial correlation and spatial heterogeneity. Only when these two properties are considered at the same time, the spatial relationship of data can be better represented, but for discrete spatial data with spatial dependence. The generalized linear model with variable coefficients can not be well analyzed, so this paper introduces the spatial autoregressive process of data into the generalized linear model with variable coefficients, and proposes a generalized spatial autoregressive model with variable coefficients. It is used to deal with spatial data with spatial dependence and spatial heterogeneity, including discrete type. The Poisson regression model is described and analyzed in detail. It is called spatial variable coefficient Poisson autoregressive model. The accuracy of spatial variable coefficient Poisson autoregressive model is also investigated by numerical simulation test. At the same time, these two models are applied to the above empirical analysis. The results of goodness of fit test show that the Poisson autoregressive model with variable coefficients is more suitable for the analysis of this kind of spatial data.
【学位授予单位】：新疆大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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