基于Moran’s I的多变量空间自相关研究与应用  

Research and Application of Multivariate Spatial Autocorrelation Based on Moran’s I

作　　者：张策 吕王勇 张萍 宋家城 ZHANG Ce;L Wangyong;ZHANG Ping;SONG Jiacheng(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2024年第6期818-829,共12页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金青年基金(11601357);四川省科技厅应用基础项目(2017JY0159)

摘　　要：针对传统空间Moran’s I只适用于分析单一变量的局限性,提出基于Moran’s I的多变量空间自相关性分析理论.首先,借助传统空间Moran’s I的向量定义,推导出适用于分析多变量空间自相关性的Moran’s I矩阵,并通过蒙特卡洛法模拟研究Moran’s I矩阵中元素的分布情况,结果显示:在样本量较小时,只有非主对角线上的元素服从正态分布,在样本量较大时,任一元素都服从正态分布.基于上述分布结论,可对Moran’s I矩阵中元素进行显著性检验.其次,当空间权重矩阵为正定矩阵时,证明Moran’s I矩阵服从Wishart分布.然后,根据Moran’s I矩阵的代数意义提出适用于多变量空间自相关理论的若干综合评价指标.最后,结合多维空气污染数据进行空间自相关分析.In response to the limitations of traditional spatial Moran’s I which only applies to the analysis of a single variable,this paper proposes a multivariate spatial autocorrelation analysis theory based on Moran’s I.Firstly,utilizing the vector definition of traditional spatial Moran’s I,a Moran’s I matrix suitable for analyzing multivariate spatial aggregation is derived.And through Monte Carlo simulation,the distribution of elements in the Moran’s I matrix is studied.The results indicate that only off-diagonal elements follow a normal distribution when the sample size is small.However,all elements follow a normal distribution when the sample size is large.Therefore the elements in Moran’s I matrix can be tested for significance.Secondly,when the spatial weight matrix is a positive definite matrix,the Moran’s I matrix follows a Wishart distribution.Thirdly,several comprehensive evaluation indicators applicable to the multivariate spatial autocorrelation theory are proposed based on the algebraic significance of the Moran’s I matrix.Finally,spatial autocorrelation study based on multidimensional air pollution data was carried out.

关 键 词：空间Moran’s I Moran’s I矩阵 蒙特卡洛模拟 正态分布 WISHART分布 综合评价 

分 类 号：O211.9[理学—概率论与数理统计]