Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing, China.
PLoS One. 2013 Jul 12;8(7):e68336. doi: 10.1371/journal.pone.0068336. Print 2013.
Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's index. Moran's scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran's index and Geary's coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran's index and Geary's coefficient will be clarified and defined. One of theoretical findings is that Moran's index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.
空间自相关在地理分析中起着重要作用；然而，该方法仍有改进的空间。莫兰指数的公式很复杂，仍有几个基本问题需要解决。因此，我将使用线性代数的数学推导来重建其数学框架，并提出四种计算莫兰指数的简单方法。莫兰散点图将得到改善，并提出新的检验方法。从空间人口和空间样本两个不同角度讨论全局莫兰指数和Geary 系数之间的关系。将明确并定义莫兰指数和Geary 系数的应用范围。理论发现之一是莫兰指数是空间权重矩阵的特征参数，因此权重函数的选择对于地理系统的自相关分析非常重要。将使用 2000 年中国 29 个城市的案例研究来验证创新模型和方法。这项工作是一项方法学研究，将简化自相关分析的过程。本研究的结果将为空间自相关的定标分析奠定基础。
