New Approaches for Calculating Moran's Index of Spatial Autocorrelation

TL;DR

This paper introduces new simplified methods for calculating Moran's index, improves its theoretical understanding, and discusses its relationship with Geary's coefficient, validated through a case study of Chinese cities.

Contribution

It reconstructs the mathematical framework of Moran's index, proposes four simple calculation approaches, and clarifies its relationship with Geary's coefficient from different perspectives.

Findings

Moran's index is a characteristic parameter of spatial weight matrices.

The new methods simplify autocorrelation analysis.

Validation with Chinese cities demonstrates effectiveness.

Abstract

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.