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. 2013 Jul 12;8(7):e68336.
doi: 10.1371/journal.pone.0068336. Print 2013.

New approaches for calculating Moran's index of spatial autocorrelation

Yanguang Chen  1
Affiliations

New approaches for calculating Moran's index of spatial autocorrelation

Yanguang Chen. PLoS One. .

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.

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Conflict of interest statement

Competing Interests: The author has declared that no competing interests exist.

Figures

Figure 1
Figure 1. A flow chart of data processing, parameter estimation, and autocorrelation analysis.
Figure 2
Figure 2. A sketch map of the geographic relationship of the principal cities of China.
Figure 3
Figure 3. The improved Moran’s scatterplots with trendlines of spatial autocorrelation for the principal cities of China (2000).
[a. Based on inverse power function; b. Based on negative exponential function].
Figure 4
Figure 4. The inverse Moran’s scatterplots with trendlines of spatial autocorrelation for the principal cities of China (2000).
[a. Based on inverse power function; b. Based on negative exponential function].
Figure 5
Figure 5. The normal histograms of error distributions based on different spatial weight functions for China’s cities (2000).
(Note: These graphs are created using standardized error series. The filled bars represent the actual distributions based on observed values, while the unfilled bars with double frames represent the normal distributions based on the expected values, which form bell-shaped histograms.) [a. Based on inverse power function; b. Based on negative exponential function].
See this image and copyright information in PMC

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References

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Grants and funding

This research was sponsored by the National Natural Science Foundation of China (grant 41171129; http://www.nsfc.gov.cn/Portal0/default166.htm). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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