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Multidimensional spatial autocorrelation analysis and it’s application based on improved Moran’s I

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Abstract

This paper aims to improve and extend the improved spatial Moran’s I theory by analyzing multi-observation samples. By constructing an expanded spatial weight matrix, a vector definition of the improved spatial Moran’s I is given. In order to improve the judgment basis of the improved spatial Moran’s I, the range of the improved spatial Moran’s I is derived using the non-negativity of variance. Since the improved Moran’s I is only applicable to the analysis of a single variable with unknown distribution, a Moran’s I matrix suitable for analyzing the spatial autocorrelation of multiple variables is proposed. The distribution of the elements of the Moran’s I matrix is studied by Monte Carlo simulation. The simulation results show that only the elements on the non-main diagonal follow a normal distribution when the sample size is small. Any element follows a normal distribution when the sample size is large. Then it is proved that the Moran’s I matrix follows a Wishart distribution when the spatial weight matrix is a positive definite matrix. Finally, several comprehensive evaluation indicators suitable for the theory of multivariate spatial autocorrelation are proposed based on the algebraic meaning of the Moran’s I matrix. Spatial autocorrelation analysis is carried out in combination with multi-dimensional air pollution data.

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Availability of data and materials

The datasets used and analyzed during the current study are available from this paper or the corresponding author on reasonable request.

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Authors and Affiliations

  1. School of Mathematical Science, Sichuan Normal University, Chengdu, 610066, China

    Ce Zhang, Wangyong Lv, Ping Zhang & Jiacheng Song

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  1. Ce Zhang
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  2. Wangyong Lv
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  3. Ping Zhang
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  4. Jiacheng Song
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Contributions

Ce Zhang: Methodology, Software, Validation, Investigation, Data curation, Writing - original draft. Wangyong Lv: Resources, Funding acquisition, Supervision. Ping Zhang: The investigation, Data curation. Jiacheng Song: Data curation.

Corresponding author

Correspondence to Wangyong Lv.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by: H. Babaie.

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Zhang, C., Lv, W., Zhang, P. et al. Multidimensional spatial autocorrelation analysis and it’s application based on improved Moran’s I. Earth Sci Inform 16, 3355–3368 (2023). https://doi.org/10.1007/s12145-023-01090-9

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  • DOI: https://doi.org/10.1007/s12145-023-01090-9

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