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Rectifying I: three point and continuous fit of the spatial autocorrelation metric, Moran’s I, to ideal form

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Abstract

Context

Interpreting spatial autocorrelation is complicated by differences in data type, spatial conformation, and contiguity definitions. Though lacking consistent meaning, Moran’s I is commonly reported, compared, and interpreted based on conceptual ideals. To provide consistent, logical, and intuitive meaning and enable broader synthetic work, a new approach to I is needed.

Objectives

We sought to standardize I and true it to conceptual ideals and existing intuition regarding regular correlations. We also wished to test performance of transformed metrics over a diversity of designed and empirical datasets.

Methods

We developed two means to rectify I. Both fit null distributions from data permutation to a target frame of [− 1, 0, 1], followed by projection of original I into this conformation. One method used three-point registration employing the distribution median and select tail percentiles. The other directly projected all I based on theory or cumulative frequencies reflecting the distribution of regular correlations. Repeatability and sensitivity of results were examined for varied permutation replication and framing parameter choices. Empirical and designed datasets were used to compare rectified to traditional metrics.

Results

Both rectification methods improved distributional characteristics of I. Three-point registration produced overly broad distributions with discontinuous peaks. Continuous projection fit the distribution for regular correlations precisely. Diverse case studies demonstrated failings of I and the clarity gained by rectification.

Conclusions

Rectified I enabled meaningful comparisons of spatial patterns for diverse data and landscape conditions. Preserving the intuitive value of Moran’s I while providing a theoretically sound and consistent approach for standardizing its values should foster sustained use.

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Funding

This project was funded by Texas A&M University T3 (Triads for Tranformation) grant to TJD, MPB, and TRI.

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Authors and Affiliations

  1. Department of Ecology & Conservation Biology, Texas A&M University, College Station, TX, 77843-2258, USA

    T. J. DeWitt & J. I. Fuentes

  2. Department of Computer Science & Engineering, Texas A&M University, College Station, TX, 77843-3112, USA

    J. I. Fuentes & T. R. Ioerger

  3. Department of Geography, Texas A&M University, College Station, TX, 77843-3147, USA

    M. P. Bishop

Authors
  1. T. J. DeWitt
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  2. J. I. Fuentes
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  3. T. R. Ioerger
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  4. M. P. Bishop
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Correspondence to T. J. DeWitt.

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DeWitt, T.J., Fuentes, J.I., Ioerger, T.R. et al. Rectifying I: three point and continuous fit of the spatial autocorrelation metric, Moran’s I, to ideal form. Landscape Ecol 36, 2897–2918 (2021). https://doi.org/10.1007/s10980-021-01256-0

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