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Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data

Author

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  • Vincent Deblauwe
  • Pol Kennel
  • Pierre Couteron

Abstract

Background: Independence between observations is a standard prerequisite of traditional statistical tests of association. This condition is, however, violated when autocorrelation is present within the data. In the case of variables that are regularly sampled in space (i.e. lattice data or images), such as those provided by remote-sensing or geographical databases, this problem is particularly acute. Because analytic derivation of the null probability distribution of the test statistic (e.g. Pearson's r) is not always possible when autocorrelation is present, we propose instead the use of a Monte Carlo simulation with surrogate data. Methodology/Principal Findings: The null hypothesis that two observed mapped variables are the result of independent pattern generating processes is tested here by generating sets of random image data while preserving the autocorrelation function of the original images. Surrogates are generated by matching the dual-tree complex wavelet spectra (and hence the autocorrelation functions) of white noise images with the spectra of the original images. The generated images can then be used to build the probability distribution function of any statistic of association under the null hypothesis. We demonstrate the validity of a statistical test of association based on these surrogates with both actual and synthetic data and compare it with a corrected parametric test and three existing methods that generate surrogates (randomization, random rotations and shifts, and iterative amplitude adjusted Fourier transform). Type I error control was excellent, even with strong and long-range autocorrelation, which is not the case for alternative methods. Conclusions/Significance: The wavelet-based surrogates are particularly appropriate in cases where autocorrelation appears at all scales or is direction-dependent (anisotropy). We explore the potential of the method for association tests involving a lattice of binary data and discuss its potential for validation of species distribution models. An implementation of the method in Java for the generation of wavelet-based surrogates is available online as supporting material.

Suggested Citation

  • Vincent Deblauwe & Pol Kennel & Pierre Couteron, 2012. "Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-9, November.
  • Handle: RePEc:plo:pone00:0048766
    DOI: 10.1371/journal.pone.0048766
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    Cited by:

    1. Yanguang Chen, 2020. "New framework of Getis-Ord’s indexes associating spatial autocorrelation with interaction," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-25, July.
    2. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    3. Agnieszka Tłuczak, 2020. "Diversity of the selected elements of agricultural potential in the European Union countries," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 66(6), pages 260-268.
    4. Elodie Allié & Raphaël Pélissier & Julien Engel & Pascal Petronelli & Vincent Freycon & Vincent Deblauwe & Laure Soucémarianadin & Jean Weigel & Christopher Baraloto, 2015. "Pervasive Local-Scale Tree-Soil Habitat Association in a Tropical Forest Community," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-16, November.
    5. Stéphane Guitet & Bruno Hérault & Quentin Molto & Olivier Brunaux & Pierre Couteron, 2015. "Spatial Structure of Above-Ground Biomass Limits Accuracy of Carbon Mapping in Rainforest but Large Scale Forest Inventories Can Help to Overcome," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-22, September.

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