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Correct testing of mark independence for marked point patterns

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  • Grabarnik, Pavel
  • Myllymäki, Mari
  • Stoyan, Dietrich

Abstract

Spatial pattern analysis provides valuable information on ecological processes. Many ecological systems can be described by marked point processes. One of the key issues in the statistical application of marked point processes is the question of spatial correlations of the marks. Therefore, the first step of analysis is a test of independence of marks. Many researchers use for this purpose the popular envelope test. However, this may lead to unreasonably high type I error probabilities, because in this test spatial correlations are inspected for a range of distances simultaneously. The paper discusses in detail the use of deviation tests for testing hypotheses of mark independence. Additionally, it demonstrates how the envelope test can be refined so that it becomes a valuable tool both for statistical inference and for understanding the reasons of possible rejections of the independence hypothesis. Two examples from forest ecology illustrate the application of both test types.

Suggested Citation

  • Grabarnik, Pavel & Myllymäki, Mari & Stoyan, Dietrich, 2011. "Correct testing of mark independence for marked point patterns," Ecological Modelling, Elsevier, vol. 222(23), pages 3888-3894.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:23:p:3888-3894
    DOI: 10.1016/j.ecolmodel.2011.10.005
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    References listed on IDEAS

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    1. Julian Besag & Peter J. Diggle, 1977. "Simple Monte Carlo Tests for Spatial Pattern," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 327-333, November.
    2. M. N. M. Van Lieshout & A. J. Baddeley, 1999. "Indices of Dependence Between Types in Multivariate Point Patterns," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 511-532, December.
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    Citations

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    Cited by:

    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Florent Bonneu & Christine Thomas-Agnan, 2015. "Measuring and Testing Spatial Mass Concentration with Micro-geographic Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(3), pages 289-316, September.
    3. O. Cronie & M. N. M. Van Lieshout, 2015. "A J -function for Inhomogeneous Spatio-temporal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 562-579, June.
    4. David J Weston & Niall M Adams & Richard A Russell & David A Stephens & Paul S Freemont, 2012. "Analysis of Spatial Point Patterns in Nuclear Biology," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-15, May.
    5. Jiří Dvořák & Tomáš Mrkvička & Jorge Mateu & Jonatan A. González, 2022. "Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 90(3), pages 592-621, December.
    6. Genet, Astrid & Grabarnik, Pavel & Sekretenko, Olga & Pothier, David, 2014. "Incorporating the mechanisms underlying inter-tree competition into a random point process model to improve spatial tree pattern analysis in forestry," Ecological Modelling, Elsevier, vol. 288(C), pages 143-154.
    7. Jesper Møller & Håkon Toftaker, 2014. "Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 414-435, June.
    8. Ivan N. Kutyavin & Alexei V. Manov, 2022. "Spatial relationships of trees in middle taiga post-pyrogenic pine forest stands in the European North-East of Russia," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 68(6), pages 228-240.
    9. Jakub Staněk & Ondřej Šedivý & Viktor Beneš, 2014. "On Random Marked Sets with a Smaller Integer Dimension," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 397-410, June.

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