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Indices of Dependence Between Types in Multivariate Point Patterns

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  • M. N. M. Van Lieshout
  • A. J. Baddeley

Abstract

We propose new summary statistics quantifying several forms of dependence between points of different types in a multi‐type spatial point pattern. These statistics are the multivariate counterparts of the J‐function for point processes of a single type, introduced by Lieshout & Baddeley (1996). They are based on comparing distances from a type i point to either the nearest type j point or to the nearest point in the pattern regardless of type to these distances seen from an arbitrary point in space. Information about the range of interaction can also be inferred. Our statistics can be computed explicitly for a range of well‐known multivariate point process models. Some applications to bivariate and trivariate data sets are presented as well.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:4:p:511-532
    DOI: 10.1111/1467-9469.00165
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    Cited by:

    1. Elvan Ceyhan, 2009. "Class‐specific tests of spatial segregation based on nearest neighbor contingency tables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 149-182, May.
    2. repec:jss:jstsof:12:i06 is not listed on IDEAS
    3. Wu, Liu-Cang & Li, Hui-Qiong, 2009. "Summary statistics for measuring the relationship among three types of points in multivariate point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2809-2816, June.
    4. 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.
    5. Ceyhan, Elvan, 2009. "Overall and pairwise segregation tests based on nearest neighbor contingency tables," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2786-2808, June.
    6. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
    7. Elvan Ceyhan, 2010. "New Tests of Spatial Segregation Based on Nearest Neighbour Contingency Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 147-165, March.
    8. Carlos Comas & Jorge Mateu & Aila Särkkä, 2010. "A third‐order point process characteristic for multi‐type point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 19-44, February.

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