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Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes

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  • Rasmus Waagepetersen
  • Yongtao Guan
  • Abdollah Jalilian
  • Jorge Mateu

Abstract

type="main" xml:id="rssc12108-abs-0001"> Multivariate log-Gaussian Cox processes are flexible models for multivariate point patterns. However, they have so far been applied in bivariate cases only. We move beyond the bivariate case to model multispecies point patterns of tree locations. In particular we address the problems of identifying parsimonious models and of extracting biologically relevant information from the models fitted. The latent multivariate Gaussian field is decomposed into components given in terms of random fields common to all species and components which are species specific. This allows a decomposition of variance that can be used to quantify to what extent the spatial variation of a species is governed by common or species-specific factors. Cross-validation is used to select the number of common latent fields to obtain a suitable trade-off between parsimony and fit of the data. The selected number of common latent fields provides an index of complexity of the multivariate covariance structure. Hierarchical clustering is used to identify groups of species with similar patterns of dependence on the common latent fields.

Suggested Citation

  • Rasmus Waagepetersen & Yongtao Guan & Abdollah Jalilian & Jorge Mateu, 2016. "Analysis of multispecies point patterns by using multivariate log-Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(1), pages 77-96, January.
    • Handle: RePEc:bla:jorssc:v:65:y:2016:i:1:p:77-96
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    File URL: http://hdl.handle.net/10.1111/rssc.2016.65.issue-1
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    Cited by:

    1. T. Rajala & D. J. Murrell & S. C. Olhede, 2018. "Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1237-1273, November.
    2. Ian Flint & Nick Golding & Peter Vesk & Yan Wang & Aihua Xia, 2022. "The saturated pairwise interaction Gibbs point process as a joint species distribution model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1721-1752, November.
    3. Kristian Bjørn Hessellund & Ganggang Xu & Yongtao Guan & Rasmus Waagepetersen, 2022. "Second‐order semi‐parametric inference for multivariate log Gaussian Cox processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 244-268, January.
    4. María P. Frías & Antoni Torres-Signes & María D. Ruiz-Medina & Jorge Mateu, 2022. "Spatial Cox processes in an infinite-dimensional framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 175-203, March.
    5. Abdollah Jalilian & Jorge Mateu, 2023. "Assessing similarities between spatial point patterns with a Siamese neural network discriminant model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 21-42, March.

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