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Keywords:

  • deletion derivative;
  • Gâteaux derivative;
  • Gibbs point process;
  • point process residuals;
  • Poisson point process;
  • pseudolikelihood;
  • raised incidence model;
  • residuals;
  • spatial clustering;
  • spatial covariates

Abstract.  For a spatial point process model fitted to spatial point pattern data, we develop diagnostics for model validation, analogous to the classical measures of leverage and influence in a generalized linear model. The diagnostics can be characterized as derivatives of basic functionals of the model. They can also be derived heuristically (and computed in practice) as the limits of classical diagnostics under increasingly fine discretizations of the spatial domain. We apply the diagnostics to two example datasets where there are concerns about model validity.