GET.spatialF function

Testing global and local dependence of point patterns on covariates

Compute the spatial F- and S-statistics and perform the one-stage global envelope tests proposed by Myllymäki et al. (2020).

GET.spatialF(
  X,
  formula.full,
  formula.reduced,
  fitfun,
  covariates,
  nsim,
  bw = spatstat.explore::bw.scott(X),
  bw.S = bw,
  dimyx = NULL,
  ...
)

Arguments

• X: A ppp object of spatstat representing the observed point pattern.
• formula.full: A formula for the trend of the full model.
• formula.reduced: A formula for the trend of the reduced model that is a submodel of the full model.
• fitfun: A function of a point pattern, model formula and covariates, giving a fitted model object that can be used with simulate.
• covariates: A list of covariates.
• nsim: The number of simulations.
• bw: The bandwidth for smoothed residuals.
• bw.S: The radius for the local S(u)-statistic.
• dimyx: Pixel array dimensions for smoothed residuals. See as.mask of spatstat.
• ...: Additional arguments to be passed to global_envelope_test.

Returns

list with three components

• F = the global envelope test based on the F(u) statistic
• S = the global envelope test based on the S(u) statistic
• coef = the coefficients of the full model given by fitfun

Examples

if(require("spatstat.model", quietly=TRUE)) {
  # Example of tropical rain forest trees
  data("bei")

  fullmodel <- ~ grad
  reducedmodel <- ~ 1
  fitppm <- function(X, model, covariates) {
    ppm(X, model, covariates=covariates)
  }
  
  
  nsim <- 19 # Increase nsim for serious analysis!
  res <- GET.spatialF(bei, fullmodel, reducedmodel, fitppm, bei.extra, nsim)
  
  plot(res$F)
  plot(res$S)

  
  # Example of forest fires
  data("clmfires")
  # Choose the locations of the lightnings in years 2004-2007:
  pp.lightning <- unmark(subset(clmfires, cause == "lightning" &
                   date >= "2004-01-01" & date < "2008-01-01"))

  covariates <- clmfires.extra$clmcov100
  covariates$forest <- covariates$landuse == "conifer" | covariates$landuse == "denseforest" |
                        covariates$landuse == "mixedforest"

  fullmodel <- ~ elevation + landuse
  reducedmodel <- ~ landuse
  nsim <- 19 # Increase nsim for serious analysis!
  res <- GET.spatialF(pp.lightning, fullmodel, reducedmodel, fitppm, covariates, nsim)
  plot(res$F)
  plot(res$S)

  # Examples of the fitfun functions for clustered and regular processes
  # fitfun for the log Gaussian Cox Process with exponential covariance function
  fitLGCPexp <- function(X, model, covariates) {
    kppm(X, model, clusters="LGCP", model="exponential", covariates=covariates)
  }
  # fitfun for the hardcore process with hardcore radius 0.01
  fitHardcore <- function(X, model, covariates) {
    ppm(X, model, interaction=Hardcore(0.01), covariates=covariates)
  }
  
}

References

Myllymäki, M., Kuronen, M. and Mrkvička, T. (2020). Testing global and local dependence of point patterns on covariates in parametric models. Spatial Statistics 42, 100436. doi: 10.1016/j.spasta.2020.100436