GET.spatialF {GET}

Testing global and local dependence of point patterns on covariates

Description

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

Usage

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.

Value

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

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

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)
  }
  
}