PP.test {NTSS}

Random shift test of independence in a bivariate point process

Description

Nonparametric test of independence between a pair of point processes based on random shifts. Either the torus correction or the variance correction can be used (note that the variance correction is not yet implemented in this package but the corresponding source codes can be obtained from the authors upon request).

Usage

PP.test(
  X,
  Y,
  N.shifts = 999,
  radius,
  correction,
  statistic,
  rmax.K = NULL,
  verbose = FALSE
)

Arguments

X

first point pattern dataset (object of class ppp)

Y

second point pattern dataset (object of class ppp)

N.shifts

integer, how many random shifts should be performed in the random shift test

radius

positive real number determining the radius of the disk on which the shift vectors are uniformly distributed

correction

which correction should be applied in the random shift test (possible choices are "torus" and "variance")

statistic

which test statistic should be used (possible choices are "K12" and "ED12")

rmax.K

positive real number, for the cross K-function determines the maximum argument to be considered

verbose

logical value indicating whether auxiliary information should be printed and auxiliary figures plotted during the computation

Details

The test statistic is either the cross K-function K12 or the expectation of the cross nearest-neighbor distance ED12, see the paper Mrkvička et al. (2021). It is recommended to use the K12 statistic for regular and Poisson processes, while it is recommended to use ED12 for cluster processes due to the potential liberality of K12 in this case.

The two observed point patterns to be tested should be supplied using the arguments X and Y. The shift vectors are generated from the uniform distribution on the disk with radius given by the argument radius and centered in the origin.

The test statistic is determined by the argument statistic. For "K12", the test statistic is functional, the stationary cross K-function. The range of arguments is from 0 to rmax.K (there is a sensible default). The outcome of the test is determined by the global envelope test in this case. Alternatively, the statistic can be set to "ED12", meaning that the test statistic is scalar, the expectation of the cross nearest-neighbor distance. The outcome of the test is determined by the classical univariate Monte Carlo test in this case.

The argument verbose determines if auxiliary information and plots should be provided.

Value

The p-value of the random shift test of independence between a pair of point processes.

References

T. Mrkvička, J. Dvořák, J.A. González, J. Mateu (2021): Revisiting the random shift approach for testing in spatial statistics. Spatial Statistics 42, 100430.

Examples

library(spatstat)
library(GET)

set.seed(123)

X <- rpoispp(150)
Y <- rpoispp(150)

# tests run with only 99 shifts to speed up the computation
out1 <- PP.test(X=X, Y=Y, N.shifts = 99, radius=0.5, statistic="K12",
                correction="torus", verbose=TRUE)
out1
plot(out1$GET.outcome)

out2 <- PP.test(X=X, Y=Y, N.shifts = 99, radius=0.5, statistic="ED12",
                correction="torus", verbose=TRUE)
out2