PM.test {NTSS}

Test of independence between marks and points of a stationary marked point process

Description

Test of independence between marks and points of a stationary marked point process based on the comparison of the mark K-function and the K-function of the underlying point process, see Guan (2006).

Usage

PM.test(X, R, R.variogram)

Arguments

X

marked point pattern dataset (object of class ppp)

R

positive real number determining the domain for the (marked) K-function used for computing the test statistic

R.variogram

positive real number determining the domain for variogram estimation

Details

The test was proposed in Guan (2006) and used in Dvořák et al. (2022) as one of the tools to determine the dependence structure between points, marks and a covariate in a marked point process setting. The marked point process is assumed to be stationary here.

The observed marked point pattern should be supplied using the argument X. The upper limit of the domain for the (marked) K-function used for constructing the test statistic is given by the argument R. Furthermore, the variance used for constructing the test statistic is determined using a fitted covariance model for the mark field. In the given implementation, the exponential model for the covariance is assumed. The model parameters are estimated by fitting the corresponding parametric model to the empirical variogram by the least-squares approach, with the upper bound on the variogram argument given by R.variogram.

Value

The p-value of the test of independence between marks and points of a stationary marked point process.

References

Y. Guan (2006): Tests for independence between marks and points of a marked point Process. Biometrics 62, 126-134.

J. Dvořák, T. Mrkvička, J. Mateu, J.A. González (2022): Nonparametric testing of the dependence structure among points-marks-covariates in spatial point patterns. International Statistical Review 90(3), 592-621.

Examples

library(spatstat)
library(geoR)

set.seed(123)

X <- rpoispp(100)
X <- X %mark% runif(n=X$n)

out <- PM.test(X, R=0.1, R.variog=1)
out