CWR.test {NTSS}

Random shift test of independence between a point process and a covariate

Description

Nonparametric test of independence between a point process and a random field (covariate of interest), taking into account the possible effect of nuisance covariates, see Dvořák and Mrkvička (2022). The test is based on random shifts. Either the torus correction or the variance correction can be used, see Mrkvička et al. (2021).

Usage

CWR.test(
  X,
  covariate.interest,
  covariates.nuisance,
  N.shifts = 999,
  radius,
  correction,
  type = "raw",
  nonparametric = TRUE,
  verbose = FALSE,
  bw.factor.rhonhat = 1
)

Arguments

X

point pattern dataset (object of class ppp)

covariate.interest

random field (object of class im)

covariates.nuisance

list of covariates (objects of class im) determining the nuisance covariates

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")

type

which type of residuals should be used when computing the test statistic (possible choices are "raw", "Pearson" and "inverse")

nonparametric

logical value indicating whether nonparametric residuals should be used when computing the test statistic

verbose

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

bw.factor.rhonhat

multiplicative factor used when determining the bandwidth in the nonparametric estimation of the intensity function depending on the nuisance covariates (defaults to 1)

Details

The test statistic is the covariate-weighted residual measure of the observation window, see the paper Dvořák and Mrkvička (2022). If no nuisance covariates are given, the null model assumes a constant intensity function of the point process. If one or more nuisance covariates are provided, the null model assumes an intensity function depending on the nuisance covariates (but not on the covariate of interest) and the residuals are constructed using this intensity function.

The residuals can be constructed in a nonparametric way (see Baddeley et al. (2012)) or in a parametric way (assuming a log-linear form of the intensity function and using the ppm function from the spatstat package, see Baddeley et al. (2015)). This choice is given by the argument nonparametric. The nonparametric residuals are recommended if the log-linear form of the intensity function is not clearly justified. Also, different types of residuals can be considered (raw, Pearson or inverse, see Baddeley et al. (2015)). This choice is given by the argument type.

The torus correction can be applied for rectangular windows. On the other hand, the variance correction is applicable both for rectangular and for irregular windows. The choice of the correction is given by the argument correction. Based on the simulation studies in Dvořák and Mrkvička (2022), the torus and variance corrections perform almost equally well for the CWR test. Hence, the torus correction is recommended for its smaller computational cost.

The observed point pattern should be supplied using the argument X. The realization of the covariate of interest should be supplied using the argument covariate.interest. The set of nuisance covariates should be supplied as a list using the argument covariates.nuisance. This list can be empty if no nuisance covariates are considered.

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

In case the observation window accompanying the point pattern is irregular, it must be specified in the form of a binary mask due to the specific implementation of the test. For details on binary masks see the help for the spatstat function owin.

Value

The p-value of the random shift test of independence between a point process and a covariate, taking into account possible effects of nuisance covariates.

References

J. Dvořák, T. Mrkvička (2022): Nonparametric testing of the covariate significance for spatial point patterns under the presence of nuisance covariates. https://arxiv.org/abs/2210.05424

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

A. Baddeley, E. Rubak, R. Turner (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman & Hall Interdisciplinary Statistics Series. CRC Press, Boca Raton, Florida.

A. Baddeley, Y.-M. Chang, Y. Song, R. Turner (2012) Nonparametric estimation of the dependence of a point process on spatial covariates. Statistics and Its Interface 5(2), 221?236.

Examples

library(spatstat)
library(ks)

# the point pattern
X <- bei
plot(X)

# two covariates are available
elevation <- bei.extra$elev
slope <- bei.extra$grad
plot(elevation)
plot(slope)

# test with no nuisance covariates, with only 99 shifts to speed up the computation
out1 <- CWR.test(X, covariate.interest=elevation, covariates.nuisance=NULL, N.shifts = 99,
                 verbose=TRUE, correction="torus", radius=250)
out1

# test with one nuisance covariate, with only 99 shifts to speed up the computation
out2 <- CWR.test(X, covariate.interest=elevation, covariates.nuisance=list(slope=slope),
                 N.shifts = 99, verbose=TRUE, correction="torus", radius=250)
out2