binspp (version 0.2.3)

rThomasInhom: Simulate a realization of Thomas-type cluster point process with complex inhomogeneities

Description

The means to simulate realizations from the Thomas-type cluster point process with complex inhomogeneities are provided.

Usage

rThomasInhom(
  kappa,
  alpha,
  omega,
  W,
  W_dil,
  betavec = NULL,
  alphavec = NULL,
  omegavec = NULL,
  z_beta = NULL,
  z_alpha = NULL,
  z_omega = NULL
)

Value

A planar point pattern, object of the type spatstat.geom::ppp()

used in the spatstat package.

Arguments

kappa

intensity or intensity function of the parent process, scalar or pixel image object of class spatstat.geom::im() from the spatstat package.

alpha

scalar, influences the mean number of points in individual clusters, see Details.

omega

scalar, influences the spread of individual clusters, see Details.

W

the observation window where the realization is to be generated, in the
spatstat.geom::owin() format of the spatstat package.

W_dil

the observation window dilated by the assumed maximal cluster radius, as a binary mask with the same resolution as the covariates.

betavec

vector of parameters describing the dependence of the intensity function of the parent process on covariates in the list z_beta.

alphavec

vector of parameters describing the dependence of the mean number of points in a cluster on covariates in the list z_alpha.

omegavec

vector of parameters describing the dependence of the spread of the clusters on covariates in the list z_omega.

z_beta

list of covariates describing the intensity function of the parent process, each covariate being a pixel image as used in the spatstat package.

z_alpha

list of covariates describing the location-dependent mean number of points in a cluster, each covariate being a pixel image as used in the spatstat package.

z_omega

list of covariates describing the location-dependent scale of a cluster, each covariate being a pixel image as used in the spatstat package.

Details

A realization of a Thomas-type cluster point process model is produced with possible inhomogeneity (described by covariates) in any or all of the following model components: intensity function of the parent process, mean number of points in a cluster, scale of the clusters. Model parametrization is described in the documentation to the function estintp(). The parent process is generated using the function spatstat.random::rpoispp() from the spatstat.random package in the dilated observation window W_dil to avoid edge-effects. The offspring points are generated directly from the appropriate normal distributions. The resulting point pattern is eventually clipped to the smaller observation window W.

Examples

library(spatstat)
# Unit square observation window:
W <- owin()

# Dilation of the observation window:
W_dil <- dilation(W, 0.1)
W_dil <- as.mask(W_dil)

# Define covariates:
f1 <- function(x, y) { x }
f2 <- function(x, y) { y }
f3 <- function(x, y) { 1 - (y - 0.5) ^ 2 }
cov1 <- as.im(f1, W = W_dil)
cov2 <- as.im(f2, W = W_dil)
cov3 <- as.im(f3, W = W_dil)


# Stationary Thomas process:
X <- rThomasInhom(kappa = 50, alpha = log(10), omega = log(0.01),
       W = W, W_dil = W_dil)
plot(X)


# Thomas-type cluster process with inhomogeneity in all model components:
X <- rThomasInhom(kappa = 10, betavec = c(1), z_beta = list(cov1),
            alpha = log(10), alphavec = c(1), z_alpha = list(cov2),
            omega = log(0.01), omegavec = c(1), z_omega = list(cov3),
            W = W, W_dil = W_dil)
plot(X)