first_step function

Estimate the first-order inhomogeneity

For exploratory purposes it may be useful to perform the first step of the analysis only, to investigate the dependence of the intensity function of the parent process on given covariates, without running the MCMC chain.

first_step(X, z_beta, W_dil, plot = TRUE)

Arguments

• X: observed point pattern in the spatstat.geom::ppp() format of the spatstat package.
• 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.
• W_dil: the observation window dilated by the assumed maximal cluster radius.
• plot: logical, should the estimates intensity function of the parent process be plotted?

Returns

List containing the output of the spatstat.model::ppm()

function from the spatstat package, along with some auxiliary objects useful for running the MCMC chain.

Details

The calling the spatstat.model::ppm() function from the spatstat

package, with some additional computations useful when preparing the run of the MCMC chain, is mainly performed in this function. The function also contains a simple way to plot the estimated intensity function of the parent process.

Examples

library(spatstat)
# Prepare the dataset:
X = trees_N4
x_left = x_left_N4
x_right = x_right_N4
y_bottom = y_bottom_N4
y_top = y_top_N4

z_beta = list(refor = cov_refor, slope = cov_slope)

# Determine the union of rectangles:
W = owin(c(x_left[1], x_right[1]), c(y_bottom[1], y_top[1]))
if (length(x_left) >= 2){
  for (i in 2:length(x_left)){
    W2 = owin(c(x_left[i], x_right[i]), c(y_bottom[i], y_top[i]))
    W = union.owin(W, W2)
  }
}

# Dilated observation window:
W_dil = dilation.owin(W, 100)

# Estimating the intensity function of the parent process:
aux = first_step(X, z_beta, W_dil, plot = TRUE)