fit.void {palm}

Fitting a model to a void point process

Description

Estimates parameters for a void point process by maximising the Palm likelihood. This approach was first proposed by Tanaka et al. (2008) for two-dimensional Thomas processes. Generalisation to d-dimensional void processes was made by Jones-Todd et al. (in press).

Usage

fit.void(
  points,
  lims,
  R,
  edge.correction = "pbc",
  start = NULL,
  bounds = NULL,
  use.bobyqa = FALSE,
  trace = FALSE
)

Arguments

points

A matrix or list of matrices containing locations of observed points, where each row corresponds to a point and each column corresponds to a dimension. If a list, then the patterns are assumed to be independent and a single process is fitted to all.

lims

A matrix or list of matrices with two columns, corresponding to the upper and lower limits of each dimension, respectively. If a list, then each matrix provides the limits for the corresponding pattern in points.

R

Truncation distance for the difference process.

edge.correction

The method used for the correction of edge effects. Either "pbc" for periodic boundary conditions, or "buffer" for a buffer-zone correction.

start

A named vector of starting values for the model parameters.

bounds

A list with named components. Each component should be a vector of length two, giving the upper and lower bounds for the named parameter.

use.bobyqa

Logical; if TRUE the bobyqa function is used for optimisation. Otherwise the nlminb function is used. Note that bobyqa seems to be less stable than nlminb, but does not require calculation of the Palm likelihood's partial derivatives.

trace

Logical; if TRUE, parameter values are printed to the screen for each iteration of the optimisation procedure.

Details

Parameters to estimate are as follows:

• Dc, the baseline density of points prior to the deletion process.

• Dp, the density of unobserved parents that cause voids.

• tau, the radius of the deletion process centred at each parent.

Value

An R6 reference class object.

References

Jones-Todd, C. M., Caie, P., Illian, J. B., Stevenson, B. C., Savage, A., Harrison, D. J., and Bown, J. L. (in press). Identifying prognostic structural features in tissue sections of colon cancer patients using point pattern analysis. Statistics in Medicine, 38: 1421–1441.

Tanaka, U., Ogata, Y., and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal, 50: 43–57.

See Also

Use coef.palm to extract estimated parameters, and plot.palm to plot the estimated Palm intensity function. Use boot.palm to run a parametric bootstrap, allowing calculation of standard errors and confidence intervals.

See sim.void to simulate from a void process.

Examples

## Not run: 
set.seed(1234)
## Simulating a two-dimensional void process.
void.data <- sim.void(c(Dc = 1000, Dp = 10, tau = 0.05), rbind(c(0, 1), c(0, 1)))
## Fitting model.
fit <- fit.void(void.data$points, rbind(c(0, 1), c(0, 1)), R = 0.5)

## End(Not run)