bw.locppm {spatstat.local}

Cross Validated Bandwidth Selection for Locally Fitted Point Process Model

Description

Uses cross-validation to select a smoothing bandwidth for locally fitting a Poisson or Gibbs point process model.

Usage

bw.locppm(...,
          method = c("fft", "exact", "taylor"), 
          srange = NULL, ns = 9, sigma = NULL,
          additive = TRUE, 
          verbose = TRUE)

Arguments

...

Arguments passed to ppm to fit the homogeneous version of the model.

method

Method of calculation. The default method="fft" is much faster than the other choices.

srange

Range of values of the smoothing parameter sigma to be searched. A numeric vector of length 2 giving the minimum and maximum values of sigma.

ns

Number of values of the smoothing parameter sigma in the range srange to be searched. A positive integer.

sigma

Vector of values of the smoothing parameter to be searched. Overrides the values of ns and srange.

additive

Logical value indicating whether to calculate the leverage approximation on the scale of the intensity (additive=TRUE) or the log intensity (additive=FALSE). Applies only when method = "taylor".

verbose

Logical value indicating whether to display progress reports.

Details

This function determines the optimal value of the smoothing parameter sigma to be used in a call to locppm.

The function locppm fits a Poisson or Gibbs point process model to point pattern data by local composite likelihood. The degree of local smoothing is controlled by a smoothing parameter sigma which is an argument to locppm.

This function bw.locppm determines the optimal value of sigma by cross-validation. For each value of sigma in a search interval, the function bw.locppm fits the model locally with smoothing bandwidth sigma, and evaluates the composite likelihood cross-validation criterion LCV(sigma) defined in Baddeley (2016), section 3.2. The value of sigma which maximises LCV(sigma) is returned.

Value

A numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim" which can be plotted.

Author(s)

Adrian Baddeley [e-mail].

References

Baddeley, A. (2017) Local composite likelihood for spatial point patterns. Spatial Statistics 22, 261–295. DOI: 10.1016/j.spasta.2017.03.001

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

See Also

locppm

Examples

  Ns <- if(interactive()) 16 else 2
  b <- bw.locppm(swedishpines, ~1, srange=c(2.5,4.5), ns=Ns)
  b
  plot(b)