spatstat (version 1.21-3)

kppm: Fit cluster point process model

Description

Fit a homogeneous or inhomogeneous cluster point process model to a point pattern.

Usage

kppm(X, trend = ~1, clusters = "Thomas", covariates = NULL, ...,
       statistic="K", statargs=list())

Arguments

X

Point pattern (object of class "ppp") to which the model should be fitted.

trend

An Rformula, with no left hand side, specifying the form of the log intensity.

clusters

Character string determining the cluster model. Partially matched. Options are "Thomas" and "MatClust".

covariates

The values of any spatial covariates (other than the Cartesian coordinates) required by the model. A named list of pixel images.

...

Arguments passed to thomas.estK or thomas.estpcf or matclust.estK or

statistic

The choice of summary statistic: either "K" or "pcf".

statargs

Optional list of arguments to be used when calculating the summary statistic. See Details.

Value

• An object of class "kppm" representing the fitted model. There are methods for printing, plotting, predicting, simulating and updating objects of this class.

Details

This function fits a cluster point process model to the point pattern dataset X.

If the trend is constant (~1) then the model is homogeneous. The empirical $K$-function of the data is computed, and the parameters of the cluster model are estimated by the method of minimum contrast (matching the theoretical $K$-function of the model to the empirical $K$-function of the data, as explained in mincontrast).

Otherwise, the model is inhomogeneous. The algorithm first estimates the intensity function of the point process, by fitting a Poisson process with log intensity of the form specified by the formula trend. Then the inhomogeneous $K$ function is estimated by Kinhom using this fitted intensity. Finally the parameters of the cluster model are estimated by the method of minimum contrast using the inhomogeneous $K$ function. If statistic="pcf" then instead of using the $K$-function, the algorithm will use the pair correlation function pcf for homogeneous models and the inhomogeneous pair correlation function pcfinhom for inhomogeneous models. In this case, the smoothing parameters of the pair correlation can be controlled using the argument statargs, as shown in the Examples.

Currently the only options for the cluster mechanism are clusters="Thomas" for the Thomas process and clusters="MatClust" for the Matern cluster process.

References

Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.

See Also

plot.kppm, predict.kppm, simulate.kppm, update.kppm, thomas.estK, matclust.estK, thomas.estpcf, matclust.estpcf, mincontrast, Kest, Kinhom, pcf, pcfinhom, ppm

Examples

data(redwood)
  kppm(redwood, ~1, "Thomas")
  kppm(redwood, ~x, "MatClust") 
  kppm(redwood, ~x, "MatClust", statistic="pcf", statargs=list(stoyan=0.2))

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