spatstat (version 1.31-3)

kppm: Fit Cluster or Cox Point Process Model

Description

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

Usage

kppm(X, trend = ~1,
       clusters = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"),
       covariates = NULL,
       ...,
       method = c("mincon", "clik"),
       weightfun=NULL,
       control=list(),
       statistic="K",
       statargs=list(),
       rmax = NULL)

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", "MatClust", "Cauchy", "VarGamma" and "LGCP".

covariates

The values of any spatial covariates (other than the Cartesian coordinates) required by the model. A named list of pixel images, functions, windows or numeric constants.

...

Additional arguments. See Details.

method

The fitting method. Either "mincon" for minimum contrast, or "clik" for composite likelihood. Partially matched.

weightfun

Optional weighting function $w$ in the composite likelihood. A function in the Rlanguage. See Details.

control

List of control parameters passed to the optimization algorithm optim.

statistic

Name of the summary statistic to be used for minimum contrast estimation: either "K" or "pcf".

statargs

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

rmax

Maximum value of interpoint distance to use in the composite likelihood.

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 clustered point process model to the point pattern dataset X.

The model may be either a Poisson cluster process or another Cox process. The type of model is determined by the argument clusters. Currently the options are clusters="Thomas" for the Thomas process, clusters="MatClust" for the Matern cluster process, clusters="Cauchy" for the Neyman-Scott cluster process with Cauchy kernel, clusters="VarGamma" for the Neyman-Scott cluster process with Variance Gamma kernel, and clusters="LGCP" for the log-Gaussian Cox process. The first four models are Poisson cluster processes.

The algorithm first estimates the intensity function of the point process. The intensity is specified by the trend argument. If the trend formula is ~1 then the model is homogeneous. The algorithm begins by estimating the intensity as the number of points divided by the area of the window. Otherwise, the model is inhomogeneous. The algorithm begins by fitting a Poisson process with log intensity of the form specified by the formula trend. (See ppm for further explanation).

The clustering parameters of the model are then fitted either by minimum contrast estimation, or by maximum composite likelihood.

[object Object],[object Object] In both methods, the optimisation is performed by the generic optimisation algorithm optim. The behaviour of this algorithm can be modified using the argument control. Useful control arguments include trace, maxit and abstol (documented in the help for optim).

References

Guan, Y. (2006) A composite likelihood approach in fitting spatial point process models. Journal of the American Statistical Association 101, 1502--1512.

Jalilian, A., Guan, Y. and Waagepetersen, R. (2012) Decomposition of variance for spatial Cox processes. Scandinavian Journal of Statistics, in press.

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

See Also

methods for kppm objects: plot.kppm, predict.kppm, simulate.kppm, update.kppm, vcov.kppm, methods.kppm, as.ppm.kppm, Kmodel.kppm, pcfmodel.kppm.

Minimum contrast fitting algorithms: thomas.estK, matclust.estK, lgcp.estK, cauchy.estK, vargamma.estK, thomas.estpcf, matclust.estpcf, lgcp.estpcf, cauchy.estpcf, vargamma.estpcf, mincontrast.

Summary statistics: Kest, Kinhom, pcf, pcfinhom.

See also ppm

Examples

data(redwood)
  kppm(redwood, ~1, "Thomas")
  kppm(redwood, ~1, "Thomas", method="c")
  kppm(redwood, ~x, "MatClust") 
  kppm(redwood, ~x, "MatClust", statistic="pcf", statargs=list(stoyan=0.2)) 
  kppm(redwood, ~1, "LGCP", statistic="pcf")
  kppm(redwood, ~x, cluster="Cauchy", statistic="K")
  kppm(redwood, cluster="VarGamma", nu.ker = 0.5, statistic="pcf")
  if(require(RandomFields)) {
     kppm(redwood, ~x, "LGCP", statistic="pcf",
           covmodel=list(model="matern", nu=0.3),
           control=list(maxit=10))
  }