Fit Cluster or Cox Point Process Model

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

models, spatial
kppm(X, ...)

## S3 method for class 'formula': kppm(X, clusters = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"), ..., data=NULL)

## S3 method for class 'ppp': kppm(X, trend = ~1, clusters = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"), data = NULL, ..., covariates=data, method = c("mincon", "clik2", "palm"), improve.type = c("none", "clik1", "wclik1", "quasi"), improve.args = list(), weightfun=NULL, control=list(), statistic="K", statargs=list(), rmax = NULL, covfunargs=NULL, use.gam=FALSE, nd=NULL, eps=NULL)

## S3 method for class 'quad': kppm(X, trend = ~1, clusters = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"), data = NULL, ..., covariates=data, method = c("mincon", "clik2", "palm"), improve.type = c("none", "clik1", "wclik1", "quasi"), improve.args = list(), weightfun=NULL, control=list(), statistic="K", statargs=list(), rmax = NULL, covfunargs=NULL, use.gam=FALSE, nd=NULL, eps=NULL)

A point pattern dataset (object of class "ppp" or "quad") to which the model should be fitted, or a formula in the Rlanguage defining the model. See Details.
An Rformula, with no left hand side, specifying the form of the log intensity.
Character string determining the cluster model. Partially matched. Options are "Thomas", "MatClust", "Cauchy", "VarGamma" and "LGCP".
The values of spatial covariates (other than the Cartesian coordinates) required by the model. A named list of pixel images, functions, windows, tessellations or numeric constants.
Additional arguments. See Details.
The fitting method. Either "mincon" for minimum contrast, "clik2" for second order composite likelihood, or "palm" for Palm likelihood. Partially matched.
Method for updating the initial estimate of the trend. Initially the trend is estimated as if the process is an inhomogeneous Poisson process. The default, improve.type = "none", is to use this initial estimate. Otherwise, the
Additional arguments passed to improve.kppm when improve.type != "none". See Details.
Optional weighting function $w$ in the composite likelihood or Palm likelihood. A function in the Rlanguage. See Details.
List of control parameters passed to the optimization algorithm optim.
Name of the summary statistic to be used for minimum contrast estimation: either "K" or "pcf".
Optional list of arguments to be used when calculating the statistic. See Details.
Maximum value of interpoint distance to use in the composite likelihood.
Arguments passed to ppm when fitting the intensity.

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

The model may be either a Neyman-Scott 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 (requires an additional argument nu to be passed through the dots; see rVarGamma for details), and clusters="LGCP" for the log-Gaussian Cox process (may require additional arguments passed through ...; see rLGCP for details on argument names). The first four models are Neyman-Scott cluster processes.

The algorithm first estimates the intensity function of the point process using ppm. The argument X may be a point pattern (object of class "ppp") or a quadrature scheme (object of class "quad"). The intensity is specified by the trend argument. If the trend formula is ~1 (the default) 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 argument X may also be a formula in the Rlanguage. The right hand side of the formula gives the trend as described above. The left hand side of the formula gives the point pattern dataset to which the model should be fitted.

If improve.type="none" this is the final estimate of the intensity. Otherwise, the intensity estimate is updated, as explained in improve.kppm. Additional arguments to improve.kppm are passed as a named list in improve.args. The clustering parameters of the model are then fitted either by minimum contrast estimation, or by maximum composite likelihood.

[object Object],[object Object],[object Object] In all three 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).


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


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.

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

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, fitted.kppm, predict.kppm, simulate.kppm, update.kppm, vcov.kppm, methods.kppm, as.ppm.kppm, Kmodel.kppm, pcfmodel.kppm.

Minimum contrast fitting algorithm: mincontrast.

Alternative fitting algorithms: thomas.estK, matclust.estK, lgcp.estK, cauchy.estK, vargamma.estK, thomas.estpcf, matclust.estpcf, lgcp.estpcf, cauchy.estpcf, vargamma.estpcf,

Summary statistics: Kest, Kinhom, pcf, pcfinhom.

See also ppm

  • kppm
  • kppm.formula
  • kppm.ppp
  • kppm.quad
# method for point patterns
  kppm(redwood, ~1, "Thomas")
  # method for formulas
  kppm(redwood ~ 1, "Thomas")

  kppm(redwood ~ 1, "Thomas", method="c")
  kppm(redwood ~ 1, "Thomas", method="p")

  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 = 0.5, statistic="pcf")
  if(require(RandomFields)) {
     kppm(redwood ~ x, "LGCP", statistic="pcf",
           model="matern", nu=0.3,

  # fit intensity with quasi-likelihood method
  kppm(redwood ~ x, "Thomas", improve.type = "quasi")
Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)

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