clusterfit: Fit Cluster or Cox Point Process Model via Minimum Contrast

In spatstat.model: Parametric Statistical Modelling and Inference for the 'spatstat' Family

Fit Cluster or Cox Point Process Model via Minimum Contrast

Description

Fit a homogeneous or inhomogeneous cluster process or Cox point process model to a point pattern by the Method of Minimum Contrast.

Usage

clusterfit(X, clusters, lambda = NULL, startpar = NULL, ...,
           q = 1/4, p = 2, rmin = NULL, rmax = NULL,
           ctrl=list(q=q, p=p, rmin=rmin, rmax=rmax),
           statistic = NULL, statargs = NULL, algorithm="Nelder-Mead",
           verbose=FALSE, pspace=NULL)

Arguments

X	Data to which the cluster or Cox model will be fitted. Either a point pattern or a summary statistic. See Details.
clusters	Character string determining the cluster or Cox model. Partially matched. Options are "Thomas", "MatClust", "Cauchy", "VarGamma" and "LGCP".
lambda	Optional. An estimate of the intensity of the point process. Either a single numeric specifying a constant intensity, a pixel image (object of class "im") giving the intensity values at all locations, a fitted point process model (object of class "ppm" or "kppm") or a function(x,y) which can be evaluated to give the intensity value at any location.
startpar	Vector of initial values of the parameters of the point process mode. If X is a point pattern sensible defaults are used. Otherwise rather arbitrary values are used.
q, p	Optional. Exponents for the contrast criterion. See mincontrast.
rmin, rmax	Optional. The interval of r values for the contrast criterion. See mincontrast.
ctrl	Optional. Named list containing values of the parameters q,p,rmin,rmax.
...	Additional arguments passed to mincontrast.
statistic	Optional. 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.
algorithm	Character string determining the mathematical optimisation algorithm to be used by optim. See the argument method of optim.
verbose	Logical value indicating whether to print detailed progress reports for debugging purposes.
pspace	For internal use by package code only.

Details

This function fits the clustering parameters of a cluster or Cox point process model by the Method of Minimum Contrast, that is, by matching the theoretical K-function of the model to the empirical K-function of the data, as explained in mincontrast.

If statistic="pcf" (or X appears to be an estimated pair correlation function) then instead of using the K-function, the algorithm will use the pair correlation function.

If X is a point pattern of class "ppp" an estimate of the summary statistic specfied by statistic (defaults to "K") is first computed before minimum contrast estimation is carried out as described above. In this case the argument statargs can be used for controlling the summary statistic estimation. The precise algorithm for computing the summary statistic depends on whether the intensity specification (lambda) is:

homogeneous:

If lambda is NUll or a single numeric the pattern is considered homogeneous and either Kest or pcf is invoked. In this case lambda is not used for anything when estimating the summary statistic.

inhomogeneous:

If lambda is a pixel image (object of class "im"), a fitted point process model (object of class "ppm" or "kppm") or a function(x,y) the pattern is considered inhomogeneous. In this case either Kinhom or pcfinhom is invoked with lambda as an argument.

After the clustering parameters of the model have been estimated by minimum contrast lambda (if non-null) is used to compute the additional model parameter \mu.

The algorithm parameters q,p,rmax,rmin are described in the help for mincontrast. They may be provided either as individually-named arguments, or as entries in the list ctrl. The individually-named arguments q,p,rmax,rmin override the entries in the list ctrl.

Value

An object of class "minconfit". There are methods for printing and plotting this object. See mincontrast.

Author(s)

\spatstatAuthors

.

References

Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, series B 46, 193 – 212.

\Moller

, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton.

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

See Also

kppm

Examples

  fit <- clusterfit(redwood, "Thomas")
  fit
  if(interactive()){
    plot(fit)
  }
  K <- Kest(redwood)
  fit2 <- clusterfit(K, "MatClust")

spatstat.model documentation built on Sept. 30, 2024, 9:26 a.m.