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

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

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.

rmin, rmax

Optional. The interval of r values for the contrast criterion.

...

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.

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.

Value

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

Author(s)

\adrian

, \rolf

and \ege

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

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  fit <- clusterfit(redwood, "Thomas")
  fit
  if(interactive()){
    plot(fit)
  }

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