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

clusterfit {spatstat.core} | R Documentation

## 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, pint=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.
`pint` | 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 μ.

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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### 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")

[Package spatstat.core version 2.3-0 Index]