# clusterfit

##### Fit Cluster or Cox Point Process Model via Minimum Contrast

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, ...,
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 - 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:

[object Object],[object Object]

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`

.

##### 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.

Waagepetersen, R. (2007).
An estimating function approach to inference for
inhomogeneous Neyman-Scott processes.
*Biometrics* **63** (2007) 252--258.
}
[object Object],[object Object]
`kppm`

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*