# kppm

##### Fit Cluster or Cox Point Process Model

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

##### Usage

```
kppm(X, trend = ~1, clusters = "Thomas", covariates = NULL, ...,
statistic="K", statargs=list())
```

##### Arguments

- X
- Point pattern (object of class
`"ppp"`

) to which the model should be fitted. - trend
- An Rformula, with no left hand side, specifying the form of the log intensity.
- clusters
- Character string determining the cluster model.
Partially matched.
Options are
`"Thomas"`

,`"MatClust"`

and`"LGCP"`

. - covariates
- The values of any spatial covariates (other than the Cartesian coordinates) required by the model. A named list of pixel images, functions, windows or numeric constants.
- ...
- Arguments passed to
`thomas.estK`

or`thomas.estpcf`

or`matclust.estK`

or - statistic
- The choice of summary statistic: either
`"K"`

or`"pcf"`

. - statargs
- Optional list of arguments to be used when calculating the summary statistic. See Details.

##### Details

This function fits a Cox point process model to the
point pattern dataset `X`

. Cox models are suitable for
spatially clustered point patterns.

The model may be either a *Poisson cluster process*
with Poisson clusters, or a more general *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,
and `clusters="LGCP"`

for the log-Gaussian Cox process.

If the trend is constant (`~1`

)
then the model is *homogeneous*.
The empirical $K$-function of the data is computed,
and the parameters of the cluster model are estimated by
the method of minimum contrast (matching the theoretical
$K$-function of the model to the empirical $K$-function
of the data, as explained in `mincontrast`

).

Otherwise, the model is *inhomogeneous*.
The algorithm first estimates the intensity function
of the point process, by fitting a Poisson process with log intensity
of the form specified by the foTrmula `trend`

.
Then the inhomogeneous $K$ function is estimated
by `Kinhom`

using this fitted intensity.
Finally the parameters of the cluster model
are estimated by the method of minimum contrast using the
inhomogeneous $K$ function. This two-step estimation
procedure is due to Waagepetersen (2007).
If `statistic="pcf"`

then instead of using the
$K$-function, the algorithm will use
the pair correlation function `pcf`

for homogeneous
models and the inhomogeneous pair correlation function
`pcfinhom`

for inhomogeneous models.
In this case, the smoothing parameters of the pair correlation
can be controlled using the argument `statargs`

,
as shown in the Examples.

##### Value

- An object of class
`"kppm"`

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

##### References

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

##### See Also

`plot.kppm`

,
`predict.kppm`

,
`simulate.kppm`

,
`update.kppm`

,
`vcov.kppm`

,
`methods.kppm`

,
`thomas.estK`

,
`matclust.estK`

,
`lgcp.estK`

,
`thomas.estpcf`

,
`matclust.estpcf`

,
`lgcp.estpcf`

,
`mincontrast`

,
`Kest`

,
`Kinhom`

,
`pcf`

,
`pcfinhom`

,
`ppm`

##### Examples

```
data(redwood)
kppm(redwood, ~1, "Thomas")
kppm(redwood, ~x, "MatClust")
kppm(redwood, ~x, "MatClust", statistic="pcf", statargs=list(stoyan=0.2))
kppm(redwood, ~1, "LGCP", statistic="pcf")
if(require(RandomFields)) {
kppm(redwood, ~x, "LGCP", statistic="pcf",
covmodel=list(model="matern", nu=0.3))
}
```

*Documentation reproduced from package spatstat, version 1.23-3, License: GPL (>= 2)*