# 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 = c("Thomas","MatClust","Cauchy","VarGamma","LGCP"),
covariates = NULL,
...,
method = c("mincon", "clik"),
weightfun=NULL,
control=list(),
statistic="K",
statargs=list(),
rmax = NULL,
covfunargs=NULL,
use.gam=FALSE,
nd=NULL, eps=NULL)
```

##### Arguments

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

) to which the model should be fitted. See Details. - 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"`

,`"Cauchy"`

,`"VarGamma"`

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.
- ...
- Additional arguments. See Details.
- method
- The fitting method. Either
`"mincon"`

for minimum contrast, or`"clik"`

for composite likelihood. Partially matched. - weightfun
- Optional weighting function $w$
in the composite likelihood. A
`function`

in the Rlanguage. See Details. - control
- List of control parameters passed to the optimization algorithm
`optim`

. - statistic
- 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. - rmax
- Maximum value of interpoint distance to use in the composite likelihood.
- covfunargs,use.gam,nd,eps
- Arguments passed to
`ppm`

when fitting the intensity.

##### Details

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

.

The model may be either a *Poisson cluster process*
or another *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,
`clusters="Cauchy"`

for the Neyman-Scott cluster process
with Cauchy kernel,
`clusters="VarGamma"`

for the Neyman-Scott cluster process
with Variance Gamma kernel,
and `clusters="LGCP"`

for the log-Gaussian Cox process.
The first four models are Poisson cluster processes.

The algorithm first estimates the intensity function
of the point process using `ppm`

.
The argument `X`

may be a point pattern
(object of class `"ppp"`

) or a quadrature scheme
(object of class `"quad"`

). The intensity is specified by
the `trend`

argument.
If the trend formula is `~1`

(the default)
then the model is *homogeneous*. The algorithm begins by
estimating the intensity as the number of points divided by
the area of the window.
Otherwise, the model is *inhomogeneous*.
The algorithm begins by fitting a Poisson process with log intensity
of the form specified by the formula `trend`

.
(See `ppm`

for further explanation).

The clustering parameters of the model are then fitted either by minimum contrast estimation, or by maximum composite likelihood.

[object Object],[object Object]
In both methods, the optimisation is performed by the generic
optimisation algorithm `optim`

.
The behaviour of this algorithm can be modified using the
argument `control`

.
Useful control arguments include
`trace`

, `maxit`

and `abstol`

(documented in the help for `optim`

).

##### 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

Guan, Y. (2006)
A composite likelihood approach in fitting spatial point process
models.
*Journal of the American Statistical Association*
**101**, 1502--1512.

Jalilian, A., Guan, Y. and Waagepetersen, R. (2012)
Decomposition of variance for spatial Cox processes.
*Scandinavian Journal of Statistics*, in press.

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

##### See Also

methods for `kppm`

objects:
`plot.kppm`

,
`fitted.kppm`

,
`predict.kppm`

,
`simulate.kppm`

,
`update.kppm`

,
`vcov.kppm`

,
`methods.kppm`

,
`as.ppm.kppm`

,
`Kmodel.kppm`

,
`pcfmodel.kppm`

.

Minimum contrast fitting algorithms:
`thomas.estK`

,
`matclust.estK`

,
`lgcp.estK`

,
`cauchy.estK`

,
`vargamma.estK`

,
`thomas.estpcf`

,
`matclust.estpcf`

,
`lgcp.estpcf`

,
`cauchy.estpcf`

,
`vargamma.estpcf`

,
`mincontrast`

.

Summary statistics:
`Kest`

,
`Kinhom`

,
`pcf`

,
`pcfinhom`

.

See also `ppm`

##### Examples

```
data(redwood)
kppm(redwood, ~1, "Thomas")
kppm(redwood, ~1, "Thomas", method="c")
kppm(redwood, ~x, "MatClust")
kppm(redwood, ~x, "MatClust", statistic="pcf", statargs=list(stoyan=0.2))
kppm(redwood, ~1, "LGCP", statistic="pcf")
kppm(redwood, ~x, cluster="Cauchy", statistic="K")
kppm(redwood, cluster="VarGamma", nu.ker = 0.5, statistic="pcf")
if(require(RandomFields)) {
kppm(redwood, ~x, "LGCP", statistic="pcf",
covmodel=list(model="matern", nu=0.3),
control=list(maxit=10))
}
```

*Documentation reproduced from package spatstat, version 1.34-1, License: GPL (>= 2)*