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,
ctrl=list(q=q, p=p, rmin=rmin, rmax=rmax),
statistic = NULL, statargs = NULL, algorithm="Nelder-Mead", verbose=FALSE)
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 afunction(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 argumentmethod
ofoptim
.- verbose
Logical value indicating whether to print detailed progress reports for debugging purposes.
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
isNUll
or a single numeric the pattern is considered homogeneous and eitherKest
orpcf
is invoked. In this caselambda
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 afunction(x,y)
the pattern is considered inhomogeneous. In this case eitherKinhom
orpcfinhom
is invoked withlambda
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 \(\mu\).
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
.
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
Examples
# NOT RUN {
fit <- clusterfit(redwood, "Thomas")
fit
if(interactive()){
plot(fit)
}
K <- Kest(redwood)
fit2 <- clusterfit(K, "MatClust")
# }