Fits the Neyman-Scott cluster point process, with Variance Gamma kernel, to a point pattern dataset by the Method of Minimum Contrast.
Data to which the model will be fitted. Either a point pattern or a summary statistic. See Details.
Vector of starting values for the parameters of the model.
Numerical value controlling the shape of the tail of the clusters.
A number greater than
Optional. An estimate of the intensity of the point process.
Optional. Exponents for the contrast criterion.
Optional. The interval of r values for the contrast criterion.
Optional arguments passed to
This algorithm fits the Neyman-Scott Cluster point process model with Variance Gamma kernel (Jalilian et al, 2013) to a point pattern dataset by the Method of Minimum Contrast, using the K function.
X can be either
An object of class
representing a point pattern dataset.
The K function of the point pattern will be computed
Kest, and the method of minimum contrast
will be applied to this.
An object of class
the values of a summary statistic, computed for a point pattern
dataset. The summary statistic should be the K function,
and this object should have been obtained by a call to
Kest or one of its relatives.
The algorithm fits the Neyman-Scott Cluster point process
with Variance Gamma kernel to
by finding the parameters of the model
which give the closest match between the
theoretical K function of the model
and the observed K function.
For a more detailed explanation of the Method of Minimum Contrast,
The Neyman-Scott cluster point process with Variance Gamma kernel is described in Jalilian et al (2013). It is a cluster process formed by taking a pattern of parent points, generated according to a Poisson process with intensity kappa, and around each parent point, generating a random number of offspring points, such that the number of offspring of each parent is a Poisson random variable with mean mu, and the locations of the offspring points of one parent have a common distribution described in Jalilian et al (2013).
The shape of the kernel is determined by the dimensionless
nu. This is the parameter
nu' = alpha/2 - 1 appearing in
equation (12) on page 126 of Jalilian et al (2013).
In previous versions of spatstat instead of specifying
nu.ker at that time) the user could specify
nu.pcf which is the parameter nu = alpha-1
appearing in equation (13), page 127 of Jalilian et al (2013).
These are related by
nu.pcf = 2 * nu.ker + 1
nu.ker = (nu.pcf - 1)/2. This syntax is still supported but
not recommended for consistency across the package. In that case
exactly one of
nu.pcf must be specified.
If the argument
lambda is provided, then this is used
as the value of the point process intensity lambda.
X is a
point pattern, then lambda
will be estimated from
X is a summary statistic and
lambda is missing,
then the intensity lambda cannot be estimated, and
the parameter mu will be returned as
The remaining arguments
rmin,rmax,q,p control the
method of minimum contrast; see
The corresponding model can be simulated using
eta appearing in
startpar is equivalent to the
omega used in
Homogeneous or inhomogeneous Neyman-Scott/VarGamma models can also be
fitted using the function
kppm and the fitted models
can be simulated using
The optimisation algorithm can be controlled through the
"..." which are passed to the
optim. For example,
to constrain the parameter values to a certain range,
use the argument
method="L-BFGS-B" to select an optimisation
algorithm that respects box constraints, and use the arguments
upper to specify (vectors of) minimum and
maximum values for each parameter.
An object of class
"minconfit". There are methods for printing
and plotting this object. It contains the following main components:
Vector of fitted parameter values.
Function value table (object of class
Abdollah Jalilian and Rasmus Waagepetersen. Adapted for spatstat by \adrian
Jalilian, A., Guan, Y. and Waagepetersen, R. (2013) Decomposition of variance for spatial Cox processes. Scandinavian Journal of Statistics 40, 119-137.
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252–258.
rVarGamma to simulate the model.
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