Interaction Distance of a Point Process
Computes the interaction distance of a point process.
## S3 method for class 'ppm': reach(x, \dots, epsilon=0)
## S3 method for class 'interact': reach(x, \dots)
## S3 method for class 'rmhmodel': reach(x, \dots)
## S3 method for class 'fii': reach(x, \dots, epsilon)
- Either a fitted point process model (object of class
"ppm"), an interpoint interaction (object of class
"interact"), a fitted interpoint interaction (object of class
"fii") or a point process model for si
- Numerical threshold below which interaction is treated as zero. See details.
- Other arguments are ignored.
The `interaction distance' or `interaction range' of a point process model is the smallest distance $D$ such that any two points in the process which are separated by a distance greater than $D$ do not interact with each other.
For example, the interaction range of a Strauss process
with parameters $\beta,\gamma,r$ is equal to
$r$, unless $\gamma=1$ in which case the model is
Poisson and the interaction
range is $0$.
The interaction range of a Poisson process is zero.
The interaction range of the Ord threshold process
OrdThresh) is infinite, since two points may
interact at any distance apart.
reach(x) is generic, with methods
for the case where
- a fitted point process model
(object of class
"ppm", usually obtained from the model-fitting function
- an interpoint interaction structure (object of class
"interact"), created by one of the functions
- a fitted interpoint interaction (object of class
"fii") extracted from a fitted point process model by the command
- a point process model for simulation (object of class
"rmhmodel"), usually obtained from
reach(x)returns the maximum possible interaction range for any point process model with interaction structure given by
x. For example,
reach(x)returns the interaction range for the point process model represented by
x. For example, a fitted Strauss process model with parameters
beta,gamma,rwill return either
r, depending on whether the fitted interaction parameter
gammais equal or not equal to 1.
For some point process models, such as the soft core process
Softcore), the interaction distance is
infinite, because the interaction terms are positive for all
pairs of points. A practical solution is to compute
the distance at which the interaction contribution
from a pair of points falls below a threshold
on the scale of the log conditional intensity. This is done
by setting the argument
epsilon to a positive value.
- The interaction distance, or
NAif this cannot be computed from the information given.
reach(Poisson()) # returns 0 reach(Strauss(r=7)) # returns 7 fit <- ppm(swedishpines ~ 1, Strauss(r=7)) reach(fit) # returns 7 reach(OrdThresh(42)) # returns Inf reach(MultiStrauss(matrix(c(1,3,3,1),2,2))) # returns 3