Interaction Distance of a Point Process
Computes the interaction distance of a point process.
reach(x, ...) ## S3 method for class 'ppm' reach(x, ..., epsilon=0) ## S3 method for class 'interact' reach(x, ...) ## S3 method for class 'rmhmodel' reach(x, ...) ## S3 method for class 'fii' reach(x, ..., epsilon)
x |
Either a fitted point process model (object of class
|
epsilon |
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 of class "ppm"
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
(see Strauss)
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
(see OrdThresh) is infinite, since two points may
interact at any distance apart.
The function reach(x) is generic, with methods
for the case where x is
a fitted point process model
(object of class "ppm", usually obtained from the model-fitting
function ppm);
an interpoint interaction structure (object of class
"interact"), created by one of the functions
Poisson,
Strauss,
StraussHard,
MultiStrauss,
MultiStraussHard,
Softcore,
DiggleGratton,
Pairwise,
PairPiece,
Geyer,
LennardJones,
Saturated,
OrdThresh
or
Ord;
a fitted interpoint interaction (object of class
"fii") extracted from a fitted point process model
by the command fitin;
a point process model for simulation (object of class
"rmhmodel"), usually obtained from rmhmodel.
When x is an "interact" object,
reach(x) returns the maximum possible interaction range
for any point process model with interaction structure given by x.
For example, reach(Strauss(0.2)) returns 0.2.
When x is a "ppm" object,
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,r will return
either 0 or r, depending on whether the fitted
interaction parameter gamma is equal or not equal to 1.
For some point process models, such as the soft core process
(see 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 epsilon,
on the scale of the log conditional intensity. This is done
by setting the argument epsilon to a positive value.
The interaction distance, or NA if this cannot be
computed from the information given.
Methods for reach are also defined for
point process models of class "kppm" and "dppm".
Their technical definition is different from this one.
See reach.kppm and reach.dppm.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz
See reach.kppm and reach.dppm
for other types of point process models.
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 3Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.