| Hardcore {spatstat.model} | R Documentation |
The Hard Core Point Process Model
Description
Creates an instance of the hard core point process model which can then be fitted to point pattern data.
Usage
Hardcore(hc=NA)
Arguments
hc |
The hard core distance |
Details
A hard core process with
hard core distance h and abundance
parameter \beta
is a pairwise interaction point process
in which distinct points are not allowed to come closer
than a distance h apart.
The probability density is zero if any pair of points
is closer than h units apart, and otherwise equals
f(x_1,\ldots,x_n) =
\alpha \beta^{n(x)}
where x_1,\ldots,x_n represent the
points of the pattern, n(x) is the number of points in the
pattern, and \alpha is the normalising constant.
The function ppm(), which fits point process models to
point pattern data, requires an argument
of class "interact" describing the interpoint interaction
structure of the model to be fitted.
The appropriate description of the hard core process
pairwise interaction is
yielded by the function Hardcore(). See the examples below.
If the hard core distance argument hc is missing or NA,
it will be estimated from the data when ppm is called.
The estimated value of hc is the minimum nearest neighbour distance
multiplied by n/(n+1), where n is the
number of data points.
Value
An object of class "interact"
describing the interpoint interaction
structure of the hard core
process with hard core distance hc.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner rolfturner@posteo.net
References
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
See Also
Strauss,
StraussHard,
MultiHard,
ppm,
pairwise.family,
ppm.object
Examples
Hardcore(0.02)
# prints a sensible description of itself
ppm(cells ~1, Hardcore(0.05))
# fit the stationary hard core process to `cells'
# estimate hard core radius from data
ppm(cells ~1, Hardcore())
# equivalent:
ppm(cells ~1, Hardcore)
# fit a nonstationary hard core process
# with log-cubic polynomial trend
ppm(cells ~ polynom(x,y,3), Hardcore(0.05))