BadGey {spatstat} | R Documentation |
Creates an instance of the Baddeley-Geyer point process model, defined as a hybrid of several Geyer interactions. The model can then be fitted to point pattern data.
BadGey(r, sat)
r |
vector of interaction radii |
sat |
vector of saturation parameters, or a single common value of saturation parameter |
This is Baddeley's generalisation of the
Geyer saturation point process model,
described in Geyer
, to a process with multiple interaction
distances.
The BadGey point process with interaction radii r[1], ..., r[k], saturation thresholds s[1],...,s[k], intensity parameter beta and interaction parameters gamma[1], ..., gamma[k], is the point process in which each point x[i] in the pattern X contributes a factor
beta gamma[1]^v(1, x_i, X) ... gamma[k]^v(k, x_i, X)
to the probability density of the point pattern, where
v(j, x_i, X) = min(s[j], t(j, x_i, X))
where t(j,x[i],X) denotes the number of points in the pattern X which lie within a distance r[j] from the point x[i].
BadGey
is used to fit this model to data.
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 piecewise constant Saturated pairwise
interaction is yielded by the function BadGey()
.
See the examples below.
The argument r
specifies the vector of interaction distances.
The entries of r
must be strictly increasing, positive numbers.
The argument sat
specifies the vector of saturation parameters
that are applied to the point counts t(j,x[i],X).
It should be a vector of the same length as r
, and its entries
should be nonnegative numbers. Thus sat[1]
is applied to the
count of points within a distance r[1]
, and sat[2]
to the
count of points within a distance r[2]
, etc.
Alternatively sat
may be a single number, and this saturation
value will be applied to every count.
Infinite values of the
saturation parameters are also permitted; in this case
v(j, x_i, X) = t(j, x_i, X)
and there is effectively no ‘saturation’ for the distance range in
question. If all the saturation parameters are set to Inf
then
the model is effectively a pairwise interaction process, equivalent to
PairPiece
(however the interaction parameters
gamma obtained from BadGey
have a complicated relationship to the interaction
parameters gamma obtained from PairPiece
).
If r
is a single number, this model is virtually equivalent to the
Geyer process, see Geyer
.
An object of class "interact"
describing the interpoint interaction
structure of a point process.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz in collaboration with Hao Wang and Jeff Picka
ppm
,
pairsat.family
,
Geyer
,
PairPiece
,
SatPiece
BadGey(c(0.1,0.2), c(1,1)) # prints a sensible description of itself BadGey(c(0.1,0.2), 1) data(cells) # fit a stationary Baddeley-Geyer model ppm(cells, ~1, BadGey(c(0.07, 0.1, 0.13), 2)) # nonstationary process with log-cubic polynomial trend ## Not run: ppm(cells, ~polynom(x,y,3), BadGey(c(0.07, 0.1, 0.13), 2)) ## End(Not run)