Gcom(object, r = NULL, breaks = NULL, ...,
correction = c("border", "Hanisch"),
conditional = !is.poisson(object),
restrict=FALSE,
model=NULL,
trend = ~1, interaction = Poisson(),
rbord = reach(interaction),
ppmcorrection="border",
truecoef = NULL, hi.res = NULL)
"ppm"
)
or a point pattern (object of class "ppp"
)
or quadrature scheme (object of class "quad"
)."border"
, "Hanisch"
and "best"
.restrict=TRUE
) or
the reweighting estimator (restrict=FALSE
, the default).
Applies only if conditional=TRUE
. See Details."ppm"
) to be re-fitted to the data
using update.ppm
, if object
is a point pattern.
Overrides the arguments ppm
.correction
argument to ppm
.hi.res
.quadscheme
.
If this argument is present, the model will be
re-fitted at high resolution as specified by these parameters.
The coefficients
of the re The first argument, object
, is usually a fitted point process model
(object of class "ppm"
), obtained from the
model-fitting function ppm
.
For convenience, object
can also be a point pattern
(object of class "ppp"
).
In that case, a point process
model will be fitted to it,
by calling ppm
using the arguments
trend
(for the first order trend),
interaction
(for the interpoint interaction)
and rbord
(for the erosion distance in the border correction
for the pseudolikelihood). See ppm
for details
of these arguments.
The algorithm first extracts the original point pattern dataset
(to which the model was fitted) and computes the
standard nonparametric estimates of the $G$ function.
It then also computes the model-compensated
$G$ function. The different functions are returned
as columns in a data frame (of class "fv"
).
The interpretation of the columns is as follows
(ignoring edge corrections):
[object Object],[object Object],[object Object],[object Object]
If the fitted model is a Poisson point process, then the formulae above
are exactly what is computed. If the fitted model is not Poisson, the
formulae above are modified slightly to handle edge effects.
The modification is determined by the arguments
conditional
and restrict
.
The value of conditional
defaults to FALSE
for Poisson models
and TRUE
for non-Poisson models.
If conditional=FALSE
then the formulae above are not modified.
If conditional=TRUE
, then the algorithm calculates
the restriction estimator if restrict=TRUE
,
and calculates the reweighting estimator if restrict=FALSE
.
See Appendix E of Baddeley, Rubak and
The border-corrected and Hanisch-corrected estimates of $G(r)$ are approximately unbiased estimates of the $G$-function, assuming the point process is stationary. The model-compensated functions are unbiased estimates of the mean value of the corresponding nonparametric estimate, assuming the model is true. Thus, if the model is a good fit, the mean value of the difference between the nonparametric and model-compensated estimates is approximately zero.
To compute the difference between the nonparametric and model-compensated
functions, use Gres
.
}
"fv"
),
essentially a data frame of function values.
There is a plot method for this class. See fv.object
.