Gcom
Model Compensator of Nearest Neighbour Function
Given a point process model fitted to a point pattern dataset, this function computes the compensator of the nearest neighbour distance distribution function $G$ based on the fitted model (as well as the usual nonparametric estimates of $G$ based on the data alone). Comparison between the nonparametric and modelcompensated $G$ functions serves as a diagnostic for the model.
Usage
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)
Arguments
 object

Object to be analysed.
Either a fitted point process model (object of class
"ppm"
) or a point pattern (object of class"ppp"
) or quadrature scheme (object of class"quad"
).  r
 Optional. Vector of values of the argument $r$ at which the function $G(r)$ should be computed. This argument is usually not specified. There is a sensible default.
 breaks
 This argument is for internal use only.
 correction

Edge correction(s) to be employed in calculating the compensator.
Options are
"border"
,"Hanisch"
and"best"
. Alternativelycorrection="all"
selects all options.  conditional
 Optional. Logical value indicating whether to compute the estimates for the conditional case. See Details.
 restrict

Logical value indicating whether to compute
the restriction estimator (
restrict=TRUE
) or the reweighting estimator (restrict=FALSE
, the default). Applies only ifconditional=TRUE
. See Details.  model

Optional. A fitted point process model (object of
class
"ppm"
) to be refitted to the data usingupdate.ppm
, ifobject
is a point pattern. Overrides the argumentstrend,interaction,rbord,ppmcorrection
.  trend,interaction,rbord

Optional. Arguments passed to
ppm
to fit a point process model to the data, ifobject
is a point pattern. Seeppm
for details.  ...

Extra arguments passed to
ppm
.  ppmcorrection

The
correction
argument toppm
.  truecoef

Optional. Numeric vector. If present, this will be treated as
if it were the true coefficient vector of the point process model,
in calculating the diagnostic. Incompatible with
hi.res
.  hi.res

Optional. List of parameters passed to
quadscheme
. If this argument is present, the model will be refitted at high resolution as specified by these parameters. The coefficients of the resulting fitted model will be taken as the true coefficients. Then the diagnostic will be computed for the default quadrature scheme, but using the high resolution coefficients.
Details
This command provides a diagnostic for the goodnessoffit of a point process model fitted to a point pattern dataset. It computes different estimates of the nearest neighbour distance distribution function $G$ of the dataset, which should be approximately equal if the model is a good fit to the data.
The first argument, object
, is usually a fitted point process model
(object of class "ppm"
), obtained from the
modelfitting 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 modelcompensated
$G$ 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):
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 nonPoisson 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 Moller (2011).
See also spatstat.options('eroded.intensity')
.
Thus, by default, the reweighting estimator is computed
for nonPoisson models.
The bordercorrected and Hanischcorrected estimates of $G(r)$ are approximately unbiased estimates of the $G$function, assuming the point process is stationary. The modelcompensated 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 modelcompensated estimates is approximately zero.
To compute the difference between the nonparametric and modelcompensated
functions, use Gres
.
Value

A function value table (object of class
"fv"
),
essentially a data frame of function values.
There is a plot method for this class. See fv.object
.
References
Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudoscore and residual diagnostics for spatial point process models. Statistical Science 26, 613646.
See Also
Related functions:
Gest
,
Gres
.
Alternative functions:
Kcom
,
psstA
,
psstG
,
psst
.
Model fitting: ppm
.
Examples
data(cells)
fit0 < ppm(cells, ~1) # uniform Poisson
G0 < Gcom(fit0)
G0
plot(G0)
# uniform Poisson is clearly not correct
# Hanisch estimates only
plot(Gcom(fit0), cbind(han, hcom) ~ r)
fit1 < ppm(cells, ~1, Strauss(0.08))
plot(Gcom(fit1), cbind(han, hcom) ~ r)
# Try adjusting interaction distance
fit2 < update(fit1, Strauss(0.10))
plot(Gcom(fit2), cbind(han, hcom) ~ r)
G3 < Gcom(cells, interaction=Strauss(0.12))
plot(G3, cbind(han, hcom) ~ r)