# 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 model-compensated $G$
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,
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
- Optional alternative to
`r`

for advanced use. - correction
- Edge correction(s) to be employed in calculating the compensator.
Options are
`"border"`

,`"Hanisch"`

and`"best"`

. - 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 if`conditional=TRUE`

. See Details. - trend,interaction,rbord
- Optional. Arguments passed to
`ppm`

to fit a point process model to the data, if`object`

is a point pattern. See`ppm`

for details. - ...
- Extra arguments passed to
`ppm`

. - ppmcorrection
- The
`correction`

argument to`ppm`

. - 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 re-fitted at high resolution as specified by these parameters. The coefficients of the re

##### Details

This command provides a diagnostic for the goodness-of-fit 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
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 Moller (2011).
Thus, by default, the reweighting estimator is computed
for non-Poisson models.

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`

.

##### 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, pseudo-score and residual
diagnostics for spatial point process models.
*Statistical Science* **26**, 613--646.

##### 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)
```

*Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)*