Given a point process model fitted to a point pattern dataset, this function computes the residual \(G\) function, which serves as a diagnostic for goodness-of-fit of the model.

`Gres(object, ...)`

object

Object to be analysed.
Either a fitted point process model (object of class `"ppm"`

),
a point pattern (object of class `"ppp"`

),
a quadrature scheme (object of class `"quad"`

),
or the value returned by a previous call to `Gcom`

.

…

Arguments passed to `Gcom`

.

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`

.

This command provides a diagnostic for the goodness-of-fit of a point process model fitted to a point pattern dataset. It computes a residual version of the \(G\) function of the dataset, which should be approximately zero if the model is a good fit to the data.

In normal use, `object`

is a fitted point process model
or a point pattern. Then `Gres`

first calls `Gcom`

to compute both the nonparametric estimate of the \(G\) function
and its model compensator. Then `Gres`

computes the
difference between them, which is the residual \(G\)-function.

Alternatively, `object`

may be a function value table
(object of class `"fv"`

) that was returned by
a previous call to `Gcom`

. Then `Gres`

computes the
residual from this object.

Baddeley, A., Rubak, E. and Moller, J. (2011)
Score, pseudo-score and residual
diagnostics for spatial point process models.
*Statistical Science* **26**, 613--646.

Related functions:
`Gcom`

,
`Gest`

.

Alternative functions:
`Kres`

,
`psstA`

,
`psstG`

,
`psst`

.

Model-fitting:
`ppm`

.

# NOT RUN { data(cells) fit0 <- ppm(cells, ~1) # uniform Poisson G0 <- Gres(fit0) plot(G0) # Hanisch correction estimate plot(G0, hres ~ r) # uniform Poisson is clearly not correct fit1 <- ppm(cells, ~1, Strauss(0.08)) plot(Gres(fit1), hres ~ r) # fit looks approximately OK; try adjusting interaction distance plot(Gres(cells, interaction=Strauss(0.12))) # How to make envelopes if(interactive()) { E <- envelope(fit1, Gres, model=fit1, nsim=39) plot(E) } # For computational efficiency Gc <- Gcom(fit1) G1 <- Gres(Gc) # }