Gres
Residual G Function
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.
Usage
Gres(object, ...)
Arguments
- 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 pr - ...
- Arguments passed to
Gcom
.
Details
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.
Value
- A function value table (object of class
"fv"
), essentially a data frame of function values. There is a plot method for this class. Seefv.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:
Gcom
,
Gest
.
Alternative functions:
Kres
,
psstA
,
psstG
,
psst
.
Model-fitting:
ppm
.
Examples
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
E <- envelope(fit1, Gres, interaction=as.interact(fit1), nsim=39)
plot(E)
# For computational efficiency
Gc <- Gcom(fit1)
G1 <- Gres(Gc)