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.
- 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
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
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.
object may be a function value table
(object of class
"fv") that was returned by
a previous call to
Gres computes the
residual from this object.
- A function value table (object of class
"fv"), essentially a data frame of function values. There is a plot method for this class. See
Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudo-score and residual diagnostics for spatial point process models. To appear in Statistical Science.
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)