spatstat (version 1.34-1)

Gres: Residual G Function

Description

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.

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.

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.

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)