spatstat (version 1.23-1)

Gcom: Model Compensator of Nearest Neighbour Function

Description

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"),
     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".

restrict

Logical value indicating whether to compute the restriction estimator (restrict=TRUE) or the reweighting estimator (restrict=FALSE, the default). 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

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 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 argument restrict. If restrict=TRUE the algorithm calculates the restriction estimator; if restrict=FALSE it calculates the reweighting estimator. See Appendix E of Baddeley, Rubak and Moller (2011). 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.

References

Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudo-score and residual diagnostics for spatial point process models. To appear in Statistical Science.

See Also

Gest, Gres, 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)