R: Residual G Function

Gres {spatstat} | R Documentation

## 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 previous call to `Gcom`.
`...` | 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. See `fv.object`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Ege Rubak rubak@math.aau.dk and Jesper Moller.

### 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
        ## Not run:
        E <- envelope(fit1, Gres, model=fit1, nsim=39)
        plot(E)

    ## End(Not run)
    # For computational efficiency
        Gc <- Gcom(fit1)
        G1 <- Gres(Gc)

[Package spatstat version 1.54-0 Index]