R: Residual K Function

Kres {spatstat.core} | R Documentation

## Residual K Function

### Description

Given a point process model fitted to a point pattern dataset, this function computes the residual K function, which serves as a diagnostic for goodness-of-fit of the model.

### Usage

       Kres(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 `Kcom`.
`...` | Arguments passed to `Kcom`.

### 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 K 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 `Kres` first calls `Kcom` to compute both the nonparametric estimate of the K function and its model compensator. Then `Kres` computes the difference between them, which is the residual K-function.

Alternatively, `object` may be a function value table (object of class `"fv"`) that was returned by a previous call to `Kcom`. Then `Kres` 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: `Kcom`, `Kest`.

Alternative functions: `Gres`, `psstG`, `psstA`, `psst`.

Point process models: `ppm`.

### Examples

        data(cells)
        fit0 <- ppm(cells, ~1) # uniform Poisson

        K0 <- Kres(fit0)
        K0
        plot(K0)
    # isotropic-correction estimate
        plot(K0, ires ~ r)
    # uniform Poisson is clearly not correct

        fit1 <- ppm(cells, ~1, Strauss(0.08))

        K1 <- Kres(fit1)

        if(interactive()) {
          plot(K1, ires ~ r)
       # fit looks approximately OK; try adjusting interaction distance
          plot(Kres(cells, interaction=Strauss(0.12)))
        }

    # How to make envelopes
        # E <- envelope(fit1, Kres, model=fit1, nsim=19)
        # plot(E)

    # For computational efficiency
        Kc <- Kcom(fit1)
        K1 <- Kres(Kc)

[Package spatstat.core version 2.0-0 Index]