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.

`Kres(object, ...)`

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`

.

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`

.

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.

Baddeley, A., Rubak, E. and Moller, J. (2011)
Score, pseudo-score and residual
diagnostics for spatial point process models.
*Statistical Science* **26**, 613--646.

Related functions:
`Kcom`

,
`Kest`

.

Alternative functions:
`Gres`

,
`psstG`

, `psstA`

, `psst`

.

Point process models: `ppm`

.

# NOT RUN { data(cells) fit0 <- ppm(cells, ~1) # uniform Poisson # } # NOT RUN { 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)) # } # NOT RUN { 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 # } # NOT RUN { E <- envelope(fit1, Kres, model=fit1, nsim=19) plot(E) # } # NOT RUN { # For computational efficiency Kc <- Kcom(fit1) K1 <- Kres(Kc) # }