Residual K Function
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.
- 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
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
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.
object may be a function value table
(object of class
"fv") that was returned by
a previous call to
Kres computes the
residual from this object.
- A function value table (object of class
"fv"), essentially a data frame of function values. There is a plot method for this class. See
Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudo-score and residual diagnostics for spatial point process models. To appear in Statistical Science.
Point process models:
data(cells) fit0 <- ppm(cells, ~1) # uniform Poisson <testonly>fit0 <- ppm(cells, ~1, nd=16)</testonly> 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)) <testonly>fit1 <- ppm(cells, ~1, Strauss(0.08), nd=16)</testonly> K1 <- Kres(fit1) 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, interaction=as.interact(fit1), nsim=19) plot(E) # For computational efficiency Kc <- Kcom(fit1) K1 <- Kres(Kc)