Log Likelihood and AIC for Fitted Cox or Cluster Point Process Model

Description

Extracts the log Palm likelihood, deviance, and AIC of a fitted Cox or cluster point process model.

Usage

## S3 method for class 'kppm'
logLik(object, ...)
## S3 method for class 'kppm'
AIC(object, ..., k=2)
## S3 method for class 'kppm'
extractAIC(fit, scale=0, k=2, ...)
## S3 method for class 'kppm'
nobs(object, ...)

Arguments

Details

These functions are methods for the generic commands logLik, extractAIC and nobs for the class "kppm".

An object of class "kppm" represents a fitted Cox or cluster point process model. It is obtained from the model-fitting function kppm.

These methods apply only when the model was fitted by maximising the Palm likelihood (Tanaka et al, 2008) by calling kppm with the argument method="palm".

The method logLik.kppm computes the maximised value of the log Palm likelihood for the fitted model object.

The methods AIC.kppm and extractAIC.kppm compute the Akaike Information Criterion AIC for the fitted model based on the Palm likelihood (Tanaka et al, 2008)

AIC = -2 * log(PL) + k * edf

where PL is the maximised Palm likelihood of the fitted model, and edf is the effective degrees of freedom of the model.

The method nobs.kppm returns the number of points in the original data point pattern to which the model was fitted.

The R function step uses these methods.

Value

logLik returns a numerical value, belonging to the class "logLik", with an attribute "df" giving the degrees of freedom.

AIC returns a numerical value.

extractAIC returns a numeric vector of length 2 containing the degrees of freedom and the AIC value.

nobs returns an integer value.

Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

References

Tanaka, U. and Ogata, Y. and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal 50, 43–57.

See Also

kppm, logLik.ppm

Examples

  fit <- kppm(redwood ~ x, "Thomas", method="palm")
  nobs(fit)
  logLik(fit)
  extractAIC(fit)
  AIC(fit)
  step(fit)