spatstat (version 1.31-3)

logLik.ppm: Log Likelihood and AIC for Point Process Model

Description

Extracts the log likelihood, deviance, and AIC of a fitted Poisson point process model, or analogous quantities based on the pseudolikelihood for a fitted Gibbs point process model.

Usage

## S3 method for class 'ppm':
logLik(object, ..., warn=TRUE)
## S3 method for class 'ppm':
extractAIC(fit, scale=0, k=2, \dots)
## S3 method for class 'ppm':
nobs(object, ...)

Arguments

object,fit

Fitted point process model. An object of class "ppm".

...

Ignored.

warn

If TRUE, a warning is given when the pseudolikelihood is returned instead of the likelihood.

scale

Ignored.

k

Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.

Value

• A numerical value.

Details

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

An object of class "ppm" represents a fitted Poisson or Gibbs point process model. It is obtained from the model-fitting function ppm. The method logLik.ppm computes the maximised value of the log likelihood for the fitted model object (as approximated by quadrature using the Berman-Turner approximation) is extracted. If object is not a Poisson process, the maximised log pseudolikelihood is returned, with a warning (if warn=TRUE).

The Akaike Information Criterion AIC for a fitted model is defined as $$AIC = -2 \log(L) + k \times \mbox{edf}$$ where $L$ is the maximised likelihood of the fitted model, and $\mbox{edf}$ is the effective degrees of freedom of the model. The method extractAIC.ppm returns the analogous quantity $AIC*$ in which $L$ is replaced by $L*$, the quadrature approximation to the likelihood (if fit is a Poisson model) or the pseudolikelihood (if fit is a Gibbs model).

The method nobs.ppm returns the number of points in the original data point pattern to which the model was fitted. The Rfunctions AIC and step use these methods.

See Also

ppm, as.owin, coef.ppm, fitted.ppm, formula.ppm, model.frame.ppm, model.matrix.ppm, plot.ppm, predict.ppm, residuals.ppm, simulate.ppm, summary.ppm, terms.ppm, update.ppm, vcov.ppm.

Examples

data(cells)
  fit <- ppm(cells, ~x)
  nobs(fit)
  logLik(fit)
  extractAIC(fit)
  AIC(fit)
  step(fit)