R: Log Likelihood and AIC for Point Process Model

logLik.ppm {spatstat}

R Documentation

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 or logistic likelihood for a fitted Gibbs point process model.

Usage

## S3 method for class 'ppm'
logLik(object, ..., new.coef=NULL, warn=TRUE, absolute=FALSE)

## S3 method for class 'ppm'
deviance(object, ...)

## S3 method for class 'ppm'
AIC(object, ..., k=2, takeuchi=TRUE)

## S3 method for class 'ppm'
extractAIC(fit, scale=0, k=2, ..., takeuchi=TRUE)

## 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 or logistic likelihood is returned instead of the likelihood.
`absolute`	Logical value indicating whether to include constant terms in the loglikelihood.
`scale`	Ignored.
`k`	Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.
`new.coef`	New values for the canonical parameters of the model. A numeric vector of the same length as `coef(object)`.
`takeuchi`	Logical value specifying whether to use the Takeuchi penalty (`takeuchi=TRUE`) or the number of fitted parameters (`takeuchi=FALSE`) in calculating AIC.

Details

These functions are methods for the generic commands logLik, deviance, 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 * penalty

where L is the maximised likelihood of the fitted model, and penalty is a penalty for model complexity, usually equal to 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 or logistic likelihood (if fit is a Gibbs model).

The penalty term is calculated as follows. If takeuchi=FALSE then penalty is the number of fitted parameters. If takeuchi=TRUE then penalty = trace(J H^(-1)) where J and H are the estimated variance and hessian, respectively, of the composite score. These two choices are equivalent for a Poisson process.

The method nobs.ppm 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

Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika 92, 519–528.

Examples

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

[Package spatstat version 1.56-0 Index]