logLik.ppm

0th

Percentile

Log Likelihood and AIC for Point Process Model

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.

Keywords
models, spatial
Usage
## S3 method for class 'ppm':
logLik(object, ..., new.coef=NULL, warn=TRUE)
## S3 method for class 'ppm':
AIC(object, \dots, k=2, takeuchi=TRUE)
## S3 method for class 'ppm':
extractAIC(fit, scale=0, k=2, \dots, 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.
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, 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 $$AIC = -2 \log(L) + k \times \mbox{penalty}$$ 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 or logistic likelihood (if fit is a Gibbs model).

The $\mbox{penalty}$ term is calculated as follows. If takeuchi=FALSE then $\mbox{penalty}$ is the number of fitted parameters. If takeuchi=TRUE then $\mbox{penalty} = \mbox{trace}(J H^{-1})$ 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 Rfunction 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.

References

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

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.

Aliases
  • logLik.ppm
  • AIC.ppm
  • extractAIC.ppm
  • nobs.ppm
Examples
data(cells)
  fit <- ppm(cells, ~x)
  nobs(fit)
  logLik(fit)
  extractAIC(fit)
  AIC(fit)
  step(fit)
Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)

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