# logLik.ppm

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##### 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 ppm
logLik(object, …, new.coef=NULL, warn=TRUE, absolute=FALSE)# S3 method for ppm
deviance(object, …)# S3 method for ppm
AIC(object, …, k=2, takeuchi=TRUE)# S3 method for ppm
extractAIC(fit, scale=0, k=2, …, takeuchi=TRUE)# S3 method for 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 $$AIC = -2 \log(L) + k \times \mbox{penalty}$$ where $L$ is the maximised likelihood of the fitted model, and $\mbox{penalty}$ 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 $\mbox{penalty}$ 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 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.

##### References

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

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
• deviance.ppm
• AIC.ppm
• extractAIC.ppm
• nobs.ppm
##### Examples
# NOT RUN {
data(cells)
fit <- ppm(cells, ~x)
nobs(fit)
logLik(fit)
deviance(fit)
extractAIC(fit)
AIC(fit)
step(fit)
# }

Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)

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