R: Log Likelihood and AIC for Fitted Determinantal Point Process...

logLik.dppm {spatstat.core} | R Documentation

## Log Likelihood and AIC for Fitted Determinantal Point Process Model

### Description

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

### Usage

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

### Arguments

`object,fit` | Fitted point process model. An object of class `"dppm"`.
`...` | Ignored.
`scale` | Ignored.
`k` | Numeric value specifying the weight of the equivalent degrees of freedom in the AIC. See Details.

### Details

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

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

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

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

The methods `AIC.dppm` and `extractAIC.dppm` 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.dppm` returns the number of points in the original data point pattern to which the model was fitted.

The R function `step` uses these methods, but it does not work for determinantal models yet due to a missing implementation of `update.dppm`.

### 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

`dppm`, `logLik.ppm`

### Examples

      fit <- dppm(swedishpines ~ x, dppGauss(), method="palm")
      nobs(fit)
      logLik(fit)
      extractAIC(fit)
      AIC(fit)

[Package spatstat.core version 2.0-0 Index]