R: Log Likelihood and AIC for Multiple Point Process Model

logLik.mppm {spatstat.core} | R Documentation

## Log Likelihood and AIC for Multiple Point Process Model

### Description

For a point process model that has been fitted to multiple point patterns, these functions extract the log likelihood and AIC, or analogous quantities based on the pseudolikelihood.

### Usage

     ## S3 method for class 'mppm'
    logLik(object, ..., warn=TRUE)

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

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

     ## S3 method for class 'mppm'
    nobs(object, ...)

     ## S3 method for class 'mppm'
    getCall(x, ...)

     ## S3 method for class 'mppm'
    terms(x, ...)

### Arguments

`object,fit,x` | Fitted point process model (fitted to multiple point patterns). An object of class `"mppm"`.
`...` | 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.
`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`, `AIC`, `extractAIC`, `terms` and `getCall` for the class `"mppm"`.

An object of class `"mppm"` represents a fitted Poisson or Gibbs point process model fitted to several point patterns. It is obtained from the model-fitting function `mppm`.

The method `logLik.mppm` extracts the maximised value of the log likelihood for the fitted model (as approximated by quadrature using the Berman-Turner approximation). If `object` is not a Poisson process, the maximised log pseudolikelihood is returned, with a warning.

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.mppm` 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 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.mppm` returns the total number of points in the original data point patterns to which the model was fitted.

The method `getCall.mppm` extracts the original call to `mppm` which caused the model to be fitted.

The method `terms.mppm` extracts the covariate terms in the model formula as a `terms` object. Note that these terms do not include the interaction component of the model.

The R function `step` uses these methods.

### Value

See the help files for the corresponding generic functions.

### Author(s)

Adrian Baddeley, Ida-Maria Sintorn and Leanne Bischoff. Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### References

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. London: Chapman and Hall/CRC Press.

### See Also

`mppm`

### Examples

      fit <- mppm(Bugs ~ x, hyperframe(Bugs=waterstriders))
      logLik(fit)
      AIC(fit)
      nobs(fit)
      getCall(fit)

[Package spatstat.core version 1.65-5 Index]