spatstat (version 1.48-0)

anova.ppm: ANOVA for Fitted Point Process Models

Description

Performs analysis of deviance for one or more fitted point process models.

Usage

"anova"(object, ..., test=NULL, adjust=TRUE, warn=TRUE, fine=FALSE)

Arguments

object

A fitted point process model (object of class "ppm").

...

Optional. Additional objects of class "ppm".

test

Character string, partially matching one of "Chisq", "LRT", "Rao", "score", "F" or "Cp", or NULL indicating that no test should be performed.

adjust

Logical value indicating whether to correct the pseudolikelihood ratio when some of the models are not Poisson processes.

warn

Logical value indicating whether to issue warnings if problems arise.

fine

Logical value, passed to vcov.ppm, indicating whether to use a quick estimate (fine=FALSE, the default) or a slower, more accurate estimate (fine=TRUE) of variance terms. Relevant only when some of the models are not Poisson and adjust=TRUE.

Value

An object of class "anova", or NULL.

Errors and warnings

Error messages

An error message that reports system is computationally singular indicates that the determinant of the Fisher information matrix of one of the models was either too large or too small for reliable numerical calculation. See vcov.ppm for suggestions on how to handle this.

Details

This is a method for anova for fitted point process models (objects of class "ppm", usually generated by the model-fitting function ppm).

If the fitted models are all Poisson point processes, then by default, this function performs an Analysis of Deviance of the fitted models. The output shows the deviance differences (i.e. 2 times log likelihood ratio), the difference in degrees of freedom, and (if test="Chi" or test="LRT") the two-sided p-values for the chi-squared tests. Their interpretation is very similar to that in anova.glm. If test="Rao" or test="score", the score test (Rao, 1948) is performed instead.

If some of the fitted models are not Poisson point processes, the `deviance' differences in this table are 'pseudo-deviances' equal to 2 times the differences in the maximised values of the log pseudolikelihood (see ppm). It is not valid to compare these values to the chi-squared distribution. In this case, if adjust=TRUE (the default), the pseudo-deviances will be adjusted using the method of Pace et al (2011) and Baddeley et al (2015) so that the chi-squared test is valid. It is strongly advisable to perform this adjustment.

References

Baddeley, A., Turner, R. and Rubak, E. (2015) Adjusted composite likelihood ratio test for Gibbs point processes. Journal of Statistical Computation and Simulation 86 (5) 922--941. DOI: 10.1080/00949655.2015.1044530.

Pace, L., Salvan, A. and Sartori, N. (2011) Adjusting composite likelihood ratio statistics. Statistica Sinica 21, 129--148.

Rao, C.R. (1948) Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society 44, 50--57.

See Also

ppm, vcov.ppm

Examples

 mod0 <- ppm(swedishpines ~1)
 modx <- ppm(swedishpines ~x)
 # Likelihood ratio test
 anova(mod0, modx, test="Chi")
 # Score test
 anova(mod0, modx, test="Rao")

 # Single argument
 modxy <- ppm(swedishpines ~x + y)
 anova(modxy, test="Chi")

 # Adjusted composite likelihood ratio test
 modP <- ppm(swedishpines ~1, rbord=9)
 modS <- ppm(swedishpines ~1, Strauss(9))
 anova(modP, modS, test="Chi")