spatstat (version 1.60-1)

anova.mppm: ANOVA for Fitted Point Process Models for Replicated Patterns

Description

Performs analysis of deviance for one or more point process models fitted to replicated point pattern data.

Usage

# S3 method for mppm
anova(object, …,
                  test=NULL, adjust=TRUE,
                  fine=FALSE, warn=TRUE)

Arguments

object

Object of class "mppm" representing a point process model that was fitted to replicated point patterns.

…

Optional. Additional objects of class "mppm".

test

Type of hypothesis test to perform. A 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.

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 the variance of the fitted coefficients of each model. Relevant only when some of the models are not Poisson and adjust=TRUE.

warn

Logical value indicating whether to issue warnings if problems arise.

Value

An object of class "anova", or NULL.

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 comparing several fitted point process models of class "mppm", usually generated by the model-fitting function mppm).

If the fitted models are all Poisson point processes, then 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") the two-sided p-values for the chi-squared tests. Their interpretation is very similar to that in anova.glm.

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, Turner and Rubak (2015) so that the chi-squared test is valid. It is strongly advisable to perform this adjustment.

The argument test determines which hypothesis test, if any, will be performed to compare the models. The argument test should be a character string, partially matching one of "Chisq", "F" or "Cp", or NULL. The first option "Chisq" gives the likelihood ratio test based on the asymptotic chi-squared distribution of the deviance difference. The meaning of the other options is explained in anova.glm. For random effects models, only "Chisq" is available, and again gives the likelihood ratio test.

References

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

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.

See Also

mppm

Examples

# NOT RUN {
 H <- hyperframe(X=waterstriders)
 #' test for loglinear trend in x coordinate
 mod0 <- mppm(X~1, data=H, Poisson())
 modx <- mppm(X~x, data=H, Poisson())
 anova(mod0, modx, test="Chi")
 # not significant
 anova(modx, test="Chi")
 # not significant

 #' test for inhibition
 mod0S <- mppm(X~1, data=H, Strauss(2))
 anova(mod0, mod0S, test="Chi")
 # significant! 

 #' test for trend after accounting for inhibition
 modxS <- mppm(X~x, data=H, Strauss(2))
 anova(mod0S, modxS, test="Chi")
 # not significant
# }