R: ANOVA for Fitted Point Process Models for Replicated Patterns

anova.mppm {spatstat.core} | R Documentation

## 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 class '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.

### 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`.

### Value

An object of class `"anova"`, or `NULL`.

### Random effects models are currently not supported

For models with random effects (i.e. where the call to `mppm` included the argument `random`), analysis of deviance is currently not supported, due to changes in the nlme package. We will try to find a solution.

### 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.

### 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.

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

     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

[Package spatstat.core version 2.0-0 Index]