ANOVA for Fitted Point Process Models
Performs analysis of deviance for one or more fitted point process models.
## S3 method for class 'ppm'
anova(object, ..., test=NULL,
adjust=TRUE, warn=TRUE, fine=FALSE)object |
A fitted point process model
(object of class |
... |
Optional. Additional objects of class |
test |
Character string, partially matching one of
|
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 |
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.
An object of class "anova", or NULL.
There may be an error message that the models are not “nested”.
For an Analysis of Deviance the models must be nested, i.e. one model
must be a special case of the other. For example the point process
model with formula ~x is a special case of the model with
formula ~x+y, so these models are nested. However
the two point process
models with formulae ~x and ~y are not nested.
If you get this error message and you believe that the models should be nested, the problem may be the inability of R to recognise that the two formulae are nested. Try modifying the formulae to make their relationship more obvious.
There may be an error message from anova.glmlist that
“models were not all fitted to the same size of dataset”.
This implies that the models were fitted using different
quadrature schemes (see quadscheme) and/or
with different edge corrections or different values of the
border edge correction distance rbord.
To ensure that models are comparable, check the following:
the models must all have been fitted to the same point pattern dataset, in the same window.
all models must have been fitted by the same
fitting method as specified by the argument method in
ppm.
If some of the models depend on covariates, then
they should all have been fitted using the same list of
covariates, and using allcovar=TRUE to ensure that the
same quadrature scheme is used.
all models must have been fitted using the same edge
correction as specified by the arguments correction
and rbord. If you did not specify the value of
rbord, then it may have
taken a different value for different models. The default value of
rbord is equal to zero for a Poisson model,
and otherwise equals the reach (interaction distance) of the
interaction term (see reach).
To ensure that the models are comparable, set rbord to
equal the maximum reach of the interactions that you
are fitting.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
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.
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")
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