"anova"(object, ..., test=NULL, adjust=TRUE, warn=TRUE, fine=FALSE)
"ppm"
).
"ppm"
.
"Chisq"
, "LRT"
,
"Rao"
, "score"
, "F"
or "Cp"
,
or NULL
indicating that no test should be performed.
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
.
"anova"
, or NULL
.
~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.
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:
method
in
ppm
.
allcovar=TRUE
to ensure that the
same quadrature scheme is used.
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.
vcov.ppm
for suggestions on how to handle this.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.
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.
ppm
,
vcov.ppm
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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