Statistics Resembling Deviance and AIC for Constrained Ordination
The functions extract statistics that resemble deviance and AIC from the
result of constrained correspondence analysis
rda. These functions are rarely
needed directly, but they are called by
automatic model building. Actually,
rda do not have
AIC and these functions
are certainly wrong.
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the result of a constrained ordination
fitted model from constrained ordination.
optional numeric specifying the scale parameter of the model,
numeric specifying the "weight" of the equivalent degrees of
The functions find statistics that
AIC in constrained
ordination. Actually, constrained ordination methods do not have a
log-Likelihood, which means that they cannot have AIC and deviance.
Therefore you should not use these functions, and if you use them, you
should not trust them. If you use these functions, it remains as your
responsibility to check the adequacy of the result.
The deviance of
cca is equal to the Chi-square of
the residual data matrix after fitting the constraints. The deviance
rda is defined as the residual sum of squares. The
deviance function of
rda is also used for
extractAIC.lm in translating deviance to AIC.
There is little need to call these functions directly. However, they
are called implicitly in
step function used in automatic
selection of constraining variables. You should check the resulting
model with some other criteria, because the statistics used here are
unfounded. In particular, the penalty
k is not properly
defined, and the default
k = 2 is not justified
theoretically. If you have only continuous covariates, the
function will base the model building on magnitude of eigenvalues, and
the value of
k only influences the stopping point (but the
variables with the highest eigenvalues are not necessarily the most
significant in permutation tests in
anova.cca). If you
also have multi-class factors, the value of
k will have a
capricious effect in model building. The
will pass arguments to
drop1.cca, and setting
test = "permutation"
will provide permutation tests of each deletion and addition which
can help in judging the validity of the model building.
deviance functions return “deviance”, and
extractAIC returns effective degrees of freedom and “AIC”.
These functions are unfounded and untested and they should not be used
directly or implicitly. Moreover, usual caveats in using
step are very valid.
Godínez-Domínguez, E. & Freire, J. (2003) Information-theoretic approach for selection of spatial and temporal models of community organization. Marine Ecology Progress Series 253, 17–24.
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