Automatic stepwise model building for constrained ordination methods
(cca, rda, dbrda,
capscale). The function ordistep is modelled
after step and can do forward, backward and stepwise
model selection using permutation tests. Function ordiR2step
performs forward model choice solely on adjusted \(R^2\) and
\(P\)-value.
ordistep(object, scope, direction = c("both", "backward", "forward"),
Pin = 0.05, Pout = 0.1, permutations = how(nperm = 199), steps = 50,
trace = TRUE, ...)
ordiR2step(object, scope, Pin = 0.05, R2scope = TRUE,
permutations = how(nperm = 499), trace = TRUE, R2permutations = 1000, ...)Functions return the selected model with one additional
component, anova, which contains brief information of steps
taken. You can suppress voluminous output during model building by
setting trace = FALSE, and find the summary of model history
in the anova item.
In ordistep, an ordination object inheriting from
cca or rda.
Defines the range of models examined in the stepwise
search. This can be a list containing components upper and
lower, both formulae. If it is a single item, it is interpreted
the target scope, depending on the direction. If
direction is "forward", a single item is interpreted as
the upper scope and the formula of the input object as
the lower scope. See step for details. In
ordiR2step, this defines the upper scope; it can also be an
ordination object from with the model is extracted.
The mode of stepwise search, can be one of "both",
"backward", or "forward", with a default of
"both". If the scope argument is missing, the default
for direction is "backward" in ordistep (and
ordiR2step does not have this argument, but only works
forward).
Limits of permutation \(P\)-values for adding (Pin) a term to
the model, or dropping (Pout) from the model. Term is added if
\(P \le\) Pin, and removed if \(P >\) Pout.
Use adjusted \(R^2\) as the stopping criterion: only models with lower adjusted \(R^2\) than scope are accepted.
a list of control values for the permutations as
returned by the function how, or the number
of permutations required, or a permutation matrix where each row
gives the permuted indices. This is passed to
anova.cca: see there for details.
Maximum number of iteration steps of dropping and adding terms.
If positive, information is printed during the model building. Larger values may give more information.
Number of permutations used in the estimation of
adjusted \(R^2\) for cca using
RsquareAdj.
Any additional arguments to add1.cca and
drop1.cca.
Jari Oksanen
The basic functions for model choice in constrained ordination are
add1.cca and drop1.cca. With these functions,
ordination models can be chosen with standard R function
step which bases the term choice on AIC. AIC-like
statistics for ordination are provided by functions
deviance.cca and extractAIC.cca (with
similar functions for rda). Actually, constrained
ordination methods do not have AIC, and therefore the step
may not be trusted. This function provides an alternative using
permutation \(P\)-values.
Function ordistep defines the model, scope of models
considered, and direction of the procedure similarly as
step. The function alternates with drop and
add steps and stops when the model was not changed during one
step. The - and + signs in the summary table indicate
which stage is performed. It is often sensible to have Pout
\(>\) Pin in stepwise models to avoid cyclic adds and drops
of single terms.
Function ordiR2step builds model forward so that it maximizes
adjusted \(R^2\) (function RsquareAdj) at every
step, and stopping when the adjusted \(R^2\) starts to decrease,
or the adjusted \(R^2\) of the scope is exceeded, or the
selected permutation \(P\)-value is exceeded (Blanchet et
al. 2008). The second criterion is ignored with option R2scope =
FALSE, and the third criterion can be ignored setting Pin = 1
(or higher). The function cannot be used if adjusted \(R^2\)
cannot be calculated. If the number of predictors is higher than the
number of observations, adjusted \(R^2\) is also unavailable.
Such models can be analysed with R2scope = FALSE, but the
variable selection will stop if models become overfitted and adjusted
\(R^2\) cannot be calculated, and the adjusted \(R^2\)
will be reported as zero. The \(R^2\) of cca is
based on simulations (see RsquareAdj) and different runs
of ordiR2step can give different results.
Functions ordistep (based on \(P\) values) and ordiR2step
(based on adjusted \(R^2\) and hence on eigenvalues) can select
variables in different order.
Blanchet, F. G., Legendre, P. & Borcard, D. (2008) Forward selection of explanatory variables. Ecology 89, 2623--2632.
The function handles constrained ordination methods
cca, rda, dbrda and
capscale. The underlying functions are
add1.cca and drop1.cca, and the function
is modelled after standard step (which also can be
used directly but uses AIC for model choice, see
extractAIC.cca). Function ordiR2step builds
upon RsquareAdj.
## See add1.cca for another example
### Dune data
data(dune)
data(dune.env)
mod0 <- rda(dune ~ 1, dune.env) # Model with intercept only
mod1 <- rda(dune ~ ., dune.env) # Model with all explanatory variables
## With scope present, the default direction is "both"
mod <- ordistep(mod0, scope = formula(mod1))
mod
## summary table of steps
mod$anova
## Example of ordistep, forward
ordistep(mod0, scope = formula(mod1), direction="forward")
## Example of ordiR2step (always forward)
## stops because R2 of 'mod1' exceeded
ordiR2step(mod0, mod1)
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