vegan (version 2.0-10)

ordistep: Choose a Model by Permutation Tests in Constrained Ordination

Description

Automatic stepwise model building for constrained ordination methods (cca, rda, 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, for ordination objects created by rda or capscale.

Usage

ordistep(object, scope, direction = c("both", "backward", "forward"),
   Pin = 0.05, Pout = 0.1, pstep = 100, perm.max = 1000, steps = 50,
   trace = TRUE, ...)
ordiR2step(object, scope, direction = c("both", "forward"),
   Pin = 0.05, R2scope = TRUE, pstep = 100, perm.max = 1000,
   trace = TRUE, ...)

Arguments

object

In ordistep, an ordination object inheriting from cca or rda. In ordiR2step, the object must inherit from

scope

Defines the range of models examined in the stepwise search. This should be either a single formula, or a list containing components upper and lower, both formulae. See step f

direction

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

Pin, Pout

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.

R2scope

Use adjusted $R^2$ as the stopping criterion: only models with lower adjusted $R^2$ than scope are accepted.

pstep

Number of permutations in one step. See add1.cca.

perm.max

Maximum number of permutation in anova.cca.

steps

Maximum number of iteration steps of dropping and adding terms.

trace

If positive, information is printed during the model building. Larger values may give more information.

...

Any additional arguments to add1.cca and drop1.cca.

Value

• 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.

Details

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 Rfunction 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. The number of permutations is selected adaptively with respect to the defined decision limit. It is often sensible to have Pout $>$ Pin in stepwise models to avoid cyclic adds and drops of single terms.

Function ordiR2step builds model 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 R2step = FALSE, and the third criterion can be ignored setting Pin = 1 (or higher). The direction has choices "forward" and "both", but it is very exceptional that a term is dropped with the adjusted $R^2$ criterion. Function uses adjusted $R^2$ as the criterion, and it cannot be used if the criterion cannot be calculated. Therefore it is unavailable for cca. Adjusted $R^2$ cannot be calculated if the number of predictors is higher than the number of observations, but such models can be analysed with R2scope = FALSE.

Functions ordistep (based on $P$ values) and ordiR2step (based on adjusted $R^2$ and hence on eigenvalues) can select variables in different order.

References

Blanchet, F. G., Legendre, P. & Borcard, D. (2008) Forward selection of explanatory variables. Ecology 89, 2623--2632.

See Also

The function handles constrained ordination methods cca, rda 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.

Examples

## 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"
ordistep(mod0, scope = formula(mod1), perm.max = 200)

## Example without scope. Default direction is "backward"
ordistep(mod1, perm.max = 200) 

## Example of ordistep, forward
ordistep(mod0, scope = formula(mod1), direction="forward", perm.max = 200)
### Mite data
data(mite)
data(mite.env)
mite.hel = decostand(mite, "hel")
mod0 <- rda(mite.hel ~ 1, mite.env)  # Model with intercept only
mod1 <- rda(mite.hel ~ ., mite.env)  # Model with all explanatory variables

## Example of ordiR2step with default direction = "both"
## (This never goes "backward" but evaluates included terms.)
step.res <- ordiR2step(mod0, mod1, perm.max = 200)
step.res$anova  # Summary table

## Example of ordiR2step with direction = "forward"
step.res <- ordiR2step(mod0, scope = formula(mod1), direction="forward") 
step.res$anova  # Summary table