A common practice in community ecology studies based on multivariate techniques such as CCA, RDA, dbRDA, etc. is to try to define a parsimonious model using procedures based on p-values and R squared (e.g. forward, backward, stepwise selection).
In my experience, the parsimonious model generally "loses" most of the variable contained in the full model although retaining a similar explanatory power compared to the full model (almost the same R2). Although this seems statistically meaningful, when plotting the triplot of the full model one is able to understand much more of the ecological "story" compared with the parsimonious. For example, the gradients in the site and species are much more clear and so the relationship between species, sites and constraints.
I think this is mostly philosophy, but someone has any consideration on it?
NB: I am referring to models in which collinearity between variables is absent.
Don't Use Stepwise. It is known to be unstable. By that I mean, successive runs over the same data produce different models. P-value selection in general works very poorly. See the references, (esp. Austin & Tu) in the attached. Best wishes, David Booth
Hello Giacomo,
I agree with your premise that it's always important to understand fully the meaning of a given model (and its implications for aims that motivated the building of a model in the first place).
Can reduced models be identified with a "tolerable" reduction in explanatory power? In many instances, absolutely.
Does it make sense therefore to seek reduced models? No, not necessarily. If there are cost or efficiency reasons to abandon specific variables, then that's a different consideration altogether. Also, as David Eugene Booth indicates, there are many technical reasons to avoid using any step-based method (forward, backward, stepwise) as a mechanism to find a "best" sub-model for a given set of IVs. Generalizability (or the lack thereof) is one good reason; overfitting is a threat with such methods.
Good luck with your workl.
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