I have a mix of continuous and categorical explanatory variables I would like to enter into a canonical redundancy analysis (RDA), but I'm not sure whether it is valid to use discontinuous variables in this type of analysis? My question stems partly from the fact that discontinuous variables aren't suitable for PCA and other associated techniques, and the structure of RDA is partly like a PCA.
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In the section regarding partial-RDA, Legendre & Legendre (2012) state that (p. 606):
Hypotheses may also be of the analysis-of-variance type, involving either a single classification criterion (factor) or several factors and their interactions, each recoded as dummy variables.
Borcard et al. (2011) furthermore indicate that (p. 155):
An RDA produces min[p, m, n − 1] canonical axes, where n is the number of objects and m is the number of degrees of freedom of the model (number of numeric explanatory variables, including levels of factors if qualitative explanatory variables are included; a factor with k classes requires (k − 1) dummy variables for coding, so there are (k − 1) degrees of freedom for this factor).
However, if you're using R, note that some RDA-related procedures and functions do not allow categorical variables. For instance, still according to Borcard et al. (2011), the packfor::forward.sel() function does not allow factors. You'd thus better do some reading before proceeding with you analyses in order to know what is allowed by which function or software.
So globally yes, you can usually include categorical explanatory variables in a RDA as long as you use dummy coding. There are also various solutions to include such variables in PCAs.
