I have a matrix of sites where not all the environmental variables I want to assess were sampled. In other words, there are sites with the whole set of variables sampled, and there are other sites where just some variables were sampled. Does Canonical Correspondence Analysis work with missing data for the environmental variables? If it does, what would be the effect of not including the missing values?
First, you cannot fully analyze pair-wise correlations between your environmental variables with NA values, and therefore cannot fully discount including covarying variables. If this is the case, you will not be able to know which of the covarying variables is responsible for any trends in your data.
Second, I don't believe CCA will work with NA values -- you will either have to eliminate the observations containing those missing values or fill them in with column averages. However, both of these methods will have an impact on your results, so move forward cautiously.
Third, I wonder if CCA is even the way you want to go. nMDS (non-metric multidimensional scaling) is much less constrained than CCA. Additionally, it doesn't suffer from as many assumptions/limitations as CCA.
From McCune & Grace (2002):
The following two questions can be used to decide whether CCA is appropriate: (1) Are you interested only in community structure that is related to your measured environmental variables? (2) Is a unimodal model of species responses to environment reasonable? If, for a specific problem you answer yes to both of these, then CCA might be appropriate
However, missing environmental data is still a problem in nMDS.