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I get an ouput for RDA and for CCA that says that my unconstrained inertia is 0, rank 0. I thought that would be a good thing, meaning that all the variance in the data is explained by my (constrained) variables. But the Anova method doesn´t work, because the residuals are missing.

So in the case the result is not significant, do I have to discard the results or can I work with it? I already looked at the following questions: CCA inertia in vegan, cca vegan output and rda or cca.

An excerpt of the summary of the CCA:

> anova.cca(cil.rda,step=1000)
No residual component

Model: rda(formula = cil.hel ~ Dino + Abun + Chla + Salinity + Cond + Temp + Depth + MaxD + Syn + Pro1 + Pro2 + Pk + Nk + Cryp + Auto + Heter + HF + bac, data = envm)
         Df Variance F Pr(>F)
Model    15  0.45721         
Residual  0  0.00000
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  • $\begingroup$ How large is your sample? $\endgroup$ – Vincent Guillemot Aug 20 '18 at 14:22
  • $\begingroup$ @Vincent Guillemot 16 obs (sites) of 76 variables (species abundance, hellinger transformed) $\endgroup$ – Ta Ani Aug 20 '18 at 14:37
  • $\begingroup$ Well, then your models are overparameterized. You either need to simplify them or consider regularized versions of the methods you want to apply. (or add more samples but I guess it is not an option) $\endgroup$ – Vincent Guillemot Aug 20 '18 at 14:51
  • $\begingroup$ @VincentGuillemot what means regularized versions in this context? $\endgroup$ – Ta Ani Aug 20 '18 at 15:01
  • $\begingroup$ It means, e.g., using a Canonical Ridge Analysis instead of a regular CCA. Before doing so, check with your local statistician that there is no simpler alternative. $\endgroup$ – Vincent Guillemot Aug 20 '18 at 16:36
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I think I got it now while I was trying to reproduce your issue with the "Doubs" data-set.

It's OK perform a redundancy analysis on your data-set. However, since your problem is over-parameterized, you are not going to be able to compute a statistic (or its significance) on your model because there are no residuals.

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