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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
chl
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  • How large is your sample? – Vincent Guillemot Aug 20 '18 at 14:22
  • @Vincent Guillemot 16 obs (sites) of 76 variables (species abundance, hellinger transformed) – Ta Ani Aug 20 '18 at 14:37
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    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) – Vincent Guillemot Aug 20 '18 at 14:51
  • @VincentGuillemot what means regularized versions in this context? – Ta Ani Aug 20 '18 at 15:01
  • It means, e.g., using a [Canonical Ridge Analysis](http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4981/pdf/imm4981.pdf) instead of a regular CCA. Before doing so, check with your local statistician that there is no simpler alternative. – Vincent Guillemot Aug 20 '18 at 16:36
  • @Vincent Guillemot thank you very much! I don´t have a local statistician, I am doing my master thesis and am pretty much on my own. I am looking now for a way to simplify my data e.g. feature selection but I don´t have a response variable but a "response dataframe" so I thought of PCA for environmental variable selection but I don´t find an example in R... I will take a look at Canonical Ridge Analysis! – Ta Ani Aug 20 '18 at 16:58
  • You can also try to apply one of the PLS methods to your data. If you know a public data-set that is close in structure to your own data-set, edit your question to include it as a "reproducible example", and I will try to give you a more complete answer. – Vincent Guillemot Aug 22 '18 at 08:30
  • @VincentGuillemot my data is similar to the doubs data of package ade4, the table with the abundance data and the table with the environmental data. But I do have abundance 16 obs of 76 variables and doubs has 20 obs of 27 variables. My environmental parameters range 16 obs of 18 variables and doubs has 30 obs of 11 variables. – Ta Ani Aug 22 '18 at 14:26

1 Answers1

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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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