I've performed a CCA using vegan and plotted with biplot arrows. the "ca" output tells me I have "Some constraints were aliased because they were collinear (redundant)". I understand that that means the constraints were dropped because they were redundant.
ca<-cca(CCA_data[3:4567]~.,data=Meta_data_2)
ca
I can also list the alias no problem:
alias(ca, names=TRUE,complete=TRUE)
However, how do I determine WHICH constraints were aliased or were collinear with other factors. I need to know what factors were redundant with what factors so I can rethink my approach.
This again gives me the listed alias, but no biplot values. While the second line here gives me biplot values, but the alias-ed ones are missing...
ca$CCA$alias
ca$CCA$biplot
Suggestions on how to get that information from "ca" would be helpful.
**Update:
Model :
CCA_data[3:4567] ~ `Assimilatory nitrate reduction, nitrate => ammonia` +
`beta-Oxidation` + `beta-Oxidation, acyl-CoA synthesis` +
`Citrate cycle (TCA cycle, Krebs cycle)` + `Dissimilatory nitrate reduction, nitrate => ammonia` +
`Fatty acid biosynthesis, elongation` + `Fatty acid biosynthesis, elongation, endoplasmic reticulum` +
`Fatty acid biosynthesis, elongation, mitochondria` + `Fatty acid biosynthesis, initiation` +
`Gluconeogenesis, oxaloacetate => fructose-6P` + `Glycolysis (Embden-Meyerhof pathway), glucose => pyruvate` +
`Glyoxylate cycle` + `Nitrate assimilation` + Photorespiration +
`Photosystem I` + `Photosystem II` + `Pyruvate oxidation, pyruvate => acetyl-CoA` +
`Reductive citrate cycle (Arnon-Buchanan cycle)` + `Reductive pentose phosphate cycle (Calvin cycle)` +
`Urea cycle`
Complete :
`Assimilatory nitrate reduction, nitrate => ammonia`
`Photosystem I` 1.23566
`Photosystem II` -0.64830
`Pyruvate oxidation, pyruvate => acetyl-CoA` -0.40986
`Reductive citrate cycle (Arnon-Buchanan cycle)` 22.01804
`Reductive pentose phosphate cycle (Calvin cycle)` 16.10217
`Urea cycle` 1.55773
`beta-Oxidation`
`Photosystem I` 0.24919
`Photosystem II` 1.20864
`Pyruvate oxidation, pyruvate => acetyl-CoA` -0.24875
`Reductive citrate cycle (Arnon-Buchanan cycle)` -1.84576
`Reductive pentose phosphate cycle (Calvin cycle)` -0.74552
`Urea cycle` 5.03302
`beta-Oxidation, acyl-CoA synthesis`
`Photosystem I` 0.08856
`Photosystem II` 1.19711
`Pyruvate oxidation, pyruvate => acetyl-CoA` 0.39169
`Reductive citrate cycle (Arnon-Buchanan cycle)` 0.23713
`Reductive pentose phosphate cycle (Calvin cycle)` -6.34640
`Urea cycle` -1.88670
^Above has been shortened
That information is given by alias command. Here a reproducible example:
library(vegan)
data(dune, dune.env)
m <- rda(dune ~ ., dune.env)
## the following gives the names of aliased variables
alias(m, names=TRUE)
# [1] "Manure^4"
## the following gives the aliasing equation
alias(m)
Complete :
A1 Moisture.L Moisture.Q Moisture.C ManagementHF ManagementNM ManagementSF Use.L Use.Q Manure.L Manure.Q Manure.C
Manure^4 8.366600 5.291503 -4.472136 2.645751
The output is wide, but it tells that one level of Manure is completely aliased when we have ManagementNM. More details are easily discerned by crosstabulation:
with(dune.env, table(Management, Manure))
Manure
Management 0 1 2 3 4
BF 0 2 1 0 0
HF 0 1 2 2 0
NM 6 0 0 0 0
SF 0 0 1 2 3
We only have Manure level 0 when we have Management level NM, and the last level of `Manure will be aliased.