R vegan CCA，确定哪些约束是别名的？

Question

我已经使用 vegan 执行了 CCA，并使用双标箭头绘制。 “ca”输出告诉我“一些约束被别名，因为它们是共线的（冗余）”。我理解这意味着约束被删除，因为它们是多余的。

ca<-cca(CCA_data[3:4567]~.,data=Meta_data_2)
ca

我也可以列出别名没问题：

alias(ca, names=TRUE,complete=TRUE)

但是，我如何确定哪些约束存在别名或与其他因素共线。我需要知道哪些因素与哪些因素是多余的，这样我才能重新考虑我的方法。

这又给了我列出的别名，但没有双标值。虽然这里的第二行给了我 biplot 值，但是缺少别名的值...

ca$CCA$alias
ca$CCA$biplot

有关如何从“ca”获取该信息的建议会很有帮助。

**更新：

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                           

^以上已被缩短

Answer 1

该信息由alias 命令提供。这是一个可重现的例子：

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

输出很宽，但是当我们有ManagementNM 时，它告诉Manure 的一级是完全别名的。通过交叉制表可以轻松识别更多细节：

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

当我们有Management 级别NM 时，我们只有Manure 级别0，并且`Manure 的最后 级别将被别名。