PCA interpretation

birdsbirds · January 19, 2020, 12:08am

I have output for a PCA I ran with vegetation components. With this output, and the correlations between the axes and nest height, i can see that axes 1&3 both have a significant positive association with nest height. I know I need to evaluate the factors to see which ones are driving the nest height, but I don't really know how. I can't get a clean conversion of the R output for the PCA columns, but I have 13 variables as rows, and the three pca axes as the columns, with the associated +-numberE-number (example:3.60E-01). Are these the p-values that will associate to the significance within the pca axis? And at what point would I correct the p-value from 0.05->0.05/13(Bonferroni, since there's 13 variables), or is it just 0.05/3 because that's how many axes I am correlating? Thank you for any help!

cor.test(pca[,1], rw.dat$NH)

Pearson's product-moment correlation

data: pca[, 1] and rw.dat$NH
t = 3.6764, df = 82, p-value = 0.0004212
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.1759662 0.5464911
sample estimates:
cor
0.3761698

cor.test(pca[,2], rw.dat$NH)

Pearson's product-moment correlation

data: pca[, 2] and rw.dat$NH
t = 1.3383, df = 82, p-value = 0.1845
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.07039908 0.34963848
sample estimates:
cor
0.1462028

cor.test(pca[,3], rw.dat$NH)

Pearson's product-moment correlation

data: pca[, 3] and rw.dat$NH
t = 7.3697, df = 82, p-value = 1.22e-10
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.4820674 0.7448213
sample estimates:
cor
0.6312238

technocrat · January 19, 2020, 1:28am

Without a reproducible example, called a reprex, I don't want to attempt an explanation. The FactoMineR package and its related website may provide the generalized context you need.

birdsbirds · January 19, 2020, 3:35am

i will try to do a "reprex" of everything, i am having trouble understanding how to use the command once it is downloaded. Or would a picture of the final cor command output be enough? That has my variables as rows, and the PCA axes as columns.

technocrat · January 19, 2020, 4:41am

Let's work with this

library(FactoMineR)
data(wine)
res <- MFA(wine, group=c(2,5,3,10,9,2), type=c("n",rep("s",5)),
    ncp=5, name.group=c("orig","olf","vis","olfag","gust","ens"),
    num.group.sup=c(1,6))

summary(res)
#> 
#> Call:
#> MFA(base = wine, group = c(2, 5, 3, 10, 9, 2), type = c("n",  
#>      rep("s", 5)), ncp = 5, name.group = c("orig", "olf", "vis",  
#>      "olfag", "gust", "ens"), num.group.sup = c(1, 6)) 
#> 
#> 
#> Eigenvalues
#>                        Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6   Dim.7
#> Variance               3.462   1.367   0.615   0.372   0.270   0.202   0.176
#> % of var.             49.378  19.494   8.778   5.309   3.857   2.887   2.506
#> Cumulative % of var.  49.378  68.873  77.651  82.960  86.816  89.703  92.209
#>                        Dim.8   Dim.9  Dim.10  Dim.11  Dim.12  Dim.13  Dim.14
#> Variance               0.126   0.105   0.079   0.074   0.060   0.029   0.022
#> % of var.              1.796   1.502   1.124   1.054   0.861   0.409   0.313
#> Cumulative % of var.  94.005  95.506  96.630  97.684  98.545  98.954  99.268
#>                       Dim.15  Dim.16  Dim.17  Dim.18  Dim.19  Dim.20
#> Variance               0.019   0.011   0.009   0.006   0.003   0.002
#> % of var.              0.273   0.156   0.131   0.091   0.047   0.035
#> Cumulative % of var.  99.541  99.697  99.827  99.918  99.965 100.000
#> 
#> Groups
#>                                  Dim.1    ctr   cos2    Dim.2    ctr   cos2  
#> olf                           |  0.782 22.591  0.380 |  0.620 45.346  0.239 |
#> vis                           |  0.855 24.688  0.728 |  0.040  2.937  0.002 |
#> olfag                         |  0.925 26.712  0.625 |  0.469 34.309  0.161 |
#> gust                          |  0.900 26.009  0.722 |  0.238 17.408  0.050 |
#>                                Dim.3    ctr   cos2  
#> olf                            0.374 60.695  0.087 |
#> vis                            0.014  2.337  0.000 |
#> olfag                          0.180 29.263  0.024 |
#> gust                           0.047  7.705  0.002 |
#> 
#> Supplementary groups
#>                                 Dim.1  cos2   Dim.2  cos2   Dim.3  cos2  
#> orig                          | 0.296 0.033 | 0.643 0.156 | 0.196 0.015 |
#> ens                           | 0.619 0.380 | 0.254 0.064 | 0.010 0.000 |
#> 
#> Individuals (the 10 first)
#>                                  Dim.1    ctr   cos2    Dim.2    ctr   cos2  
#> 2EL                           |  0.239  0.078  0.016 | -0.797  2.211  0.182 |
#> 1CHA                          | -2.045  5.751  0.419 | -1.383  6.667  0.192 |
#> 1FON                          | -1.220  2.048  0.367 | -0.459  0.734  0.052 |
#> 1VAU                          | -4.381 26.404  0.874 |  0.995  3.446  0.045 |
#> 1DAM                          |  2.696  9.996  0.754 | -0.120  0.050  0.002 |
#> 2BOU                          |  0.869  1.038  0.219 | -0.326  0.371  0.031 |
#> 1BOI                          |  1.553  3.318  0.617 | -0.280  0.272  0.020 |
#> 3EL                           |  0.129  0.023  0.003 |  0.789  2.167  0.115 |
#> DOM1                          | -0.066  0.006  0.002 | -0.253  0.222  0.027 |
#> 1TUR                          | -1.202  1.987  0.310 | -0.375  0.489  0.030 |
#>                                Dim.3    ctr   cos2  
#> 2EL                            0.936  6.775  0.250 |
#> 1CHA                           1.514 17.725  0.229 |
#> 1FON                           0.062  0.030  0.001 |
#> 1VAU                          -0.033  0.009  0.000 |
#> 1DAM                          -0.690  3.683  0.049 |
#> 2BOU                           0.391  1.183  0.044 |
#> 1BOI                          -0.414  1.324  0.044 |
#> 3EL                            1.858 26.707  0.636 |
#> DOM1                          -0.459  1.629  0.090 |
#> 1TUR                          -0.716  3.964  0.110 |
#> 
#> Continuous variables (the 10 first)
#>                                  Dim.1    ctr   cos2    Dim.2    ctr   cos2  
#> Odor.Intensity.before.shaking |  0.591  4.497  0.349 |  0.667 14.530  0.445 |
#> Aroma.quality.before.shaking  |  0.835  8.989  0.698 | -0.075  0.186  0.006 |
#> Fruity.before.shaking         |  0.716  6.606  0.513 | -0.151  0.741  0.023 |
#> Flower.before.shaking         |  0.439  2.480  0.192 | -0.409  5.469  0.168 |
#> Spice.before.shaking          |  0.038  0.019  0.001 |  0.865 24.420  0.748 |
#> Visual.intensity              |  0.881  7.912  0.776 |  0.238  1.466  0.057 |
#> Nuance                        |  0.862  7.577  0.744 |  0.234  1.408  0.055 |
#> Surface.feeling               |  0.950  9.198  0.903 |  0.049  0.063  0.002 |
#> Odor.Intensity                |  0.627  2.416  0.393 |  0.576  5.155  0.331 |
#> Quality.of.odour              |  0.791  3.844  0.626 | -0.410  2.612  0.168 |
#>                                Dim.3    ctr   cos2  
#> Odor.Intensity.before.shaking -0.023  0.039  0.001 |
#> Aroma.quality.before.shaking  -0.354  9.092  0.125 |
#> Fruity.before.shaking         -0.537 20.939  0.289 |
#> Flower.before.shaking          0.637 29.439  0.406 |
#> Spice.before.shaking           0.128  1.187  0.016 |
#> Visual.intensity               0.141  1.139  0.020 |
#> Nuance                         0.142  1.155  0.020 |
#> Surface.feeling               -0.027  0.043  0.001 |
#> Odor.Intensity                 0.214  1.581  0.046 |
#> Quality.of.odour              -0.221  1.684  0.049 |
#> 
#> Supplementary continuous variables
#>                                  Dim.1   cos2    Dim.2   cos2    Dim.3   cos2  
#> Overall.quality               |  0.747  0.558 | -0.504  0.254 |  0.130  0.017 |
#> Typical                       |  0.766  0.586 | -0.466  0.217 |  0.039  0.001 |
#> 
#> Supplementary categories
#>                                  Dim.1   cos2 v.test    Dim.2   cos2 v.test  
#> Saumur                        |  0.533  0.483  1.343 |  0.350  0.209  1.405 |
#> Bourgueuil                    | -0.392  0.176 -0.596 | -0.504  0.291 -1.219 |
#> Chinon                        | -0.877  0.537 -1.022 | -0.207  0.030 -0.384 |
#> Reference                     |  1.437  0.823  2.442 | -0.567  0.128 -1.534 |
#> Env1                          | -0.949  0.614 -1.613 | -0.467  0.149 -1.263 |
#> Env2                          | -0.794  0.554 -1.067 |  0.191  0.032  0.409 |
#> Env4                          |  0.277  0.008  0.216 |  3.141  0.971  3.899 |
#>                                Dim.3   cos2 v.test  
#> Saumur                         0.235  0.094  1.404 |
#> Bourgueuil                    -0.216  0.054 -0.780 |
#> Chinon                        -0.322  0.072 -0.889 |
#> Reference                     -0.164  0.011 -0.662 |
#> Env1                           0.455  0.141  1.834 |
#> Env2                          -0.382  0.129 -1.218 |
#> Env4                          -0.062  0.000 -0.116 |
barplot(res$eig[,1],main="Eigenvalues",names.arg=1:nrow(res$eig))

^{Created on 2020-01-18 by the reprex package (v0.3.0)}

system · February 9, 2020, 4:41am

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