Principal component regression loadings show nothing

Question

In my experiment, I diluted a chemical in water and recorded its Raman spectra. Then I repeated this with different concentrations. As I can clearly see some peaks decreasing in intensity when I dilute my solution, I hope that through Principal Component Regression, I would be able to automatically figure out which wavenumbers are useful for determining the concentration of my solution.

If I understand PCA correctly, I am looking for the loadings of the first few components.

I have the following data that I prepared:

> concentration.hcl
0.001 0.001 0.001 1e-04 1e-04 1e-04 1e-04 1e-09 1e-09 1e-09 1e-09 1e-11 1e-11
1e-03 1e-03 1e-03 1e-04 1e-04 1e-04 1e-04 1e-09 1e-09 1e-09 1e-09 1e-11 1e-11
1e-11 1e-11 1e-11
1e-11 1e-11 1e-11

and spectra.hcl with each row being a reading corresponding to an entry in concentration.hcl and the columns being a specific wavenumber.

> dim(spectra.hcl)
[1]   16 2048

> colnames(spectra.hcl)
   [1] "-818.41" "-813.78" "-809.16" "-804.53" "-799.92" "-795.31" "-790.7"
   [8] "-786.1"  "-781.5"  "-776.91" "-772.32" "-767.74" "-763.16" "-758.59"
  [15] "-754.02" "-749.45" "-744.9"  "-740.34" "-735.79" "-731.25" "-726.71" ...

I ran the following code:

pmodel <- pcr(concentration.hcl ~ spectra.hcl)

> summary(pmodel)
Data:   X dimension: 16 2048
    Y dimension: 16 1
Fit method: svdpc
Number of components considered: 15
TRAINING: % variance explained
                   1 comps  2 comps  3 comps  4 comps  5 comps  6 comps
X                     85.7    96.91    99.29    99.64    99.81    99.92
concentration.hcl     45.4    90.14    98.35    98.72    98.73    99.27
...

Unfortunately, I am not seeing anything in my loadings:

> pmodel$loadings
... (truncated) 
3291.07
3291.68
3292.29
3292.89
3293.49
3294.1
3294.7
3295.3
3295.9
3296.5
3297.09
3297.69
3298.29
3298.88
3299.48
3300.07
3300.66
3301.26
3301.85
3302.44
3303.03
3303.62
3304.2
3304.79
3305.38
3305.96
3306.55
3307.14

               Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6 Comp 7 Comp 8 Comp 9
SS loadings         1  1.000  1.000  1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var      0  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000
Cumulative Var      0  0.001  0.001  0.002  0.002  0.003  0.003  0.004  0.004
               Comp 10 Comp 11 Comp 12 Comp 13 Comp 14 Comp 15
SS loadings      1.000   1.000   1.000   1.000   1.000   1.000
Proportion Var   0.000   0.000   0.000   0.000   0.000   0.000
Cumulative Var   0.005   0.005   0.006   0.006   0.007   0.007

1. Why can't I see my loadings?
2. How can I find out which wavenumbers are contributing the most to the varying concentrations in my experiments?

NOTE: The data is available at https://gist.githubusercontent.com/anonymous/1d994685c3b3a5133b29/raw/696662a3aa199890958c162483c0cb7aa95e18ec/file1.txt You just need to download this file and then type load('file1.txt') and the variables will show up in your R environment

Answer 1

There are 2 things going on here:

• the print method for loadings objects in package pls tidies the printed values so that close-to-zero values are zapped, and
• you look only at the last lines of the output.

E.g. if you look at the PCR example with the yarn data, the first few lines of the output are

loadings (model)

Loadings:
       Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6
NIR1                 -0.115               -0.243
NIR2                 -0.134         0.170 -0.325
NIR3                 -0.113         0.206 -0.369
NIR4                                0.154 -0.352
NIR5                                      -0.269
NIR6                                      -0.180
NIR7    0.108                             -0.114

You can plot your loadings (which is probably better to get an overview):

matplot (loadings (model), type = "l")