"R": PLS Regression (Gasoline) - 003

The gasoline data set has the spectra of 60 samples acquired by diffuse reflectance from 900 to 1700 nm. We saw how to plot the spectra in the previous post.

Now, following the tutorial of Bjorn-Helge Mevik published in "R-News Volume 6/3, August 2006", we will do the PLS regression:

gas1 <- plsr(octane~NIR, ncomp = 10,data = gasoline, validation = "LOO")

This will fit a model of 10 components.
We will use the "Leave one out Cross Validation" (LOO)
The constituent is the octane number.

> summary(gas1)

Data:   X dimension: 60 401

        Y dimension: 60 1

Fit method: kernelpls

Number of components considered: 10

VALIDATION: RMSEP

Cross-validated using 60 leave-one-out segments.

       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps

CV           1.543    1.328   0.3813   0.2579   0.2412   0.2412   0.2294

adjCV        1.543    1.328   0.3793   0.2577   0.2410   0.2405   0.2288

       7 comps  8 comps  9 comps  10 comps

CV      0.2191   0.2280   0.2422    0.2441

adjCV   0.2183   0.2273   0.2411    0.2433

TRAINING: % variance explained

        1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps

X         70.97    78.56    86.15    95.40    96.12    96.97    97.32    98.10

octane    31.90    94.66    97.71    98.01    98.68    98.93    99.06    99.11

        9 comps  10 comps

X         98.32     98.71

octane    99.20     99.24

One way to decide better the number of components to use, is to plot the RMSEPs:

> plot(RMSEP(gas1), legendpos = "topright")

adjCV is the RMSEP Bias corrected which in the case of  "LOO" is almost the same that the RMSEP without correction.

The plot suggest three components giving a RMSEP of 0.258.

Now we can see the different plots like the prediction plot:

> plot(gas1, ncomp = 3, asp = 1, line = TRUE)

We will continue with more plots in the next post.

Bibliography:
Tutorials of :
Bjorn-Helge Mevik

Norwegian University of Life Sciences

Ron Wehrens

Radboud University Nijmegen

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