"R": PLS Regression (Gasoline) - 004

In the previous post we plot the Cross Validation predictions with:

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

We can plot the fitted values instead with:

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

Graphics are different:

Of course, using "train" we get  overoptimisc statistics and we should look better at the Cross Validation or to an independant test set for validation.
We decided 3 components to develop the PLS Regressions looking to the RMSEP plot. We can use other plots as the MSEP plot (changing RMSEP for MSEP), or to the RSQ plot.

> plot(R2(gas1),legendpos = "topright")

We can see how after the 3th component becomes almost flat.

We can see it better with numbers:

> R2(gas1)

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

   -0.03419      0.23374      0.93684      0.97111      0.97474      0.97474 

    6 comps      7 comps      8 comps      9 comps     10 comps 

    0.97713      0.97914      0.97742      0.97453      0.97413 

We can see also the residuals in "R" for the different number of component (1, 2,...,10). In these values the calculation for the statistics are based.
These are the residual values for the PLSR model with 3 components:

         octane

1   0.100769634     

2   0.369121232

3   0.251715938

4  -0.209263557

5  -0.473107996

6   0.158305081

7   0.080218313

8  -0.141445641

9  -0.099252992

10 -0.077775217

11  0.561603527

12  0.488456018

13 -0.023514480

14 -0.106796820

15 -0.015477061

16  0.010451476

17  0.547102944

18  0.215613857

19 -0.290225797

20  0.238646916

21  0.115224011

22 -0.219819205

23 -0.040436420

24 -0.313450043

25 -0.161174139

26  0.065222607

27  0.032299933

28 -0.120728914

29 -0.394899511

30 -0.116389549

31 -0.242168963

32 -0.100928743

33 -0.003314534

34  0.152746720

35  0.092815472

36  0.029039668

37  0.020761125

38  0.339468953

39  0.019163788

40  0.192727538

41 -0.077437540

42 -0.267717370

43  0.161465598

44  0.101965851

45 -0.022411411

46 -0.322253768

47 -0.272445813

48 -0.151183595

49  0.063073375

50 -0.001254795

51  0.008358151

52  0.297159695

53  0.015659145

54  0.033326901

55 -0.141411827

56  0.280361574

57 -0.491022823

58 -0.332150710

59  0.269220723

60 -0.082606528

Bibliography:

Tutorials PLS Package for "R" :

Bjorn-Helge Mevik

Ron Wehrens

R Help Web page

Tweet Radboud University Nijmegen

Norwegian University of Life Sciences