MODELO DE MÍNIMOS CUADRADOS PARCIALES (PLS) – Statgraphics
Resumen
El procedimiento Mínimos Cuadrados Parciales (PLS – Partial Least Squares) está diseñado
para construir un modelo estadístico que relaciona múltiples variables independientes X con
múltiples variables dependientes Y. El procedimiento es mucho más útil cuando hay muchos
factores y el objetivo principal es predecir las variables respuesta. Los mínimos cuadrados
parciales (PLS) son ampliamente usados por ingenieros químicos y quimiométricos para
calibración espectrométrica.
StatFolio de Ejemplo: pls.sgp
Datos de Ejemplo:
El archivo spectra.sf6 contiene los espectros observados de n = 33 muestras que contienen
concentraciones conocidas de dos aminoácidos, tirosina (tyrosine) y triptofano (tryptophan). Los
espectros están medidos a k = 30 frecuencias. Una porción de los datos, tomados de McAvoy et
al. (1989), se muestra a continuación:
Sample
|
Tryptophan
|
Tyrosine
|
f1
|
f2
|
f3
|
f4
|
f5
|
f6
|
f7
|
f8
|
f9
|
f10
|
f11
|
f12
|
17mix35
|
0.00003
|
0.00000001
|
-6.215
|
-5.809
|
-5.114
|
-3.963
|
-2.897
|
-2.269
|
-1.675
|
-1.235
|
-0.9
|
-0.659
|
-0.497
|
-0.395
|
19mix35
|
0.0000297
|
0.0000003
|
-5.516
|
-5.294
|
-4.823
|
-3.858
|
-2.827
|
-2.249
|
-1.683
|
-1.218
|
-0.907
|
-0.658
|
-0.501
|
-0.4
|
21mix35
|
0.00002925
|
0.00000075
|
-5.519
|
-5.294
|
-4.501
|
-3.863
|
-2.827
|
-2.28
|
-1.716
|
-1.262
|
-0.939
|
-0.694
|
-0.536
|
-0.444
|
23mix35
|
0.0000285
|
0.0000015
|
-5.294
|
-4.705
|
-4.262
|
-3.605
|
-2.726
|
-2.239
|
-1.681
|
-1.25
|
-0.925
|
-0.697
|
-0.534
|
-0.437
|
25mix35
|
0.000027
|
0.000003
|
-4.6
|
-4.069
|
-3.764
|
-3.262
|
-2.598
|
-2.191
|
-1.68
|
-1.273
|
-0.958
|
-0.729
|
-0.573
|
-0.47
|
27mix35
|
0.0000225
|
0.0000075
|
-3.812
|
-3.376
|
-3.026
|
-2.726
|
-2.249
|
-1.919
|
-1.541
|
-1.198
|
-0.951
|
-0.764
|
-0.639
|
-0.57
|
29mix35
|
0.000015
|
0.000015
|
-3.053
|
-2.641
|
-2.382
|
-2.194
|
-1.977
|
-1.913
|
-1.728
|
-1.516
|
-1.317
|
-1.158
|
-1.029
|
-0.963
|
28mix35
|
0.0000075
|
0.0000225
|
-2.626
|
-2.248
|
-2.004
|
-1.839
|
-1.742
|
-1.791
|
-1.786
|
-1.772
|
-1.728
|
-1.666
|
-1.619
|
-1.591
|
26mix35
|
0.000003
|
0.000027
|
-2.37
|
-1.99
|
-1.754
|
-1.624
|
-1.56
|
-1.655
|
-1.772
|
-1.899
|
-1.982
|
-2.074
|
-2.157
|
-2.211
|
24mix35
|
0.0000015
|
0.0000285
|
-2.326
|
-1.952
|
-1.702
|
-1.583
|
-1.507
|
-1.629
|
-1.771
|
-1.945
|
-2.115
|
-2.297
|
-2.448
|
-2.585
|
22mix35
|
0.00000075
|
0.00002925
|
-2.277
|
-1.912
|
-1.677
|
-1.556
|
-1.487
|
-1.63
|
-1.791
|
-1.969
|
-2.203
|
-2.437
|
-2.655
|
-2.844
|
20mix35
|
0.0000003
|
0.0000297
|
-2.266
|
-1.912
|
-1.688
|
-1.546
|
-1.5
|
-1.64
|
-1.801
|
-2.011
|
-2.277
|
-2.545
|
-2.823
|
-3.094
|
18mix35
|
0.00000001
|
0.00003
|
-2.258
|
-1.9
|
-1.666
|
-1.524
|
-1.479
|
-1.621
|
-1.803
|
-2.043
|
-2.308
|
-2.626
|
-2.895
|
-3.214
|
trp2
|
0.0001
|
0.00000001
|
-5.922
|
-5.435
|
-4.366
|
-3.149
|
-2.124
|
-1.392
|
-0.78
|
-0.336
|
-0.002
|
0.233
|
0.391
|
0.49
|
mix5
|
0.00009
|
0.00001
|
-3.932
|
-3.411
|
-2.964
|
-2.462
|
-1.836
|
-1.308
|
-0.796
|
-0.39
|
-0.076
|
0.147
|
0.294
|
0.394
|
mix4
|
0.000075
|
0.000025
|
-2.996
|
-2.479
|
-2.099
|
-1.803
|
-1.459
|
-1.126
|
-0.761
|
-0.424
|
-0.144
|
0.06
|
0.195
|
0.288
|
mix3
|
0.00005
|
0.00005
|
-2.128
|
-1.661
|
-1.344
|
-1.16
|
-0.996
|
-0.877
|
-0.696
|
-0.495
|
-0.313
|
-0.165
|
-0.042
|
0.032
|
mix6
|
0.00001
|
0.00009
|
-1.14
|
-0.757
|
-0.497
|
-0.362
|
-0.329
|
-0.412
|
-0.513
|
-0.647
|
-0.772
|
-0.877
|
-0.958
|
-1.04
|
43trp6
|
0.000001
|
0.00000001
|
-5.915
|
-5.918
|
-6.908
|
-5.428
|
-4.117
|
-5.103
|
-4.66
|
-4.351
|
-4.023
|
-3.849
|
-3.634
|
-3.634
|
59mix6
|
0.0000009
|
0.0000001
|
-5.903
|
-5.903
|
-5.903
|
-5.082
|
-4.213
|
-5.083
|
-4.838
|
-4.639
|
-4.474
|
-4.213
|
-4.001
|
-4.098
|
51mix6
|
0.00000075
|
0.00000025
|
-5.907
|
-5.907
|
-5.415
|
-4.843
|
-4.213
|
-4.843
|
-4.843
|
-4.483
|
-4.343
|
-4.006
|
-4.006
|
-3.912
|
49mix6
|
0.0000005
|
0.0000005
|
-5.419
|
-5.091
|
-5.091
|
-4.648
|
-4.006
|
-4.846
|
-4.648
|
-4.483
|
-4.343
|
-4.22
|
-4.22
|
-4.22
|
53mix6
|
0.00000025
|
0.00000075
|
-5.083
|
-4.837
|
-4.837
|
-4.474
|
-3.826
|
-4.474
|
-4.639
|
-4.838
|
-4.837
|
-4.639
|
-4.639
|
-4.641
|
57mix6
|
0.0000001
|
0.0000009
|
-5.082
|
-4.836
|
-4.639
|
-4.474
|
-3.826
|
-4.636
|
-4.638
|
-4.638
|
-4.837
|
-5.082
|
-5.082
|
-5.408
|
41tyro6
|
0.00000001
|
0.000001
|
-5.104
|
-4.662
|
-4.662
|
-4.358
|
-3.705
|
-4.501
|
-4.662
|
-4.859
|
-5.104
|
-5.431
|
-5.433
|
-5.918
|
28trp5
|
0.00001
|
0.00000001
|
-5.937
|
-5.937
|
-5.937
|
-4.526
|
-3.544
|
-3.17
|
-2.573
|
-2.115
|
-1.792
|
-1.564
|
-1.4
|
-1.304
|
37mix5
|
0.000009
|
0.000001
|
-5.109
|
-4.865
|
-4.501
|
-4.029
|
-3.319
|
-3.07
|
-2.569
|
-2.207
|
-1.895
|
-1.684
|
-1.516
|
-1.423
|
33mix5
|
0.0000075
|
0.0000025
|
-4.366
|
-4.129
|
-3.781
|
-3.467
|
-3.037
|
-2.939
|
-2.593
|
-2.268
|
-1.988
|
-1.791
|
-1.649
|
-1.565
|
31mix5
|
0.000005
|
0.000005
|
-3.79
|
-3.373
|
-3.119
|
-2.915
|
-2.671
|
-2.718
|
-2.555
|
-2.398
|
-2.229
|
-2.085
|
-1.971
|
-1.902
|
35mix5
|
0.0000025
|
0.0000075
|
-3.321
|
-2.97
|
-2.765
|
-2.594
|
-2.446
|
-2.548
|
-2.616
|
-2.617
|
-2.572
|
-2.55
|
-2.508
|
-2.487
|
39mix5
|
0.000001
|
0.000009
|
-3.142
|
-2.812
|
-2.564
|
-2.404
|
-2.281
|
-2.502
|
-2.589
|
-2.706
|
-2.842
|
-2.964
|
-3.068
|
-3.103
|
26tyro5
|
0.00000001
|
0.00001
|
-3.037
|
-2.696
|
-2.464
|
-2.321
|
-2.239
|
-2.444
|
-2.602
|
-2.823
|
-3.144
|
-3.396
|
-3.742
|
-4.063
|
tyro2
|
0.00000001
|
0.0001
|
-1.081
|
-0.71
|
-0.47
|
-0.337
|
-0.327
|
-0.433
|
-0.602
|
-0.841
|
-1.119
|
-1.423
|
-1.75
|
-2.121
| |
