To isolate a few underlying spectral factors that provide a good predictive model, you can fit a PLS model to the 16 samples by using the following SAS statements:

proc hppls data=sample; model ls ha dt = v1-v27; run;

By default, the HPPLS procedure extracts at most 15 factors. The default output from this analysis is presented in Figure 11.1 through Figure 11.3.

Figure 11.1 displays the "Performance Information," "Data Access Information," and "Model Information" tables.

The "Performance Information" table shows that PROC HPPLS executes in single-machine mode—that is, the model is fit on the machine where the SAS session executes. This run of the HPPLS procedure was performed on a multicore machine that has four CPUs; one computational thread was spawned per CPU.

The "Data Access Information" table shows that the input data set is accessed with the V9 (base) engine on the client machine where the MVA SAS session executes.

The "Model Information" table identifies the data source and shows that the factor extraction method is partial least squares regression (which is the default) and that the nonlinear iterative partial least squares (NIPALS) algorithm (which is also the default) is used to compute extracted PLS factors.

Figure 11.2 displays the "Number of Observations" and "Dimensions" tables. The "Number of Observations" table shows that all 16 of the sample observations in the input data are used in the analysis because all samples contain complete data. The "Dimensions" table shows the number of dependent variables, the number of effects, the number of predictor parameters, and the number of factors to extract.

Figure 11.3 lists the amount of variation, both individual and cumulative, that is accounted for by each of the 15 factors. All the variation in both the predictors and the responses is accounted for by only 15 factors because there are only 16 sample observations. More important, almost all the variation is accounted for with even fewer factors—one or two for the predictors and three to eight for the responses.

Figure 11.3: PLS Variation Summary

Percent Variation Accounted for by Partial Least Squares Factors | ||||
---|---|---|---|---|

Number of Extracted Factors |
Model Effects | Dependent Variables | ||

Current | Total | Current | Total | |

1 | 97.46068 | 97.46068 | 41.91546 | 41.91546 |

2 | 2.18296 | 99.64365 | 24.24355 | 66.15900 |

3 | 0.17806 | 99.82170 | 24.53393 | 90.69293 |

4 | 0.11973 | 99.94143 | 3.78978 | 94.48271 |

5 | 0.04146 | 99.98289 | 1.00454 | 95.48725 |

6 | 0.01058 | 99.99347 | 2.28084 | 97.76809 |

7 | 0.00168 | 99.99515 | 1.16935 | 98.93744 |

8 | 0.00097586 | 99.99613 | 0.50410 | 99.44153 |

9 | 0.00142 | 99.99755 | 0.12292 | 99.56446 |

10 | 0.00097037 | 99.99852 | 0.11027 | 99.67472 |

11 | 0.00032725 | 99.99884 | 0.15227 | 99.82699 |

12 | 0.00029338 | 99.99914 | 0.12907 | 99.95606 |

13 | 0.00024792 | 99.99939 | 0.03121 | 99.98727 |

14 | 0.00042742 | 99.99981 | 0.00651 | 99.99378 |

15 | 0.00018639 | 100.00000 | 0.00622 | 100.00000 |