The HPPLS Procedure

Fitting a PLS Model

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;

By default, the HPPLS procedure extracts at most 15 factors. The default output from this analysis is presented in Figure 12.1 through Figure 12.3.

Figure 12.1 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 12.1: Performance, Data Access, and Model Information

The HPPLS Procedure

Performance Information
Execution Mode Single-Machine
Number of Threads 4

Data Access Information
Data Engine Role Path
WORK.SAMPLE V9 Input On Client

Model Information
Factor Extraction Method Partial Least Squares
PLS Algorithm NIPALS
Validation Method None

Figure 12.2 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 12.2: Number of Observations and Dimensions

Number of Observations Read 16
Number of Observations Used 16

Number of Response Variables 3
Number of Effects 27
Number of Predictor Parameters 27
Number of Factors 15

Figure 12.3 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 12.3: PLS Variation Summary

Percent Variation Accounted for by Partial Least Squares Factors
Number of
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