The first time you click Go in the Model Launch control panel (Partial Least Squares Model Launch Control Panel), the Validation Method panel is removed from the Model Launch window. If you specified a Validation column or if you selected Holdback in the Validation Method panel, all model fits in the report are based on the training data. Otherwise, all model fits are based on the entire data set.
If you selected None as the CV method, two reports appear:
Model Comparison Summary
In Model Comparison Summary, models for 7 and then 6 factors have been fit. The report includes the following summary information:
Cross Validation Report
When the Standardize X option is selected, cross validation is applied once to the entire data table. It is not reapplied to the individual training sets. However, when any combination of the Centering or Scaling options are selected, this combination of selections is applied to each cross validation training set. Cross validation proceeds by using the training sets, which are individually centered and scaled if these options are selected.
p-value for the van der Voet T2 test. For more details, see van der Voet T2.
Q2
Here PRESSi and SSYi correspond to their values for i factors.
R2X
Sum of values R2X for i = 1 to the given number of factors.
R2Y
Sum of values R2Y for i = 1 to the given number of factors.
For a specified number of factors, a, Root Mean PRESS is calculated as follows:
1.
Fit a model with a factors to each training set (with None as the Validation Method).
4.
Root Mean PRESS for a factors is the square root of the average of the PRESS values across all responses.
The statistic Q2 is defined as . The PRESS statistic is the predicted error sum of squares across all responses for the model developed based on training data, but evaluated on the validation set. The value of SSY is the sum of squares for Y across all responses based on the observations in the validation set.
The statistic Q2 in the Cross Validation report is computed in the following ways, depending on the selected Validation Method:
Q2 is the average of the values computed for the validation sets based on the models constructed by leaving out one observation at a time.
Q2 is the average of the values computed for the validation sets based on the K models constructed by leaving out each of the K folds.
Q2 is the value of computed for the validation set based on the model constructed using the single set of training data.
Calculation of R2X and R2Y When Validation Is Used
The statistics R2X and R2Y in the Cross Validation report are computed in the following ways, depending on the selected Validation Method:
Note: For all of these computations, R2Y is calculated analogously.
R2X is the average of the Percent Variation Explained for X Effects for the models constructed by leaving out one observation at a time.
R2X is the average of the Percent Variation Explained for X Effects for the K models constructed by leaving out each fold.
R2X is the Percent Variation Explained for X Effects for the model constructed using the training data.
Model Fit Report