Modeling and Multivariate Methods - SAS

Chapter 4 Fitting Stepwise Regression Models 151
The Model Averaging Option
The models are listed in increasing order of the number of parameters that they contain. The model with
the highest R 2 for each number of parameters is highlighted. The radio button column at the right of the
table enables you to select one model at a time and check the results.
Note: The recommended criterion for selecting a model is to choose the one corresponding to the smallest
BIC or AICc value. Some analysts also want to see the C p statistic. Mallow’s C p statistic is computed, but
initially hidden in the table. To make it visible, Right-click (Control-click on the Macintosh) in the table
and select Columns > Cp from the menu that appears.
The Model Averaging Option
The model averaging technique enables you to average the fits for a number of models, instead of picking a
single best model. The result is a model with excellent prediction capability. This feature is particularly
useful for new and unfamiliar models that you do not want to overfit. When many terms are selected into a
model, the fit tends to inflate the estimates. Model averaging tends to shrink the estimates on the weaker
terms, yielding better predictions. The models are averaged with respect to the AICc weight, calculated as
follows:
AICcWeight = exp[-0.5(AICc - AICcBest)]
AICcBest is the smallest AICc value among the fitted models. The AICc Weights are then sorted in
decreasing order. The AICc weights cumulating to less than one minus the cutoff of the total AICc weight
are set to zero, allowing the very weak terms to have true zero coefficients instead of extremely small
coefficient estimates.
Example Using the Model Averaging Option
1. Open the Fitness.jmp sample data table.
2. Select Analyze > Fit Model.
3. Select Oxy and click Y.
4. Select Runtime, RunPulse, RstPulse, and MaxPulse and click Add.
5. For Personality, select Stepwise.
6. Click Run.
7. From the red triangle menu next to Stepwise, select Model Averaging.
8. Enter 3 for the maximum number of terms, and keep 0.95 for the weight cutoff.
Figure 4.17 Model Averaging Window