Modeling and Multivariate Methods - SAS

Chapter 4 Fitting Stepwise Regression Models 147
Using the Make Model Command for Hierarchical Terms
• The method first splits Position into two groups with the term Position2{wr&db&o&lb&te–ki&l}. One
group (the slower group) consists of the wide receivers (wr), defensive backs (db), offensive backs (o),
linebackers (lb), and tight ends (te). The other group (the faster group) is the kickers (ki), and linemen
(l), which ultimately split as Position2{ki-l}.
• The next split subdivides the slower group into wide receivers (wr), defensive backs (db), and offensive
backs(o) versus linebackers (lb) and tight ends (te), shown as Position2{wr&db&o–lb&te}. The
linebackers (lb) and tight ends split (te) to form Position2{lb–te}.
• The slower group divides again giving Position2{wr&db-o}, wide receivers (wr) and defensive backs (db)
versus offensive backs (o).
• The last subdivision is the wide receivers (wr) and defensive backs (db), Position2{wr–db}.
These terms can be illustrated by the tree hierarchy shown at the top in Figure 4.12.
Figure 4.12 Tree Structure of Terms and Corresponding Current Estimates Table
Using the default Combine rule for terms to enter a model or the Restrict rule, a term cannot enter the
model unless all the terms above it in the hierarchy have been entered. Therefore, it is simple to bring in the
term Position2{wr&db&o&lb&te-ki&l} because there is nothing above it in the hierarchy. But to enter
Position2{lb-te} requires that the two other terms above it in the hierarchy are entered:
Position2{wr&db&o-lb&te}, and Position2{wr&db&o&lb&te-ki&l}.
Reasons to choose a hierarchical coding include:
• The hierarchy leads to natural stepping rules.
• The groupings that make the greatest initial separation enter the model early.
Using the Make Model Command for Hierarchical Terms
If you have a model with nominal or ordinal terms, when you click Make Model or Run Model, the Fit
Model platform creates a new set of columns in the data table. The model appears in a new Fit Model
window for the response variable. The next example uses the Hotdogs2 sample data to illustrate how
Stepwise constructs a model with hierarchical effects.