Modeling and Multivariate Methods - SAS

146 Fitting Stepwise Regression Models Chapter 4
Models with Nominal and Ordinal Terms
The progress of multiterm inclusion is a balance between numerator degrees of freedom and opportunities
to improve the fit. When there are significant interaction terms, often several terms enter at the same step. If
the Step button is clicked once, Ct*T is entered along with its two contained effects Ct and T. However, a
step back is not symmetric because a crossed term can be removed without removing its two component
terms. Note that Ct now has 2 degrees of freedom because if Stepwise removes Ct, it also removes Ct*T.
Models with Nominal and Ordinal Terms
Traditionally, stepwise regression has not addressed the situation when there are categorical terms in the
model. When nominal or ordinal terms are in regression models, they are carried as sets of dummy or
indicator columns. When there are only two levels, there is no problem because they generate only a single
column. However, for more than two levels, multiple columns must be handled. The convention in JMP for
nominal variables in standard platforms is to model these terms so that the parameter estimates average out
to zero across all the levels.
In the stepwise platform, categorical variables (nominal and ordinal) are coded in a hierarchical fashion,
which is different from the other least squares fitting platforms. In hierarchical coding, the levels of the
categorical variable are considered in some order and a split is made to make the two groups of levels that
most separate the means of the response. Then, each group is further subdivided into its most separated
subgroups, and so on, until all the levels are distinguished into k - 1 terms for k levels.
For nominal terms, the order of levels is determined by the means of the Ys. For ordinal terms, the order is
fixed.
Example of a Model with a Nominal Term
1. Open the Football.jmp sample data table.
2. Select Analyze > Fit Model.
3. Select Speed and click Y.
4. Select Weight and Position2 and click Add.
Notice that Position2 is a nominal variable with values representing football positions.
5. For Personality, select Stepwise.
6. Click Run.
Figure 4.11 Position Hierarchy