Modeling and Multivariate Methods - SAS

Chapter 3 Fitting Standard Least Squares Models 67
Estimates
Example of Expanded Estimates
To recreate the reports in Figure 3.6, follow the steps in “Example of a Prediction Expression” on page 65,
except instead of selecting Show Prediction Expression, select Expanded Estimates.
Figure 3.6 Comparison of Parameter Estimates and Expanded Estimates
Notice that the coefficient for Drug(f) appears in the Expanded Estimates report.
Statistical Details for Expanded Estimates
When you have nominal terms in your model, the platform constructs a set of dummy columns to represent
the levels in the classification. Full details are shown in the appendix “Statistical Details” on page 651 in the
“Statistical Details” appendix. For n levels, there are n - 1 dummy columns. Each dummy variable is a
zero-or-one indicator for a particular level, except for the last level, which is coded -1 for all dummy
variables. The following table shows an example of the A1 and A2 dummy columns when column A has
levels A1, A2, and A3.
A A1 dummy A2 dummy
A1 1 0
A2 0 1
A3 -1 -1
These columns do not appear in the report, but they help conceptualize the fitting process. The parameter
estimates are the coefficients fit to these columns. In this case, there are two, labeled A[A1] and A[A2]. This
coding causes the parameter estimates to be interpreted as how much the response for each level differs from
the average across all levels. Suppose, however, that you want the coefficient for the last level, A[A3]. The
coefficient for the last level is the negative of the sum across the other levels, because the sum across all levels
is constrained to be zero. Although many other codings are possible, this coding has proven to be practical
and interpretable.