I.2 The 'Reference' Parameterization

Examples 20.1−20.3 in Chapter 20 all use a 'reference' parameterization, specified by the PARAM=REF option in the CLASS statement of PROC LOGISTIC. This means that model estimates for each level of the nominal factor are incremental to that of a specified reference level. If there are m levels of a main effect X, there would be m-1 parameters associated with the incremental effects over the reference.

In Output 20.1 for Example 20.1, a portion of which is replicated in Output I.1, the Intercept estimate of 2.6135 refers to the reference value of the Group effect, namely PBO (recall that PBO was designated as the reference level). Since Group has only two levels (m=2), there is one parameter (m-1) for the group factor, with estimate of −1.1191. This is the incremental effect for the active group (ACT) relative to the placebo group (PBO), so that the estimate for the active group would be 2.6135-1.1191 = 1.4944.