Modeling and Multivariate Methods - SAS

Chapter 7 Performing Logistic Regression on Nominal and Ordinal Responses 207
Logistic Fit Platform Options
Figure 7.8 Parameter Estimates with Confidence Intervals
Odds Ratios (Nominal Responses Only)
When you select Odds Ratios, a report appears showing Unit Odds Ratios and Range Odds Ratios, as
shown in Figure 7.9.
Figure 7.9 Odds Ratios
From the introduction (for two response levels), we had
Prob( Y = r 1
)
log-------------------------------
Prob( Y = r 2
)
=
Xb
where r 1 and r 1 are the two response levels
so the odds ratio
Prob( Y = r 1
)
------------------------------- = exp( Xβ)
= exp( β 0
) ⋅ exp ( β 1
X 1
)… exp( β i
X i
)
Prob( Y = r 2
)
Note that exp(β i (X i + 1)) = exp(β i X i ) exp(β i ). This shows that if X i changes by a unit amount, the odds is
multiplied by exp(β i ), which we label the unit odds ratio. As X i changes over its whole range, the odds are
multiplied by exp((X high - X low )β i ) which we label the range odds ratio. For binary responses, the log odds
ratio for flipped response levels involves only changing the sign of the parameter, so you might want the
reciprocal of the reported value to focus on the last response level instead of the first.