Interpretation of intercepts(ag)
ag¼log odds ofDgwhere all
independent variables equal
zero;
g¼ 1 ; 2 ; 3 ;...;G 1
ag>agþ 1
+
a 1 >a 2 > >aG 1With this ordinal model, there are two inter-
cepts, one for each comparison, but there is
only one estimated beta for the effect of
RACE. The odds ratio for RACE is e tob 1 .In
our example, the odds ratio equals exp(0.7555)
or 2.13. [Note: SAS’s LOGISTIC procedure was
used with a “descending” option so that Inter-
cept 1 compares D2toD<2, whereas Inter-
cept 2 compares D1toD<1].The results indicate that for this sample of
women with invasive endometrial cancer,
black women were over twice (i.e., 2.13) as
likely as white women to have tumors that
were categorized as poorly differentiated vs.
moderately differentiated or well differentiated
andover twice as likely as white women to have
tumors classified as poorly differentiated or
moderately differentiated vs. well differen-
tiated. To summarize, in this cohort, black
women were over twice as likely to have a
more severe grade of endometrial cancer com-
pared with white women.What is the interpretation of the intercept? The
interceptagis the log odds ofDgwhere all
the independent variables are equal to zero.
This is similar to the interpretation of the inter-
cept for other logistic models except that, with
the proportional odds model, we are modeling
the log odds of several inequalities. This yields
several intercepts, with each intercept
corresponding to the log odds of a different
inequality (depending on the value ofg). More-
over, the log odds ofDgis greater than the
log odds ofD(gþ1) (assuming categorygis
nonzero). This means thata 1 >a 2
>aG 1.EXAMPLE (continued)
Variable Estimate S.E.
Intercept 1 (^a 2 ) 1.7388 0.1765
Intercept 2 (^a 1 ) 0.0089 0.1368
RACE 0.7555 0.2466
dOR¼expð 0 : 7555 Þ¼ 2 : 13Interpretation of OR
Black vs. white women with
endometrial cancer over twice as likely
to have more severe tumor grade:SincedORðD 2 Þ¼dORðD 1 Þ¼ 2 : 13474 13. Ordinal Logistic Regression