Test 1. Given the following logistic model
logit P(X)¼aþbCATþg 1 AGEþg 2 CHL,
where CAT is a dichotomous exposure variable and
AGE and CHL are continuous,answer the following
questions concerning the odds ratio that compares
exposed to unexposed persons controlling for the effects
of AGE and CHL:
a. Give an expression for the odds ratio for theE, D
relationship, assuming that CAT is coded as
(0¼low CAT, 1¼high CAT).
b. Give an expression for the odds ratio, assuming
CAT is coded as (0, 5).
c. Give an expression for the odds ratio, assuming that
CAT is coded as (1, 1).
d. Assuming that the same dataset is used for com-
puting odds ratios described in parts a–c above,
what is the relationship among odds ratios com-
puted by using the three different coding schemes
of parts a–c?
e. Assuming the same data set as in part d above, what
is the relationship between thebs that are computed
from the three different coding schemes?
- Suppose the model in Question 1 is revised as follows:
logit P(X)¼aþbCATþg 1 AGEþg 2 CHLþCAT(d 1 AGE
þd 2 CHL).
For this revised model, answer the same questions as
given in parts a–e of Question 1.a.b.c.d.e.- Given the model
logit P(X)¼a þbSSUþg 1 AGEþg 2 SEX
þSSU(d 1 AGEþd 2 SEX),
where SSU denotes “social support score” and is an
ordinal variable ranging from 0 to 5, answer the
following questions about the above model:
98 3. Computing the Odds Ratio in Logistic Regression