Practice Exercises
Practice Exercises
- Consider the following logistic regression model in
which all predictors are (0,1) variables:
logit PðXÞ¼aþb 1 E 1 þb 2 E 2 þb 3 E 3 þg 1 C 1 þg 2 C 2 þg 3 C 3
þg 12 C 1 C 2 þd 11 E 1 C 1 þd 21 E 2 C 1 þd 12 E 1 C 2
þd 22 E 2 C 2 þd 33 E 3 C 3 þde 13 E 1 E 3 þde 23 E 2 E 3
þd 112 E 1 C 1 C 2 þd 212 E 2 C 1 C 2
For the above model, determine which of the following
statements areTrueorFalse.
(i.e.,Circle T or F)
T F a. The above model is hierarchically well-formu-
lated.
T F b. Suppose the chunk test for the null hypothesis
H 0 :d 112 ¼d 212 ¼0 is found to be significant and
backward elimination involving these two three-
factor product terms results in only E 2 C 1 C 2
remaining in the model. Then based on the “hier-
archy principle,” the final model must contain
the variablesC 1 C 2 ,C 1 ,C 2 ,E 2 C 1 C 2 ,E 2 C 1 ,E 2 C 2 ,
E 2 E 3 ,andE 2.
T F c. Suppose the chunk test for the null hypothesis
H 0 :d 112 ¼d 212 ¼0 is found to be significant and,
as in the previous question, backward elimina-
tion involving these two three-factor product
terms results in onlyE 2 C 1 C 2 remaining in the
model. Then, based on the hierarchy principle
and the hierarchical backward elimination
approach, the only variables that remain as can-
didates for being dropped from the model at this
point areE 1 ,E 3 ,E 1 E 3 ,E 2 E 3 ,E 1 C 1 ,E 3 C 3 , andC 3.
T F d. Suppose that after the interaction assessment
stage, the only terms remaining in the model
areE 2 C 1 C 2 ,E 2 C 1 ,E 2 C 2 ,E 3 C 3 ,C 1 C 2 ,C 1 ,C 2 ,C 3 ,
E 1 ,E 2 , andE 3. Then, at this point, the odds ratio
formula for comparing a person for whomE 1 ¼
E 2 ¼E 3 ¼1 to a person for whomE 1 ¼E 2 ¼E 3
¼0 is given by the expression
OR¼exp[b 1 þb 2 þb 3 þd 21 C 1 þd 22 C 2 þd 33 C 3
þd 212 C 1 C 2 ] where the coefficients in the formula
are estimated from the reduced model obtained
after interaction assessment.
T F e. Suppose that neither E 1 C 1 C 2 nor E 2 C 1 C 2
remains in the model after interaction assess-
ment of these two three-factor products (but
prior to interaction assessment of two-factor
products). Suppose further that separate Wald
(and corresponding likelihood ratio) tests for
Practice Exercises 289