d. The deviance of 0.9544 is equivalent to the LR test
that compares Model 1 with Model 2. Since this
test statistic (df¼3) is highly nonsignificant, we
would choose Model 1 over Model 2.
e. Neither of the two models of part c perfectly fit the
data for each subject. However, since Model 2 is
fully parameterized, it perfectly predicts the group
proportions.
- Yes, the interaction model is fully parameterized since
the model contains eight parameters and there are
eight distinct covariate patterns.
- No, as with the no-interaction model, the interaction
model does not perfectly predict the case/noncase sta-
tus of each of the 609 subjects in the data.
- a. No. The deviance value of 0.0000 is not calculated
using the deviance formula
Devð^bÞ¼ 2 lnðL^c=L^maxÞ:
In particular 2 lnL^c¼ 417 : 226 and 2 lnL^max¼ 0 ,
so Devð^bÞ¼ 417 : 226.
b. 0 : 0000 ¼ 2 lnL^Model 2 ð 2 lnL^Model 2 Þ. The two
log likelihood functions are identical since the
deviance statistic is comparing the current model
(i.e., Model 2) to the fully parameterized model
(i.e., Model 2).
c. What is actually being tested is whether or not
Model 2 is a fully parameterized model.
- a. The HL statistic of 0.0000 indicates that the inter-
action model is a fully parameterized model and
therefore perfectly predicts the group proportion
for each covariate pattern.
b. The same two models are being compared by the
HL statistic of 0.0000, i.e., Model 2.
c. No and Yes. The interaction model does not per-
fectly predict each subject’s response but it does
perfectly predict the group proportion for each
covariate pattern.
Answers to Practice Exercises 343
