Introduction to Categorical Data Analysis

368 BRIEF SOLUTIONS TO SOME ODD-NUMBERED PROBLEMS
19. b. The λ XY term is not in the model, so X and Y are conditionally independent.
All terms in the saturated model that are not in model (WXZ,WYZ) involve
X and Y , and so permit XY conditional association.
21. a. G 2 = 31.7, df = 48. The model with three-factor terms has G 2 = 8.5, df =
16; the change is 23.1, df = 32, not a significant improvement.
b. (ii) For the result at the beginning of Section 7.4.4, identify set B ={E,L}
and sets A and C each to be one of other variables.
23. (a) No.
(b) Yes; in the result in Section 7.4.4, take A ={Y }, B ={X1,X2}, C ={X3}.
25. a. Take β = 0.
b. LR statistic comparing this to model (XZ, YZ).
d. No, this is a heterogeneous linear-by-linear association model. The XY
odds ratios vary according to the level of Z, and there is no longer homogeneous
association. For scores {ui = i} and {vj = j}, local odds ratio equals
exp(βk).
27. (a)T, (b) F, (c)T.
CHAPTER 8
1. z = 2.88, two-sided P -value = 0.004; there is strong evidence that MI cases are
more likely than MI controls to have diabetes.
3. a. Population odds of belief in heaven estimated to be 2.02 times population
odds of belief in hell.
b. For each subject, odds of belief in heaven estimated to equal 62.5 times odds
of belief in hell.
5. a. This is probability, under H0, of observed or more extreme result, with more
extreme defined in direction specified by Ha.
b. Mid P -value includes only half observed probability, added to probability of
more extreme results.
c. When binomial parameter = 0.50, binomial is symmetric, so two-sided
P -value = 2(one-sided P -value) in (a) and (b).
7. 0.022 ± 0.038, or (−0.016, 0.060), wider than for dependent samples.
9. ˆβ = log(132/107) = 0.21.