Introduction to Categorical Data Analysis

CHAPTER 8 369
11. 95% CI for β is log(132/107) ± 1.96 √ 1/132 + 1/107, which is (−0.045,
0.465). The corresponding CI for odds ratio is (0.96, 1.59).
13. a. More moves from (2) to (1), (1) to (4), (2) to (4) than if symmetry truly held.
b. Quasi-symmetry model fits well.
c. Difference between deviances = 148.3, with df = 3. P -value < 0.0001 for
H0: marginal homogeneity.
15. a. Subjects tend to respond more in always wrong direction for extramarital sex.
b. z =−4.91/0.45 =−10.9, extremely strong evidence against H0.
c. Symmetry fits very poorly but quasi symmetry fits well. The difference
of deviances = 400.8, df = 3, gives extremely strong evidence against
H0: marginal homogeneity (P -value < 0.0001).
d. Also fits well, not significantly worse than ordinary quasi symmetry. The
difference of deviances = 400.1, df = 1, gives extremely strong evidence
against marginal homogeneity.
e. From model formula in Section 8.4.5, for each pair of categories, a
more favorable response is much more likely for premarital sex than
extramarital sex.
19. G 2 = 4167.6 for independence model (df = 9), G 2 = 9.7 for quasiindependence
(df = 5). QI model fits cells on main diagonal perfectly.
21. G 2 = 13.8, df = 11; fitted odds ratio = 1.0. Conditional on change in brand,
new brand plausibly independent of old brand.
23. a. G 2 = 4.3, df = 3; prestige ranking: 1. JRSS-B, 2.Biometrika, 3.JASA, 4.
Commun. Statist.
25. a. e 1.45 − 0.19 /(1 + e 1.45 − 0.19 ) = 0.78.
b. Extremely strong evidence (P -value < 0.0001) of at least one difference
among {βi}. Players do not all have same probability of winning.
27. a. log(πij /πji) = log(μij /μji) = (λX i − λY i ) − (λX j − λY j ). Take βi = (λX i −
λY i ).
b. Under this constraint, μij = μji.
c. Under this constraint, model adds to independence model a term for each cell
on main diagonal.