Introduction to Categorical Data Analysis

CHAPTER 4 361
15. a. exp(−2.38 + 1.733) = 0.522 for blacks and exp(−2.38) = 0.092 for whites.
b. Exponentiate endpoints of 1.733 ± 1.96(0.147), which gives (e 1.44 , e 2.02 ).
c. CI based on negative binomial model, because overdispersion for Poisson
model.
d. Poisson is a special case of negative binomial with dispersion parameter = 0.
Here, there is strong evidence that dispersion parameter > 0, because the
estimated dispersion parameter is almost 5 standard errors above 0.
17. CI for log rate is 2.549 ± 1.96(0.04495), so CI for rate is (11.7, 14.0).
19. a. Difference between deviances = 11.6, with df = 1, gives strong evidence
Poisson model with constant rate inadequate.
b. z = ˆβ/SE =−0.0337/0.0130 =−2.6 (or z 2 = 6.7 with df = 1).
c. [exp(−0.060), exp(−0.008)], or (0.94, 0.99), quite narrow around point
estimate of e −0.0337 = 0.967.
21. μ = αt + β(tx), form of GLM with identity link, predictors t and tx, no intercept
term.
CHAPTER 4
1. a. ˆπ = 0.068.
b. ˆπ = 0.50 at −ˆα/ ˆβ = 3.7771/0.1449 = 26.
c. At LI = 8, ˆπ = 0.068, rate of change = 0.1449(0.068)(0.932) = 0.009.
d. e ˆβ = e0.1449 = 1.16.
3. a. Proportion of complete games estimated to decrease by 0.07 per decade.
b. At x = 12, ˆπ =−0.075, an impossible value.
c. At x = 12, logit( ˆπ) =−2.636, and ˆπ = 0.067.
5. a. logit( ˆπ) = 15.043 − 0.232x.
b. At temperature = 31, ˆπ = 0.9996.
c. ˆπ = 0.50 at x = 64.8 and ˆπ >0.50 at x