Introduction to Categorical Data Analysis

CHAPTER 6 365
19. a. logit(π) = α + β1d1 +···+β6d6, where di = 1 for department i and di = 0
otherwise.
b. Model fits poorly.
c. Only lack of fit in Department 1, where more females were admitted than
expected if the model lacking gender effect truly holds.
d. −4.15, so fewer males admitted than expected if model lacking gender effect
truly holds.
e. Males apply in relatively greater numbers to departments that have relatively
higher proportions of acceptances.
27. zα/2 = 2.576,zβ = 1.645, and n1 = n2 = 214.
29. logit( ˆπ) =−12.351 + 0.497x. Probability at x = 26.3 is 0.674; probability at
x = 28.4 (i.e., one standard deviation above mean) is 0.854. Odds ratio is 2.83,
so λ = 1.04, δ = 5.1. Then n = 75.
CHAPTER 6
1. a. log( ˆπR/ ˆπD) =−2.3 + 0.5x. Estimated odds of preferring Republicans over
Democrats increase by 65% for every $10,000 increase.
b. ˆπR > ˆπD when annual income >$46,000.
c. ˆπI = 1/[1 + exp(3.3 − 0.2x) + exp(1 + 0.3x)].
3. a. SE values in parentheses
Logit Intercept Size ≤ 2.3 Hancock Oklawaha Trafford
log(πI /πF ) −1.55 1.46(0.40) −1.66(0.61) 0.94(0.47) 1.12(0.49)
log(πR/πF ) −3.31 −0.35(0.58) 1.24(1.19) 2.46(1.12) 2.94(1.12)
log(πB/πF ) −2.09 −0.63(0.64) 0.70(0.78) −0.65(1.20) 1.09(0.84)
log(πO/πF ) −1.90 0.33(0.45) 0.83(0.56) 0.01(0.78) 1.52(0.62)
5. a. Job satisfaction tends to increase at higher x1 and lower x2 and x3.
b. x1 = 4 and x2 = x3 = 1.
7. a. Two cumulative probabilities to model and hence 2 intercept parameters. Proportional
odds have same predictor effects for each cumulative probability,
so only one effect reported for income.
b. Estimated odds of being at low end of scale (less happy) decrease as income
increases.
c. LR statistic = 0.89 with df = 1, and P -value = 0.35. It is plausible that
income has no effect on marital happiness.