Problem 15.8 from Statistical Methods for the Social Sciences, Fourth Edition: L
ID: 3226294 • Letter: P
Question
Problem 15.8 from Statistical Methods for the Social Sciences, Fourth Edition:
Let P( y = 1) denote the probability that a randomly selected respondent supports current laws legalizing abortion, estimated using sex of respondent (s = 0, male; s = 1, female), religious affiliation (r1 = 1, protestant, 0 otherwise; r2 = 1, Catholic, 0 otherwise; r1 = r2 = 0, Jewish), and political party affiliation (p1 = 1, Democrat, 0 otherwise; p2 = 1, Republican, 0 otherwise, p1 = p2 = 0, Independent). The logistic model with main effect has prediction equation logit(P(y = 1)) = 0.11 + 0.16s - 0.57r1 - 0.66r2 + 0.47p1 - 1.67p2.
a) Give the effect of sex on the odds of supporting legalized abortion; that is, if the odds of support for females equal 0 times the odds of support for males, report 0 hat.
b) Give the effect of being Democrat instead of Independent on the estimated odds of support for legalized abortion.
c) Give the effect of being Democrat instead of Republican on the estimated odds of support for legalized abortion.
d) Find the estimated probability of supporting legalized abortion, for (i) female Jewish Democrats, (ii) male Catholic Republicans.
Explanation / Answer
(1) effect of sex on the odds of supporting legalized abortion=exp(.16)=1.173511
(2)effect of being Democrat instead of Independent =exp(.47)=1.5999
(3)effect of being Democrat instead of Republican=exp(.47-(-1.67))=8.499
(4)estimated probability of supporting legalized abortion,
for (i) female Jewish Democrats,
s=1, r1=0, r2=0, p1=1, p2=0
logit(P(y = 1)) =.74
P[Y=1]=.6769
(ii) male Catholic Republicans.
s=0, r1=0, r2=1, p1=0, p2=1
logit(P(y = 1)) =-2.22
P[Y=1]=.0979