Introduction to Categorical Data Analysis

PROBLEMS 165
c. The concordance index c equals 0.658 for the model with the four main
effects and the six interaction terms, 0.640 for the model with only the four
main effect terms, and 0.568 for the model with only T/F as a predictor.
According to this criterion, which model would you choose (i) if you want
to maximize sample predictive power (ii) if you think model parsimony is
important?
5.7 From the same survey referred to in Problem 4.16, Table 5.11 cross-classifies
whether a person smokes frequently with the four scales of the MBTI personality
test. SAS reports model −2 log likelihood values of 1130.23 with only
an intercept term, 1124.86 with also the main effect predictors, 1119.87 with
also all the two-factor interactions, and 1116.47 with also all the three-factor
interactions.
a. Write the model for each case, and show that the numbers of parameters
are 1, 5, 11, and 15.
b. According to AIC, which of these four models is preferable?
c. When a classification table for the model containing the four main effect
terms uses the sample proportion of frequent smokers of 0.23 as the cutoff,
sensitivity = 0.48 and specificity = 0.55. The area under the ROC curve
is c = 0.55. Does knowledge of personality type help you predict well
whether someone is a frequent smoker? Explain.
Table 5.11. Data on Smoking Frequently and Four Scales of Myers–Briggs
Personality Test
Extroversion/Introversion E I
Sensing/iNtuitive S N S N
Smoking Frequently
Thinking/ Judging/
Feeling Perceiving Yes No Yes No Yes No Yes No
T J 13 64 6 17 32 108 4 9
P 11 31 4 14 9 43 9 26
F J 16 89 6 25 34 104 4 27
P 19 60 23 57 29 76 22 57
Source: Reproduced with special permission of CPP Inc., Mountain View, CA 94043. Copyright 1996 by
CPP Inc. All rights reserved. Further reproduction is prohibited without the Publisher’s written consent.
5.8 Refer to the classification table in Table 5.3 with π0 = 0.50.
a. Explain how this table was constructed.
b. Estimate the sensitivity and specificity, and interpret.
5.9 Problem 4.1 with Table 4.8 used a labeling index (LI) to predict π = the
probability of remission in cancer patients.