Exercise 4.12 introduced four scales of the Myers–Briggs personality test. Table 5.6 shows SAS…

Exercise 4.12 introduced four scales of the Myers–Briggs
personality test. Table 5.6 shows SAS output for fitting a model using the four
scales as predictors of whether a subject drinks alcohol frequently.

a. Conduct a model goodness-of-fit test, and interpret. If
you were to simplify the model by removing a predictor, which would you remove?
Why?

b. Software reports AIC values of 642.1 for the model with
the four main effects and the six interaction terms, 637.5 for the model with
only the four binary main effect terms, and 648.8 for the model with no
predictors. According to this criterion, which model is preferred? Explain the
rational for using AIC.

c. Using the MBTI data file at the website   use
model-building methods to select a model for this alcohol response variable.

Exercise 4.12

At the website  for the 2nd edition of this book, the MBTI
data file cross-classifies a sample of people from the MBTI Step II National
Sample on whether they report drinking alcohol frequently and on the four binary
scales of the Myers–Briggs personality test: Extroversion/Introversion (E/I),
Sensing/iNtuitive (S/N), Thinking/Feeling (T/F) and Judging/Perceiving (J/P).
The 16 predictor combinations correspond to the 16 personality types: ESTJ,
ESTP, ESFJ, ESFP, ENTJ, ENTP, ENFJ, ENFP, ISTJ, ISTP, ISFJ, ISFP, INTJ, INTP,
INFJ, INFP. (e.g., of the 77 people of type ESTJ, 13 reported smoking
frequently.) Fit a model using the four scales as predictors of the probability
of drinking alcohol frequently. Report the prediction equation, specifying how
you set up the indicator variables. Based on the model parameter estimates,
explain why the personality type with the highest estimated probability of
drinking alcohol is ENTP.