5.9 Problem 4.1 with Table 4.8 used a labeling index (LI) to predict = the probability...
Question:
5.9 Problem 4.1 with Table 4.8 used a labeling index (LI) to predict π = the probability of remission in cancer patients.
a. When the data for the 27 subjects are 14 binomial observations (for the 14 distinct levels of LI), the deviance for this model is 15.7 with df = 12. Is it appropriate to use this to check the fit of the model? Why or why not?
b. The model that also has a quadratic term for LI has deviance = 11.8.
Conduct a test comparing the two models.
c. Themodel in
(b) has fit, logit(πˆ ) = −13.096 + 0.9625(LI ) − 0.0160(LI)2, with SE = 0.0095 for ˆ β2 = −0.0160. If you know basic calculus, explain why ˆπ is increasing for LI between 0 and 30. Since LI varies between 8 and 38 in this sample, the estimated effect of LI is positive over most of its observed values.
d. For the model with only the linear term, the Hosmer–Lemeshow test statistic = 6.6 with df = 6. Interpret.
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