Problem 4.1 with Table 4.8 used a labeling index (LI) to predict $pi$ 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. The model in (b) has fit, $logit(hat{pi}) = -13.096 + 0.9625(LI) - 0.0160(LI)^2$, with $SE = 0.0095$ for $eta_2 = -0.0160$. If you know basic calculus, explain why $hat{pi}$ 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. Table 4.8. Data for Exercise 4.1 on Cancer Remission Number of Number of Number of Number of Number of Number of LI Cases Remissions LI Cases Remissions LI Cases Remissions 8 2 0 18 1 1 28 1 1 10 2 0 20 3 2 32 1 0 12 3 0 22 2 1 34 1 1 14 3 0 24 1 0 38 3 2 16 3 0 26 1 1 Source: Reprinted with permission from E. T. Lee, Computer Prog. Biomed., 4: 80-92, 1974.
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Yes, it is appropriate to use the deviance to check the fit of the model. The deviance is a measure of the goodness of fit of a statistical model. The smaller the deviance, the better the model fits the data. However, the deviance should be compared to the degrees Show more…
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