5.20 Refer to Table 2.7 on mother’s drinking and infant malformations.

a. Fit the logistic regression model using scores {0, 0.5, 1.5, 4, 7} for alcohol consumption. Check goodness of fit.

b. Test independence using the likelihood-ratio test for the model in (a). (The trend test of Section 2.5.1 is the score test for this model.)

c. The sample proportion of malformations is much higher in the highest alcohol category because, although it has only one malformation, its sample size is only 38. Are the results sensitive to this single observation? Re-fit the model without it, entering 0 malformations for 37 observations, and compare the results of the likelihood-ratio test. (Because results are sensitive to a single observation, it is hazardous to make conclusions, even though n was extremely large.)

d. Fit the model and conduct the test of independence for all the data using scores {1, 2, 3, 4, 5}. Compare the results with (b). (Results for highly unbalanced data can be sensitive to the choice of scores.)