Description
1. The following table gives data from a retrospective study between esophageal cancer
and daily alcohol consumption adjusted for age.
Age
Case
Daily Alcohol Consumption
Control
Daily Alcohol Consumption
0-79 g 80+ g 0-79 g 80+ g
25-34 0 1 106 9
35-44 5 4 164 26
45-54 21 25 138 29
55-64 34 42 139 27
65-74 36 19 88 18
75+ 8 5 31 0
(a) Fit a prospective model to the data to study the relation between alcohol
consumption, age, and disease (model age as a continuous variable taking values
25, 35, 45, 55, 65, and 75). Interpret the result.
(b) Let Ψj be the odds ratio relating alcohol consumption and disease in the jth age
group (j = 1, …, 6). Assume different age groups have different odds. Compare
the following two models: M0 : Ψj = 1 for all j;
M1 : Ψj = Ψ (where Ψ is an unknown constant);
(Hint: First write out the models and check if they are nested; if so, use
deviance analysis to compare the two models.)
2. The following table provides data from a study of the germination of two species
of Orobanche seeds. The seeds were grown on 1/125 dilutions of two different root
extract media (cucumber or bean) in a 2×2 factorial layout with replicates. The
data (yi/mi) consist of the number of seeds, mi
, and the number germinating, yi
,
for each batch. Interest focuses on the possible differences in germination rates for
the two types of seed and root extract.
O. aegyptiaca 75 O. aegyptiaca 73
Bean Cucumber Bean Cucumber
10/39 5/6 8/16 3/12
23/62 53/74 10/30 22/41
23/81 55/72 8/28 15/30
26/51 32/51 23/45 32/51
17/39 46/79 0/4 3/7
10/13
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(a) Fit a logistic regression model to study the relation between germination rates
and different types of seed and root extract. Interpret the result.
(b) Is there over dispersion? If so, what is the estimate of dispersion parameter?
Update your model and reinterpret the result.
(c) What is a plausible cause of the over dispersion?
2 P8131
