10.21 Table 10.13 reports results of a study of fish hatching under three environments.

Eggs from seven clutches were randomly assigned to three treatments, and the response was whether an egg hatched by day 10. The three treatments were (1) carbon dioxide and oxygen removed, (2) carbon dioxide only removed, and (3) neither removed.

a. Let πit denote the probability of hatching for an egg from clutch i in treatment t . Assuming independent binomial observations, fit the model

where zt = 1 for treatment t and 0 otherwise. What does your software report for ˆ β1. (It should be −∞, since treatment 1 has no successes.)

b. Model these data using random effects for the clutches. Compare the results with (a).

Transcribed Image Text:

logit (it) a + B1Z1 + B2Z2 ==