Homework 5
STAT 8320
Due May 5, 2007
Problem 1: An animal study is designed to address the effects of a set of different drugs
on the amount of immuno-response to an allergen. It is believed that the age of the animal
may effect this response, and to address this, eight animals from each of three ages (young,
adolescent, adult) are used in the study. Each animal will receive the four drugs of interest,
and measures of their immuno-response will be taken. Hypothetical data from a study of
this sort are included in the attached file. Address the following questions:
a. Describe an appropriate model for this data. First, define the model for Yijk and describe
which terms in the model are fixed and which are random. Also indicate how we could write
this model in the mixed model form, by finding the forms of Zand X.
b. What assumptions do you think are reasonable about the structure of the covariance
within an animal? To test your intuition, run your model in SAS for CS, AR(1), and un-
structured covariance matrices. Which model(s) do the fit statistics suggest are best? When
possible, perform likelihood ratio tests to compare the models.
c. For your favorite model, interpret the output in SAS. Be sure to mention which of your
fixed effects are significant, and describe which drug(s) are best (smallest response).
d. What would have happened if you had ignored the correlation within the animals? To
answer this question, consider a model which does not involve any correlation between the
observations on a particular animal. What are the conclusion for this model, and how are
they different from your results in part (c)?
Problem 2: The power of rechargeable camera batteries is of interest to a major photog-
rapher. To understand which batteries are the best, it is desired to measure the length
of time that batteries will run a camera on the first charge. Additionally, it is desired to
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