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# hw3 - Stat 771 Fall 2011 Homework 3 Due Wednesday March 23...

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Stat 771, Fall 2011: Homework 3 Due Wednesday, March 23 The file insulin.dat contains longitudinal data from a study on m = 36 rabbits; 12 rabbits were randomly assigned to each of 3 groups: group 1 rabbits received the standard insulin mixture, group 2 rabbits received a mixture containing 1% less protamine than the standard, and group 3 rabbits received a mixture containing 5% less protamine. Rabbits were injected with the assigned mixture at time 0, and blood sugar measurements taken on each rabbit at the time of injection (time 0) and 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 hours post-injection. Each data record in the file insulin.dat represents a single observation; the columns of the data set are (1) rabbit number, (2) hours (time), (3) response (blood sugar level), and (4) insulin group (1, 2, or 3). 1. Fit general model to get an idea of the covariance structure Recall from homework two that the es- timated LOESS means are not quite linear from the spaghetti plots. Fit a model with the most general mean (completely unstructured) and an unstructured covariance matrix in each group, e.g. proc mixed method=ml data=sugar; class rabbit hours group; model sugar=hours group hours*group / noint; repeated / subject=rabbit type=un group=group r=1,13,25 rcorr=1,13,25; Within each group, which (if any) of the available covariance matrices seem most plausible based on the fit? Do you think separate covariance matrices in each group is necessary? 2. Choose a covariance matrix based on AIC Using completely unstructured means as in 1, fit 14 differ- ent models covering all covariance matrix assumptions discussed in class: type=un , type=cs , type=csh , type=ar(1) , type=arh(1) , type=toep(2) , type=toeph(2) ; with both group=group included and not included. Prepare a table with the AIC and BIC for each of the 14 fits (these are given in the SAS output).

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