Sep 25, 2017 term paper 2

# DOWNER DATA FOR UNKNOWN REASONS, DAIRY COWS SOMETIMES BECOME RECUMBENT—THEY LAY DOWN. CALLED…

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Downer data For unknown reasons, dairy cows sometimes become recumbent—they lay down. Called downers, these cows may have a serious illness that may lead to death of the cow. These data are from a study of blood samples of over 400 downer cows studied at the Ruakura New Zealand Animal Health Laboratory during 1983–1984. A variety of blood tests were performed, and for many of the animals, the outcome (survived, died, or animal was killed) was determined. The goal is to see if survival can be predicted from the blood measurements. The variables in the data file downer.txt are described in Table 12.7. These data were collected from veterinary records, and not all variables were recorded for all cows.

1.       Consider first predicting Outcome from Myopathy. Find the fraction of surviving cows of Myopathy = 0 and for Myopathy = 1.

2.       Fit the logistic regression with response Outcome, and the single predictor Myopathy. Obtain a 95% confidence interval for coefficient for Myopathy, and compute the estimated decrease in odds of survival when Myopathy = 1. Obtain the estimated probability of survival when Myopathy = 0 and when Myopathy = 1, and compare with the observed survival fractions in Problem 12.1.1.

3.       Next, consider the regression problem with only CK as a predictor (CK is observed more often than is Myopathy, so this regression will be based on more cases than were used in the first two parts of this problem). Draw separate density estimates of CK, for Outcome = 0 and for Outcome = 1. Also, draw separate density estimates for log(CK) for the two groups. Comment on the graphs.

4.       Fit the logistic regression mean function with log(CK) as the only term beyond the intercept. Summarize results.

5.       Fit the logistic mean function with terms for log(CK), Myopathy and a Myopathy × log(CK) interaction. Interpret each of the coefficient estimates. Obtain a sequential deviance table for fitting the terms in the order given above, and summarize results. (Missing data can cause a problem here: if your computer program requires that you fit three separate mean functions to get the analysis of deviance, then you must be sure that each fit is based on the same set of observations, those for which CK and Myopathy are both observed.)

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