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Continuing Exercise 4 in Chapter 2, consider the model using temperature as the only explanatory variable.
(a) Refit the model using a probit and a complementary log-log link instead of a logit link. Plot all three curves with the data, using a temperature range of 31? to 81? on the x-axis. Does one appear to fit better than the others? Do they provide similar probabilities of failure at 31??
(b) Compare BIC values for the three different links. Which link appears to fit best?
(c) Compute the BMA model probabilities for the three links. Comment on the uncertainty of the model selection among these three links.
The failure of an O-ring on the space shuttle Challenger's booster rockets led to its destruction in 1986. Using data on previous space shuttle launches, Dalal et al. (1989) examine the probability of an O-ring failure as a function of temperature at launch and combustion pressure. Data from their paper is included in the challenger.csv file. Below are the variables:
• Flight: Flight number
• Temp: Temperature (F) at launch
• Pressure: Combustion pressure (psi)
• O.ring: Number of primary field O-ring failures
• Number: Total number of primary field O-rings (six total, three each for the two booster rockets)
The response variable is O.ring, and the explanatory variables are Temp and Pressure. Complete the following:
(a) The authors use logistic regression to estimate the probability an O-ring will fail. In order to use this model, the authors needed to assume that each O-ring is independent for each launch. Discuss why this assumption is necessary and the potential problems with it. Note that a subsequent analysis helped to alleviate the authors' concerns about independence.
(b) Estimate the logistic regression model using the explanatory variables in a linear form.
(c) Perform LRTs to judge the importance of the explanatory variables in the model.
(d) The authors chose to remove Pressure from the model based on the LRTs. Based on your results, discuss why you think this was done. Are there any potential problems with removing this variable?