II. Variable Selection Problem (Reference: Lemeshow et al. (1988), Journal of the American Statistical Association, 348-356.) Hosmer and Lemeshow's ICU study considers a sample of 200 subjects who were part of a larger study on the survival of patients following admission to an adult intensive care unit (ICU). The goal is to develop a logistic regression model to predict the probability of survival to hospital discharge of these patients. That means use icu$sta as the response variable. You can get this dataset from the aplore3 package.

library(aplore3)

data(icu)

A detailed description of the variables can be found here https://rdrr.io/cran/ aplore3/man/icu.html For the following analysis, exclude the race variable, and convert loc to a binary variable, 1 for no coma or deep stupor and 0 otherwise.

(a) Use the forward selection, backward elimination, and forward/backward (a procedure for both ways) method of stepwise regression procedure to select the "best" models among those models without interaction terms. Use the AIC and BIC criteria. Discuss the results in the end. You may use the stepwise function of the RcmdrMisc package.

(b) Use the best subset regression procedure to choose the best model. Use both the AIC and BIC criteria. Here you may use the bestglm function of the bestglm package. Since the bestglm can take at most 15 covariates, you should start the analysis by excluding race, ser, inf, po2, type.

(c) Discuss the relationship, similarities, differences if any, of these models you found in parts a) and b). Compare the models using the area under the ROC curve.