Use the baseline information from the Catheter Study. We model the binary catheter blockage outcome with age, gender, and education as predictors. Assuming additive effect for all these covariates, we may have five models using the four link functions: logit, probit, c-log-log, and identity. Note that by using the c-loglog link, we have two different models by modeling the probabilities of death \(=1\) or death \(=0\).

(a) Assess the goodness of fit for all the models.

(b) Perform an overall test on the association between age groups and the outcome. What is the p-value?

(c) Calculate the correlation matrix the fitted probabilities under the five models.