Question 1. Consider the following example from help(ridge):
fit1 <- coxph(Surv(futime, fustat) ~ rx + ridge(age, ecog.ps, theta=1), ovarian)
As I understand, this builds a model in which `rx' is the predictor, whereas ridge penalty term contains variables `age' and `ph.ecog'. Could someone explain what it me...
The ridge term introduces age as a predictor AND penalizes it. The model above has 3 predictors, 2 of them penalized. Later in the post you have a model with both age and ridge(age). This puts age in the model twice, once as a free parameter and once as a penalized one. Not surprisingly, the second ends up with a coefficient of 0 (within machine precision of zero). The warning message you got about NaN is likely related to this, that there are redundant terms in the model. Terry Therneau