[R] Logistic regression with rcs() and inequality constraints?

[Stephan Kolassa]

Dear guRus,

I am doing a logistic regression using restricted cubic splines via 
rcs(). However, the fitted probabilities should be nondecreasing with 
increasing predictor. Example:

predictor <- seq(1,20)
y <- c(rep(0,9),rep(1,10),0)
model <- glm(y~rcs(predictor,n.knots=3),family="binomial")
print(1/(1+exp(-predict(model))))

The last expression should be a nondecreasing sequence, as fitted 
probabilities make no sense to decrease in this case.

Is there any elegant way to constrain the model fit?

Right now, I am trying to do this by defining a "large" set of linear 
inequalities and using constrOptim() on the log-likelihood. However, 
this seems to be very sensitive to the starting values, and I am not 
really happy with the results.

BTW: yes, working with lrm() would probably be more natural, but lrm() 
breaks down on my data because of a rank-deficient information matrix.

Thank you for your time!
Stephan Kolassa