Stephan Kolassa wrote:
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.
You may be mixing the concepts of population parameters and sample
estimates. Also, the confidence intervals for the fit will include
almost anything because of the limited sample size.
Is there any elegant way to constrain the model fit?
Not with these methods. Bootstrap bumping can be used though.
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.
You can try different tolerances for singularities with lrm.
Frank
Thank you for your time!
Stephan Kolassa
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Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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