Shrinkage invalidates the Hosmer-Lemeshow test: goodness of fit for penalized logistic regression, with an application to glaucoma diagnosis

Clinical prediction models are increasingly fitted by penalized logistic regression, because collinearity or many candidate predictors makes maximum likelihood unstable or impossible. Calibration is then almost always assessed by a grouped goodness-of-fit test such as the Hosmer-Lemeshow test. We sh