Smooth supersaturated polynomials have been used for building emulators in computer experiments. The response surfaces built with this method are simple to interpret and have spline-like properties (Bates et al., 2014). We extend the methodology to build smooth logistic regression models. The approach we follow is to regularize the likelihood with a penalization term that accounts for the roughness of the regression model.
The response surface follows data closely yet it is smooth and does not oscillate. We illustrate the method with simulated data and we also present a recent application to build a prediction rule for psychiatric hospital readmissions of patients with a diagnosis of psychosis. This application uses data from the OCTET clinical trial (Burns et al., 2013).