Monotonic Regression Based on Bayesian P–Splines

In many practical situations, it is desirable to restrict the flexibility of nonparametric estimation to accommodate a presumed monotonic relationship between a covariate and the response variable. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for brands of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response functions considerably.