Generalized monotonic regression based on B-splines with an application to air pollution data

In many studies, it is known that one or more of the covariates have a monotonic effect on the response variable. In these circumstances, standard fitting methods for generalized additive models (GAMs) generate implausible results.A fitting procedure is proposed that incorporates monotonicity assumptions on one or more smooth components within a GAM framework.The algorithm uses the monotonicity restriction for B-spline coefficients and provides componentwise selection of smooth components.Stopping criteria and approximate pointwise confidence bands are derived.The method is applied to the data from a study conducted in the metropolitan area of São Paulo, Brazil, where the influence of several air pollutants like SO2 on respiratory mortality is investigated.