Generalized Monotonic Regression Based on B-Splines with an Application to Air Pollution Data

In many studies where it is known that one or more of the certain
covariates have monotonic effect on the response variable, common
fitting methods for generalized additive models (GAM) may be
affected by a sparse design and often generate implausible results.
A fitting procedure is proposed that incorporates the monotonicity
assumptions on one or more smooth components within a GAM
framework. The flexible likelihood based boosting 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 data from a study conducted in the metropolitan area of
Sao Paulo, Brazil, where the influence of several air pollutants
like SO_2 on respiratory mortality of children is investigated.