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 SO(2) on respiratory mortality is investigated.
Leitenstorfer
Florian
F
Department of Statistics, Ludwig-Maximilians-Universität München, 80799 München, Germany. florian.leitenstorfer@stat.uni-muenchen.de
Tutz
Gerhard
G
D000368:Aged; D000397:Air Pollution / Q000009:adverse effects* / Q000706:statistics & numerical data*; D000465:Algorithms; D001499:Bayes Theorem; D001699:Biometry; D001938:Brazil / Q000453:epidemiology; D006801:Humans; D016013:Likelihood Functions; D012044:Regression Analysis; D012140:Respiratory Tract Diseases / Q000209:etiology / Q000401:mortality; D012307:Risk Factors