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Biostatistics Advance Access published online on October 24, 2006
Biostatistics, doi:10.1093/biostatistics/kxl036
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received June 2, 2005
Revised July 27, 2006
Accepted October 20, 2006

Article

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

Florian Leitenstorfer 1 * and Gerhard Tutz 1

1 Department of Statistics, Ludwig-Maximilians-Universität München, Akademiestraße 1, 80799 München, Germany

* To whom correspondence should be addressed.
Florian Leitenstorfer, E-mail: florian.leitenstorfer{at}stat.uni-muenchen.de


  Abstract

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 (GAM) 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 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.

Keywords: Monotonic regression; Generalized additive models; Likelihood based boosting; Air pollution data.
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