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Biostatistics Advance Access originally published online on October 24, 2006
Biostatistics 2007 8(3):654-673; 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.

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

Florian Leitenstorfer* and Gerhard Tutz

Department of Statistics, Ludwig-Maximilians-Universität München, Akademiestraße 1, 80799 München, Germany florian.leitenstorfer{at}stat.uni-muenchen.de

* To whom correspondence should be addressed.

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.

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

Received June 2, 2005; revised March 21, 2006; revised July 27, 2006; accepted for publication October 20, 2006.


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