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04:35
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Generalized monotonic regression based on B-splines with an application to air pollution data
Florian Leitenstorfer1, Gerhard Tutz
1Department of Statistics, Ludwig-Maximilians-Universität München, 80799 München, Germany. florian.leitenstorfer@stat.uni-muenchen.de
Biostatistics (Oxford, England)
|October 26, 2006
Summary
This study introduces a new method for generalized additive models (GAMs) to ensure monotonic relationships between variables. This approach yields more plausible results when standard methods fail, improving environmental health research.
Area of Science:
- Environmental Health
- Biostatistics
- Statistical Modeling
Background:
- Standard generalized additive models (GAMs) can produce implausible results when covariates have a monotonic effect on the response variable.
- Monotonic relationships are common in scientific studies, particularly in environmental health research investigating pollutant effects.
Purpose of the Study:
- To propose a novel fitting procedure for GAMs that incorporates monotonicity assumptions.
- To address the limitations of standard GAM fitting methods when dealing with monotonic covariate effects.
Main Methods:
- The proposed algorithm integrates monotonicity constraints on B-spline coefficients within the GAM framework.
- It features componentwise selection of smooth components, along with derived stopping criteria and approximate pointwise confidence bands.
Main Results:
- The developed method successfully incorporates monotonicity assumptions into GAM fitting.
- Componentwise selection and derived confidence bands enhance the reliability of model components.
Conclusions:
- The new fitting procedure offers a robust solution for GAMs with monotonic covariate effects.
- This method improves the analysis of environmental data, such as air pollutant impacts on respiratory mortality in São Paulo.
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