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Regularization for generalized additive mixed models by likelihood-based boosting.

A Groll1, G Tutz

  • 1Department of Statistics, University of Munich, Akademiestrasse 1, 80799 Munich, Germany. gerhard.tutz@stat.uni-muenchen.de

Methods of Information in Medicine
|March 2, 2012
PubMed
Summary
This summary is machine-generated.

We developed a boosting algorithm for generalized additive mixed models that effectively selects relevant predictors, even with many variables. This method is more stable and accurate than conventional approaches in high-dimensional settings.

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Generalized linear mixed models (GLMMs) are extended by semi- and nonparametric regression to include additive predictors.
  • Existing fitting methods for GLMMs struggle in high-dimensional settings with numerous explanatory variables.
  • Boosting offers a potential solution for enhancing GLMMs in complex data scenarios.

Purpose of the Study:

  • To extend the concept of boosting to generalized additive mixed models (GAMMs).
  • To present a novel algorithm for fitting GAMMs, particularly addressing challenges in high-dimensional data.
  • To introduce two distinct approaches for fitting the variance components of random effects within the boosting framework.

Main Methods:

  • Developed a likelihood-based componentwise boosting algorithm for variable selection in GAMMs.
  • The algorithm is designed for high-dimensional settings where covariate influence is unknown.
  • Model complexity is managed using information criteria, and performance is validated through simulations and real-world data application.

Main Results:

  • The proposed boosting methods demonstrate superior stability and accuracy in estimating regression functions compared to conventional methods, especially with numerous predictors.
  • Simulations for binary and Poisson responses confirm the enhanced performance.
  • The methods yield reasonable results when applied to real-world clinical data, such as the Multicenter AIDS Cohort Study.

Conclusions:

  • The boosting algorithm effectively identifies relevant predictors in generalized additive mixed models.
  • This approach is robust and performs well in high-dimensional statistical settings.
  • The developed methods offer a stable and accurate solution for complex regression problems.