Bayesian varying-coefficient models using adaptive regression splines

Author:

Biller Clemens1,Fahrmeir Ludwig2

Affiliation:

1. Ludwig Maximilians University, Munich, Germany

2. Ludwig Maximilians University, Munich, Germany,

Abstract

Varying-coefficient models provide a flexible framework for semi- and nonparametric generalized regression analysis. We present a fully Bayesian B-spline basis function approach with adaptive knot selection. For each of the unknown regression functions or varying coefficients, the number and location of knots and the B-spline coefficients are estimated simultaneously using reversible jump Markov chain Monte Carlo sampling. The overall procedure can therefore be viewed as a kind of Bayesian model averaging. Although Gaussian responses are covered by the general framework, the method is particularly useful for fundamentally non-Gaussian responses, where less alternatives are available. We illustrate the approach with a thorough application to two data sets analysed previously in the literature: the kyphosis data set with a binary response and survival data from the Veteran’s Administration lung cancer trial.

Publisher

SAGE Publications

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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