Statistical Modelling 1 (2001), 195211
Bayesian Varying-coefficient Models using Adaptive Regression Splines
Clemens Biller and Ludwig Fahrmeir
Ludwig Maximilians University Munich, Germany
Department of Statistics
Ludwig Maximilians University Munich
Ludwigstr. 33, D80539 Munich, Germany
email: fahrmeir@stat.uni-muenchen.de
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 analyzed previously
in the literature: the kyphosis data set with a binary response and survival
data from the Veteran's Administration lung cancer trial.
Keywords:
B-spline basis; Knot selection; Non-Gaussian response;
Non- and semiparametric regression;
Reversible jump Markov chain Monte Carlo.
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