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Bayesian varying-coefficient models using adaptive regression splines

Ludwig Maximilians University, Munich, Germany

Ludwig Fahrmeir

Ludwig Maximilians University, Munich, Germany, fahrmeir{at}stat.uni-muenchen.de

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.

Key Words: B-spline basis • knot selection: non-Gaussian response • non- and semi-parametric regression • reversible jump Markov chain Monte Carlo

Statistical Modelling, Vol. 1, No. 3, 195-211 (2001)
DOI: 10.1177/1471082X0100100303


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