Additive cubic spline regression with Dirichlet process mixture errors
The goal of this article is to develop a flexible Bayesian analysis of regression models for continuous and categorical outcomes. In the models we study, covariate (or regression) effects are modeled additively by cubic splines, and the error distribution (that of the latent outcomes in the case of categorical data) is modeled as a Dirichlet process mixture. We employ a relatively unexplored but attractive basis in which the spline coefficients are the unknown function ordinates at the knots. We exploit this feature to develop a proper prior distribution on the coefficients that involves the first and second differences of the ordinates, quantities about which one may have prior knowledge. We also discuss the problem of comparing models with different numbers of knots or different error distributions through marginal likelihoods and Bayes factors which are computed within the framework of Chib (1995) as extended to DPM models by Basu and Chib (2003). The techniques are illustrated with simulated and real data.
Year of publication: |
2010
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Authors: | Chib, Siddhartha ; Greenberg, Edward |
Published in: |
Journal of Econometrics. - Elsevier, ISSN 0304-4076. - Vol. 156.2010, 2, p. 322-336
|
Publisher: |
Elsevier |
Keywords: | Additive regression Bayes factors Cubic spline Non-parametric regression Dirichlet process Dirichlet process mixture Marginal likelihood Markov chain Monte Carlo Metropolis-Hastings Model comparison Ordinal data |
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