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 ofÂ Chib (1995) as extended to DPM models by Basu and Chib (2003). The techniques are illustrated with simulated and real data.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Basu S. & Chib S., 2003. "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 224-235, January.
- Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
- Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
- Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
- Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
- Tiwari, R C & Jammalamadaka, S R & Chib, Siddhartha, 1988. "Bayes Prediction Density and Regression Estimation--A Semiparametric Approach," Empirical Economics, Springer, vol. 13(3/4), pages 209-22.
- David B. Dunson & Natesh Pillai & Ju-Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183.
- Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
- Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
- M. Vannucci & F. Corradi, 1999. "Covariance structure of wavelet coefficients: theory and models in a Bayesian perspective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 971-986.
- Altman, Edward I. & Rijken, Herbert A., 2004. "How rating agencies achieve rating stability," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2679-2714, November.
- Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2007. "Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures," Working Paper Series 211, Sveriges Riksbank (Central Bank of Sweden).
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:156:y:2010:i:2:p:322-336. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.