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Additive cubic spline regression with Dirichlet process mixture errors

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  • Chib, Siddhartha
  • Greenberg, Edward

Abstract

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 156 (2010)
Issue (Month): 2 (June)
Pages: 322-336

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Handle: RePEc:eee:econom:v:156:y:2010:i:2:p:322-336

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Web page: http://www.elsevier.com/locate/jeconom

Related research

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;

References

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  6. 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).
  7. 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.
  8. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
  9. 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.
  10. 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.
  11. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
  12. 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.
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Cited by:
  1. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
  2. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2012. "Bayesian Nonparametric Instrumental Variable Regression based on Penalized Splines and Dirichlet Process Mixtures," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 127, Courant Research Centre PEG.
  3. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
  4. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer, vol. 66(1), pages 1-31, February.

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