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Fast computation of the deviance information criterion for latent variable models

Author

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  • Chan, Joshua C.C.
  • Grant, Angelia L.

Abstract

The deviance information criterion (DIC) has been widely used for Bayesian model comparison. However, recent studies have cautioned against the use of certain variants of the DIC for comparing latent variable models. For example, it has been argued that the conditional DIC–based on the conditional likelihood obtained by conditioning on the latent variables–is sensitive to transformations of latent variables and distributions. Further, in a Monte Carlo study that compares various Poisson models, the conditional DIC almost always prefers an incorrect model. In contrast, the observed-data DIC–calculated using the observed-data likelihood obtained by integrating out the latent variables–seems to perform well. It is also the case that the conditional DIC based on the maximum a posteriori (MAP) estimate might not even exist, whereas the observed-data DIC does not suffer from this problem. In view of these considerations, fast algorithms for computing the observed-data DIC for a variety of high-dimensional latent variable models are developed. Through three empirical applications it is demonstrated that the observed-data DICs have much smaller numerical standard errors compared to the conditional DICs. The corresponding Matlab code is available upon request.

Suggested Citation

  • Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
  • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:847-859
    DOI: 10.1016/j.csda.2014.07.018
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    1. Bauwens, Luc & Rombouts, Jeroen V.K., 2012. "On marginal likelihood computation in change-point models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3415-3429.
    2. Brendan Kline & Justin L. Tobias, 2008. "The wages of BMI: Bayesian analysis of a skewed treatment-response model with nonparametric endogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(6), pages 767-793.
    3. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.
    4. Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2007. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9780521671736, June.
    5. Joshua C. C. Chan & Gary Koop & Simon M. Potter, 2013. "A New Model of Trend Inflation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 94-106, January.
    6. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    7. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
    8. Joshua C. C. Chan & Eric Eisenstat, 2015. "Marginal Likelihood Estimation with the Cross-Entropy Method," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 256-285, March.
    9. Miguel A.G. Belmonte & Gary Koop & Dimitris Korobilis, 2014. "Hierarchical Shrinkage in Time‐Varying Parameter Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(1), pages 80-94, January.
    10. Ward, Eric J., 2008. "A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools," Ecological Modelling, Elsevier, vol. 211(1), pages 1-10.
    11. Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
    12. Xiao, Ni & Zarnikau, Jay & Damien, Paul, 2007. "Testing functional forms in energy modeling: An application of the Bayesian approach to U.S. electricity demand," Energy Economics, Elsevier, vol. 29(2), pages 158-166, March.
    13. McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
    14. Yong Li & Zeng Tao & Jun Yu, "undated". "Robust Deviance Information Criterion for Latent Variable Models," Working Papers CoFie-04-2012, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    15. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    16. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    17. Chan,Joshua & Koop,Gary & Poirier,Dale J. & Tobias,Justin L., 2019. "Bayesian Econometric Methods," Cambridge Books, Cambridge University Press, number 9781108437493.
    18. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607, July.
    19. Nardari, Federico & Scruggs, John T., 2007. "Bayesian Analysis of Linear Factor Models with Latent Factors, Multivariate Stochastic Volatility, and APT Pricing Restrictions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(4), pages 857-891, December.
    20. Chen, Xiaoshan & Kontonikas, Alexandros & Montagnoli, Alberto, 2012. "Asset prices, credit and the business cycle," Economics Letters, Elsevier, vol. 117(3), pages 857-861.
    21. Canova, Fabio, 1993. "Modelling and forecasting exchange rates with a Bayesian time-varying coefficient model," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 233-261.
    22. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    23. Eric Eisenstat & Joshua C. C. Chan & Rodney W. Strachan, 2016. "Stochastic Model Specification Search for Time-Varying Parameter VARs," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1638-1665, December.
    24. Russell B. Millar, 2009. "Comparison of Hierarchical Bayesian Models for Overdispersed Count Data using DIC and Bayes' Factors," Biometrics, The International Biometric Society, vol. 65(3), pages 962-969, September.
    25. Berg, Andreas & Meyer, Renate & Yu, Jun, 2004. "Deviance Information Criterion for Comparing Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 107-120, January.
    26. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    27. Hedibert F. Lopes & Esther Salazar, 2006. "Bayesian Model Uncertainty In Smooth Transition Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 99-117, January.
    28. Dale J. Poirier & Gary Koop & Justin Tobias, 2005. "Semiparametric Bayesian inference in multiple equation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 723-747.
    29. 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.
    30. Haroon Mumtaz & Paolo Surico, 2012. "Evolving International Inflation Dynamics: World And Country-Specific Factors," Journal of the European Economic Association, European Economic Association, vol. 10(4), pages 716-734, August.
    31. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
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    More about this item

    Keywords

    Bayesian model comparison; State space; Factor model; Vector autoregression; Semiparametric model;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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