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Deviance information criterion for latent variable models and misspecified models

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  • Li, Yong
  • Yu, Jun
  • Zeng, Tao

Abstract

Deviance information criterion (DIC) has been widely used for Bayesian model comparison, especially after Markov chain Monte Carlo (MCMC) is used to estimate candidate models. This paper first studies the problem of using DIC to compare latent variable models when DIC is calculated from the conditional likelihood. In particular, it is shown that the conditional likelihood approach undermines theoretical underpinnings of DIC. A new version of DIC, namely DICL, is proposed to compare latent variable models. The large sample properties of DICL are studied. A frequentist justification of DICL is provided. Like AIC, DICL provides an asymptotically unbiased estimator to the expected Kullback–Leibler (KL) divergence between the DGP and a predictive distribution. Some popular algorithms, such as the EM, Kalman and particle filtering algorithms, are introduced to compute DICL for latent variable models. Moreover, this paper studies the problem of using DIC to compare misspecified models. A new version of DIC, namely DICM, is proposed and it can be regarded as a Bayesian version of TIC. A frequentist justification of DICM is provided under misspecification. DICL and DICM are illustrated using asset pricing models and stochastic volatility models.

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  • Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    • Handle: RePEc:eee:econom:v:216:y:2020:i:2:p:450-493
    DOI: 10.1016/j.jeconom.2019.11.002
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    as
    1. Atsushi Inoue & Mototsugu Shintani, 2018. "Quasi‐Bayesian model selection," Quantitative Economics, Econometric Society, vol. 9(3), pages 1265-1297, November.
    2. Arnaud Doucet & Neil Shephard, 2012. "Robust inference on parameters via particle filters and sandwich covariance matrices," Economics Papers 2012-W05, Economics Group, Nuffield College, University of Oxford.
    3. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
    4. Jorge Galán & Helena Veiga & Michael Wiper, 2014. "Bayesian estimation of inefficiency heterogeneity in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 42(1), pages 85-101, August.
    5. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    6. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    7. Steven Stern, 1997. "Simulation-Based Estimation," Journal of Economic Literature, American Economic Association, vol. 35(4), pages 2006-2039, December.
    8. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    9. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    10. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    11. Andrews, Donald W K, 1987. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers [On Unification of the Asymptotic Theory of Nonlinear Econometric Models]," Econometrica, Econometric Society, vol. 55(6), pages 1465-1471, November.
    12. 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.
    13. 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.
    14. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    15. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    16. Geweke, John & Amisano, Gianni, 2011. "Optimal prediction pools," Journal of Econometrics, Elsevier, vol. 164(1), pages 130-141, September.
    17. R. B. Millar & S. McKechnie, 2014. "A one-step-ahead pseudo-DIC for comparison of Bayesian state-space models," Biometrics, The International Biometric Society, vol. 70(4), pages 972-980, December.
    18. 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.
    19. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    20. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    21. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
    22. Joshua C. C. Chan & Angelia L. Grant, 2016. "On the Observed-Data Deviance Information Criterion for Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 14(4), pages 772-802.
    23. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    24. Iskrev, Nikolay, 2008. "Evaluating the information matrix in linearized DSGE models," Economics Letters, Elsevier, vol. 99(3), pages 607-610, June.
    25. Doron Avramov & Guofu Zhou, 2010. "Bayesian Portfolio Analysis," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 25-47, December.
    26. Geweke, John & Keane, Michael, 2001. "Computationally intensive methods for integration in econometrics," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 56, pages 3463-3568, Elsevier.
    27. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    28. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    29. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    30. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    31. Renate Meyer & Jun Yu, 2000. "BUGS for a Bayesian analysis of stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 198-215.
    32. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    33. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Linde, 2014. "The deviance information criterion: 12 years on," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 485-493, June.
    34. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    35. 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.
    36. Vignat, C., 2012. "A generalized Isserlis theorem for location mixtures of Gaussian random vectors," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 67-71.
    37. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    38. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    39. Davidson, James, 1992. "A Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes," Econometric Theory, Cambridge University Press, vol. 8(3), pages 313-329, September.
    40. Andriy Norets, 2009. "Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables," Econometrica, Econometric Society, vol. 77(5), pages 1665-1682, September.
    41. Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(3), pages 402-412, June.
    42. Jushan Bai & Peng Wang, 2015. "Identification and Bayesian Estimation of Dynamic Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 221-240, April.
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    More about this item

    Keywords

    AIC; TIC; DIC; Latent variable models; Misspecified models; Markov chain Monte Carlo;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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