Deviance information criterion for latent variable models and misspecified models

Yong Li, Jun Yu and Tao Zeng

Journal of Econometrics, 2020, vol. 216, issue 2, 450-493

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.

Keywords: AIC; TIC; DIC; Latent variable models; Misspecified models; Markov chain Monte Carlo (search for similar items in EconPapers)
JEL-codes: C11 C12 G12 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:216:y:2020:i:2:p:450-493

DOI: 10.1016/j.jeconom.2019.11.002

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