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Deviance Information Criterion for Model Selection:Theoretical Justification and Applications

Author

Listed:
  • Yong Li

    (Renmin University of China)

  • Sushanta K. Mallick

    (Queen Mary University of London)

  • Nianling Wang

    (Capital University of Economics and Business)

  • Jun Yu

    (University of Macau)

  • Tao Zeng

    (Zhejiang University)

Abstract

This paper gives a rigorous justification to the Deviance information criterion (DIC), which has been extensively used for model selection based on MCMC output. It is shown that, when a plug-in predictive distribution is used and under a set of regularity conditions, DIC is an asymptotically unbiased estimator of the expected Kullback-Leibler divergence between the data generating process and the plug-in predictive distribution. High-order expansions to DIC and the effective number of parameters are developed, facilitating investigating the effect of the prior. DIC is used to compare alternative discrete-choice models, stochastic frontier models, and copula models in three empirical applications.

Suggested Citation

  • Yong Li & Sushanta K. Mallick & Nianling Wang & Jun Yu & Tao Zeng, 2024. "Deviance Information Criterion for Model Selection:Theoretical Justification and Applications," Working Papers 202415, University of Macau, Faculty of Business Administration.
    • Handle: RePEc:boa:wpaper:202415
    as

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    File URL: https://fba.um.edu.mo/wp-content/uploads/RePEc/doc/202415.pdf
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    References listed on IDEAS

    as
    1. Jim Griffin & Mark Steel, 2007. "Bayesian stochastic frontier analysis using WinBUGS," Journal of Productivity Analysis, Springer, vol. 27(3), pages 163-176, June.
    2. Yoichi Miyata, 2004. "Fully Exponential Laplace Approximations Using Asymptotic Modes," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1037-1049, December.
    3. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    4. Vignat, C., 2012. "A generalized Isserlis theorem for location mixtures of Gaussian random vectors," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 67-71.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    AIC; DIC; Expected loss function; Kullback-Leibler divergence; Model comparison; Plug-in predictive distribution;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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