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Bayesian Model Averaging for Generalized Linear Models with Missing Covariates


  • Valentino Dardanoni

    (University of Palermo)

  • Giuseppe De Luca

    (University of Palermo)

  • Salvatore Modica

    (University of Palemo)

  • Franco Peracchi

    (University of Rome "Tor Vergata" and EIEF)


We address the problem of estimating generalized linear models (GLMs) when the outcome of interest is always observed, the values of some covariates are missing for some observations, but imputations are available to fill-in the missing values. Under certain conditions on the missing-data mechanism and the imputation model, this situation generates a trade-off between bias and precision in the estimation of the parameters of interest. The complete cases are often too few, so precision is lost, but just filling-in the missing values with the imputations may lead to bias when the imputation model is either incorrectly specified or uncongenial. Following the generalized missing-indicator approach originally proposed by Dardanoni et al. (2011) for linear regression models, we characterize this bias-precision trade- off in terms of model uncertainty regarding which covariates should be dropped from an augmented GLM for the full sample of observed and imputed data. This formulation is attractive because model uncertainty can then be handled very naturally through Bayesian model averaging (BMA). In addition to applying the generalized missing-indicator method to the wider class of GLMs, we make two extensions. First, we propose a block-BMA strategy that incorporates information on the available missing-data patterns and has the advantage of being computationally simple. Second, we allow the observed outcome to be multivariate, thus covering the case of seemingly unrelated regression equations models, and ordered, multinomial or conditional logit and probit models. Our approach is illustrated through an empirical application using the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE).

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  • Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2013. "Bayesian Model Averaging for Generalized Linear Models with Missing Covariates," EIEF Working Papers Series 1311, Einaudi Institute for Economics and Finance (EIEF), revised May 2013.
  • Handle: RePEc:eie:wpaper:1311

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    References listed on IDEAS

    1. Dardanoni, Valentino & Modica, Salvatore & Peracchi, Franco, 2011. "Regression with imputed covariates: A generalized missing-indicator approach," Journal of Econometrics, Elsevier, vol. 162(2), pages 362-368, June.
    2. Magnus, J.R. & Powell, O.R. & Prüfer, P., 2008. "A Comparison of Two Averaging Techniques with an Application to Growth Empirics," Other publications TiSEM 0392dffa-51e0-4bc9-9644-f, Tilburg University, School of Economics and Management.
    3. Valentino Dardanoni & Giuseppe De Luca & Salvatore Modica & Franco Peracchi, 2012. "A generalized missing-indicator approach to regression with imputed covariates," Stata Journal, StataCorp LP, vol. 12(4), pages 575-604, December.
    4. Mazzonna, Fabrizio & Peracchi, Franco, 2012. "Ageing, cognitive abilities and retirement," European Economic Review, Elsevier, vol. 56(4), pages 691-710.
    5. Dimitrios Christelis, 2011. "Imputation of Missing Data in Waves 1 and 2 of SHARE," CSEF Working Papers 278, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    6. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    7. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    8. Cheti Nicoletti & Franco Peracchi, 2006. "The effects of income imputation on microanalyses: evidence from the European Community Household Panel," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 625-646, July.
    9. repec:hal:journl:peer-00815561 is not listed on IDEAS
    10. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
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