Bayesian Model Averaging for Generalized Linear Models with Missing Covariates
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).
|Date of creation:||2013|
|Date of revision:||May 2013|
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- Valentino Dardanoni & Salvatore Modica & Franco Peracchi, 2011. "Regression with imputed covariates: A generalized missing-indicator approach," Post-Print hal-00815561, HAL.
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- 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.
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