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Bayesian Model Averaging for Generalized Linear Models with Missing Covariates
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In this article, the authors 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.Abstract:
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).read more
Citations
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Journal ArticleDOI
Journal of the American Statistical Association: William S. Cleveland, Marylyn E. McGill and Robert McGill, “The shape parameter for a two variable graph” 83 (1988) 289–300
Journal ArticleDOI
Imputation of Missing Data in Waves 1 and 2 of SHARE
TL;DR: In this article, the authors describe the imputation methodology used in the first two waves of SHARE, which is the fully conditional specification approach of van Buuren, Brand, Groothuis-Oudshoorn, and Rubin (2006).
Book ChapterDOI
Frequentist Model Averaging
TL;DR: In this paper, the authors provide an overview of frequentist model averaging, including different methods for selecting the model weights, including bagging, weighted AIC, stacking and focussed methods.
References
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Journal ArticleDOI
On the harm that ignoring pretesting can cause
DL Dmitry Danilov,Jan R. Magnus +1 more
TL;DR: In this paper, the first and second moments of the WALS estimator were analyzed and the error in not reporting the correct moments can be large, and this error can vary substantially between different model selection procedures.
Posted Content
Ageing, cognitive abilities and retirement
Fabrizio Mazzona,Franco Peracchi +1 more
TL;DR: This paper investigated the relationship between ageing, cognitive abilities and retirement using the Survey on Health, Ageing and Retirement in Europe (SHARE), a household panel that offers the possibility of comparing several European countries using nationally representative samples of the population aged 50+.
Journal ArticleDOI
Estimation of Regression Coefficients of Interest when Other Regression Coefficients are of no Interest
Jan R. Magnus,James Durbin +1 more
Journal ArticleDOI
Weighted average least squares estimation with nonspherical disturbances and an application to the Hong Kong housing market
TL;DR: The recently proposed 'weighted average least squares' (WALS) estimator is a Bayesian combination of frequentist estimators and Monte Carlo evidence shows that the WALS estimator performs significantly better than standard BMA and pretest alternatives.
Journal ArticleDOI
Imputation of Missing Data in Waves 1 and 2 of SHARE
TL;DR: In this article, the authors describe the imputation methodology used in the first two waves of SHARE, which is the fully conditional specification approach of van Buuren, Brand, Groothuis-Oudshoorn, and Rubin (2006).