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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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Markov chain monte carlo methods for computing bayes factors: A comparative review
Cong Han,Bradley P. Carlin +1 more
TL;DR: It is found that the joint model-parameter space search methods perform adequately but can be difficult to program and tune, whereas the marginal likelihood methods often are less troublesome and require less additional coding.
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Bayesian Information Criterion for Censored Survival Models
Chris Volinsky,Adrian E. Raftery +1 more
TL;DR: A revision of the penalty term in BIC is proposed so that it is defined in terms of the number of uncensored events instead of thenumber of observations, which corresponds to a more realistic prior on the parameter space and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.
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Aging, Cognitive Abilities and Retirement
TL;DR: This article 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.
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A new look at the Bayes procedure
TL;DR: In this article, an objective procedure of evaluation of the prior distribution in a Bayesian model is developed and the classical ignorance prior distribution is newly interpreted as the locally impartial prior distribution.
Journal ArticleDOI
Model uncertainty and health effect studies for particulate matter
TL;DR: This paper presents objective prior distributions for Bayesian Model Averaging in generalized linear models so that Bayesian model selection corresponds to standard methods of model selection, such as the Akaike Information Criterion or Bayes information Criterion, and inferences within a model are based on standard maximum likelihood estimation.