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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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The risk inflation criterion for multiple regression
Dean P. Foster,Edward I. George +1 more
TL;DR: In this article, a new criterion called risk inflation is proposed for the evaluation of variable selection procedures in multiple regression, which is based on an adjustment to the risk, i.e., the maximum increase in risk due to selecting rather than knowing the "correct" predictors.
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Correction: Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Generalized Linear Models
Ludwig Fahrmeir,Heinz Kaufmann +1 more
TL;DR: In this paper, mild general conditions which assure weak or strong consistency or asymptotic normality are presented for categorical responses with a bounded range, and stochastic regressors also are treated.
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
Bayesian Model Selection in Structural Equation Models
TL;DR: A Bayesian approach to model selection for structural equation models is outlined, which tends to select simpler models than strategies based on multiple P -value-based tests, and may help to overcome the criticism that they are too complicated for the data they are applied to.
Journal ArticleDOI
A comparison of two model averaging techniques with an application to growth empirics
TL;DR: In this paper, the authors compared the performance of various model averaging techniques and proposed a new method called weighted-average least squares (WALS), which is based on a transparent definition of prior ignorance.