Bayesian model pooling for the analysis of generalized linear models with missing-not-at-random covariates

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2020-9

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Çiftçi, Sezgin

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Missing data in modeling is one of the main problems of researchers. If the missingness mechanism is related to the value of the variable itself, then the missing is defined as not-at-random (MNAR). Additionally, finding the best model in statistics has always been the focus of researchers. However, it's known from examples that there may be any other model with the same best fit but has different estimated coefficients. Hence, an uncertainty about model selection that may be problematic in estimation especially when there is also uncertainty about the accuracy of the estimations caused by MNAR mechanism can cause misleading inferences. In this thesis, a hybrid Bayesian method is developed for the analysis of a generalized linear model (GLM) with MNAR covariates. In the analysis of GLM with MNAR covariates, main response and missingness probabilities of the MNAR covariates are modeled jointly. In our approach, we create a model space as a set of the best fits among all possible joint models. This is accomplished by the Reversible Jump Monte Carlo Markov Chain (RJMCMC) approach that is adopted here. Coefficient estimates are obtained by pooling the posterior estimations of each model with the posterior model probabilities, which are also calculated within RJMCMC algorithm.

Subject Keywords

Missing-Not-At-Random, Bayesian Approach, Generalized Linear Models, Reversible Jump Monte Carlo Markov Chain, Bayesian Model Averaging

URI

https://hdl.handle.net/11511/69056

Collections

Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

S. Çiftçi, “Bayesian model pooling for the analysis of generalized linear models with missing-not-at-random covariates,” Ph.D. - Doctoral Program, Middle East Technical University, 2020.