Bayesian Selection Model With Shrinking Priors For Nonignorable Missingness PDF Download

This dissertation focuses on model selection in logistic regression with incompletely observed data. In particular, methods are presented for using Markov Chain Monte Carlo imputation and Bayesian variable selection to model a binary outcome. We consider multivariate missing covariates, with different types of predictors, such as continuous, counts, and categorical variables. Such type of data is considered in the analysis of Project Talent recorded from a longitudinal study. Roughly 400,000 were selected for the study from United States high school students in grades 9 through 12 during the year 1960; follow-up surveys were conducted 1, 5, and 11 years after graduation. We extend a methodology developed by Yang, Belin, and Boscardin (2005), to this Project Talent for a logistic regression model with incomplete covariates. The idea is to use data information as much as possible to fill in the missing values and study associations between a binary response variable and covariates. According to Yang, Belin, and Boscardin, one approach under a multivariate normal assumption for data, is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs Sampling process, called "Simultaneously Impute And Select" (SIAS). A modified strategy of SIAS is extended to a mixed data structure that allows for categorical, counts, and continuous variables. The first chapter consists of an introduction to some approaches to variable selection for missing data. The fact that missing data arise commonly in statistical analyses, leads to a variety of methods to handle missing data. The missing data mechanism needs to be considered in imputations. The multiple imputation methods and Markov Chain Mote Carlo (MCMC) algorithms are presented as general statistical approaches to missing data analysis. In the MCMC computational toolbox, various implementation methods for imputation are discussed: Metropolis-Hasting, Gibbs Sampler, and Data Augmentation. Compared to model selection methods in frequentist and likelihood inference, Bayesian inference takes an entirely different approach. The frequentist approach only looks at the current data to make inference. The Bayesian approach requires the specification of the prior distribution, which can come from historical data or expert opinion. Stochastic Search Variable Selection (SSVS) and Gibbs Variable Selection (GVS) are reviewed for model selection. Two alternative strategies, Impute Then Select (ITS) and Simultaneously Impute And Select (SIAS), are studied. In the second chapter, imputation and Bayesian variable selection methods for linear regression are extended to a binary response variable that is completely observed, but some covariates have missing values. We focus on extending SIAS strategy to logistic regression models via two alternative imputations, decomposition and Fully Conditional Specification (FCS). The decomposition method breaks a multivariate distribution into a series of univariate ones by decomposing the joint density function p(Y, X1, ..., X[p]) into the product of conditional distributions, using the factorization p(A, B) = p(A[vertical line]B)p(B). The FCS aims to involve iteratively sampling from the conditional distributions for one random variable, given all the others. These two methods are implemented in the imputation step of the SIAS procedure then applied to the Project Talent data. Simulations are also performed to validate these results and demonstrate the superiority of FCS over the decomposition method under certain circumstances. The third chapter presents a new approach for incorporating the sampling weight into imputation and Bayesian variable selection in logistic regression models. We develop the approach that extends SIAS by a Bayesian version of iterative weighted least squares algorithm to include a sampling step based on Gibbs sampler. This approach is illustrated using both simulation studies and Project Talent data.