Small Sample and Asymptotic Relationships between Multiple Imputation, Maximum Likelihood, and Fully Bayesian Methods for Missing Data in Linear Regression Models

• Activity Number: 92
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Qingxia Chen*+ and Joseph G. Ibrahim
• Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill
• Keywords: Missing data ; multiple imputation ; maximum likelihood ; prior distribution ; posterior distribution

Abstract

Multiple Imputation (MI), Maximum Likelihood (ML), and Fully Bayesian (FB) methods are the three most commonly used model-based approaches in missing data problems. In this paper, we derive small sample and asymptotic expressions of the estimates and standard errors for these three methods. We also investigate the small and large sample properties of the estimates and fully examine how these estimates are related for the three approaches in the linear regression model when the responses or covariates are missing at random (MAR). We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case (CC) estimates under very general conditions. With MAR continuous covariates in the linear model, we derive the imputation distribution under proper MI, the iterative formula of the estimates and closed form expressions for the standard errors under the ML method via the EM algorithm, and the closed form full conditional distributions for Gibbs sampling under the FB framework.