A new framework for multiple imputation and applications to a binary variable

摘要

Imputation is a common method for replacing a missing value with one or more fabricated values. The terminology and methodology of imputation is often confusing because no general framework exists. This paper is an attempt to develop such a framework, while including traditional terms and methods. Our imputation process consists of two steps: (ⅰ) the imputation model and (ⅱ) the imputation task. This is nothing new, but their integration together is a key point of this paper. The framework is compact and fairly easy to implement. To illustrate the framework, we use a binary variable in our simulation examples. This variable is interesting because we now have the two types of binary variables; one as the dependent variable of the imputation model (the variable being imputed), and the other as the binary response indicator. The applications of the paper are focused on multiple imputation, which is traditionally Bayesian. Consequently, general software applications, such as SAS and SPSS, are implemented with Bayesian rules. We develop some multiple imputation methods without Bayesian rules and call them non-Bayesian, and compare the results of various methods.