Multiple imputation and access to likelihood based tools in missing data problems

Abstract

Multiple imputation and maximum likelihood estimation (via the expectation- maximization algorithm) are two well-known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation-maximization approximation to the likelihood. In this thesis we show how these two methods are equivalent, and further, exploit this result to show that familiar likelihood-based approaches can be used to enhance multiple imputation’s performance in: (1) model selection, where familiar Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) can be used to choose the imputation model that best fits the observed data; (2) hypothesis testing, where the familiar likelihood-ratio statistic can be used to perform composite hypothesis testing with multiple imputed data; (3) measurement error modelling, where familiar functional methods, such as Simulation-extrapolation and Corrected score, can be used to account for measurement error with multiple imputed data. We verify these results empirically and demonstrate the use of the methods on several classical missing data examples.