Using mixtures of tt densities to make inferences in the presence of missing data with a small number of multiply imputed data sets

Strategies for making inference in the presence of missing data after conducting a Multiple Imputation (MI) procedure are considered. An approach which approximates the posterior distribution for parameters using a mixture of tt-distributions is proposed. Simulated experiments show this approach improves inferences in some aspects, making them more stable over repeated analysis and creating narrower bounds for certain common statistics of interest. Extensions to the existing literature have been executed that provide further stability to inferences and also a strong potential to identify ways to make the analysis procedure more flexible. The competing methods have been first compared using simulated data sets and then a real data set concerning analysis of the effect of breastfeeding duration on children’s cognitive ability. R code to implement the methods used is available as online supplementary material.