A Cautious Note on Auxiliary Variables That Can Increase Bias in Missing Data Problems

The treatment of missing data in the social sciences has changed tremendously during the last decade. Modern missing data techniques such as multiple imputation and full-information maximum likelihood are used much more frequently. These methods assume that data are missing at random. One very common approach to increase the likelihood that missing at random is achieved consists of including many covariates as so-called auxiliary variables. These variables are either included based on data considerations or in an inclusive fashion; that is, taking all available auxiliary variables. In this article, we point out that there are some instances in which auxiliary variables exhibit the surprising property of increasing bias in missing data problems. In a series of focused simulation studies, we highlight some situations in which this type of biasing behavior can occur. We briefly discuss possible ways how one can avoid selecting bias-inducing covariates as auxiliary variables.