Imputing With Predictive Mean Matching Can Be Severely Biased When Values Are Missing At Random

Predictive mean matching (PMM) is a popular imputation strategy that imputes missing values by borrowing observed values from other cases with similar expectations. We show that, unlike other imputation strategies, PMM is not guaranteed to be consistent -- and in fact can be severely biased -- when values are missing at random (when the probability a value is missing depends only on values that are observed). We demonstrate the bias in a simple situation where a complete variable $X$ is both strongly correlated with $Y$ and strongly predictive of whether $Y$ is missing. The bias in the estimated regression slope can be as large as 80 percent, and persists even when we reduce the correlation between $X$ and $Y$. To make the bias vanish, the sample must be large ($n$=1,000) \emph{and} $Y$ values must be missing independently of $X$ (i.e., missing completely at random). Compared to other imputation methods, it seems that PMM requires larger samples and is more sensitive to the pattern of missing values. We cannot recommend PMM as a default approach to imputation.