Should a Normal Imputation Model be Modified to Impute Skewed Variables?

Abstract

Researchers often impute continuous variables under an assumption of normality–yet many incomplete variables are skewed. We find that imputing skewed continuous variables under a normal model can lead to bias. The bias is usually mild for popular estimands such as means, standard deviations, and linear regression coefficients, but the bias can be severe for more shape-dependent estimands such as percentiles or the coefficient of skewness. We test several methods for adapting a normal imputation model to accommodate skewness, including methods that transform, truncate, or censor (round) normally imputed values as well as methods that impute values from a quadratic or truncated regression. None of these modifications reliably reduces the biases of the normal model, and some modifications can make the biases much worse. We conclude that, if one has to impute a skewed variable under a normal model, it is usually safest to do so without modifications–unless you are more interested in estimating percentiles and shape than in estimating means, variances, and regressions. In the conclusion, we briefly discuss promising developments in the area of continuous imputation models that do not assume normality.