  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 that in estimated means,
variance, and regressions. In the conclusion, we briefly discuss promising
developments in the area of continuous imputation models that do not assume
normality.
