Using calibration to improve rounding in imputation.

Since the 1990s, imputation methods have become increasingly accessible in standard software that typically assume a multivariate normal (MVN) distribution for incompletely observed variables. When these variables are not normally distributed but rather categorical (binary or ordinal), practitioners are often advised to round the MVN imputations to the nearest integer, but this simple procedure can lead to biased estimates. We propose practical rounding rules to be used with the existing imputation methods (e.g., under MVN) to obtain usable imputations with small biases for estimation of means and correlations. The rounding rules are calibrated in the sense that values reimputed for observed data have distributions similar to those of the observed data. Calibration in this sense is a form of posterior predictive check that can be used to evaluate any imputation procedure. It is readily implemented by duplicating the data and comparing the distributions of observed and imputed data. We calculate asymptotic biases of marginal means and slope coefficients under plausible models to assess the performance of our method. (May 2008)