Rounding non-binary categorical variables following multivariate normal imputation: evaluation of simple methods and implications for practice

We study bias arising from rounding categorical variables following multivariate normal (MVN) imputation. This task has been well studied for binary variables, but not for more general categorical variables. Three methods that assign imputed values to categories based on fixed reference points are compared using 25 specific scenarios covering variables with k = 3,...,7 categories, and five distributional shapes, and for each k = 3,...,7, we examine the distribution of bias arising over 100,000 distributions drawn from a symmetric Dirichlet distribution. We observed, on both empirical and theoretical grounds, that one method (projected-distance-based rounding) is superior to the other two methods, and that the risk of invalid inference with the best method may be too high at sample sizes n >= 150 at 50% missingness, n >= 250 at 30% missingness and n >= 1500 at 10% missingness. Therefore, these methods are generally unsatisfactory for rounding categorical variables (with up to seven categories) following MVN imputation.