Bias Introduced by Rounding in Multiple Imputation for Ordered Categorical Variables

ABSTRACT

Multivariate normality is frequently assumed when multiple imputation is applied for missing data. When data are ordered categorical, imputing missing data using the fully normal imputation results in implausible values falling outside of the categorical values. Naïve rounding has been suggested to round the imputed values to their categorical neighbors for further analysis. Previous studies showed that, for binary data, the rounded values can result in biased mean estimation when the population distribution is asymmetric. However, it has been conjectured that as the number of categories increases, the bias will decrease. To investigate this conjecture, the present study derives the formulas for the biases of the mean and standard deviation for ordered categorical variables with naïve rounding. Results show that both the biases of the mean and standard deviation decrease as the number of categories increases from 3 to 9. This study also finds that although symmetric population distributions lead to unbiased means of the rounded values, the standard deviations may still be largely biased. A simulation study further shows that the biases due to naïve rounding can result in substantially low coverage rates for the population mean parameter.

KEYWORDS:

• Missing completely at random
• Nonresponse
• Ordinal variable

Acknowledgments

The authors thank the editors and anonymous reviewers for helpful comments on the earlier versions of this article.