On the Performance of Sequential Regression Multiple Imputation Methods with Non Normal Error Distributions

Abstract

Sequential regression multiple imputation has emerged as a popular approach for handling incomplete data with complex features. In this approach, imputations for each missing variable are produced based on a regression model using other variables as predictors in a cyclic manner. Normality assumption is frequently imposed for the error distributions in the conditional regression models for continuous variables, despite that it rarely holds in real scenarios. We use a simulation study to investigate the performance of several sequential regression imputation methods when the error distribution is flat or heavy tailed. The methods evaluated include the sequential normal imputation and its several extensions which adjust for non normal error terms. The results show that all methods perform well for estimating the marginal mean and proportion, as well as the regression coefficient when the error distribution is flat or moderately heavy tailed. When the error distribution is strongly heavy tailed, all methods retain their good performances for the mean and the adjusted methods have robust performances for the proportion; but all methods can have poor performances for the regression coefficient because they cannot accommodate the extreme values well. We caution against the mechanical use of sequential regression imputation without model checking and diagnostics.

Keywords:

• Extreme value
• Multivariate missing data
• Non normal error distribution
• Predictive mean matching
• Residuals
• Tukey's g-and-h distribution

Mathematics Subject Classification:

• 62F40
• 62J05

Acknowledgments

The authors thank the Editor, the Associate Editor, the referee, Alan Zaslavsky, and Stef van Buuren for their valuable comments. The work was supported by the grants SES-0106914 from the National Science Foundation, U01-CA93344 from the National Cancer Institute and HS09869 from the Agency for Healthcare Research and Quality.

Notes

Note: The results when both ε₂ and ε₃ are Uniform are shown in Table 1 and are omitted here.

Note: The results when both ε₂ and ε₃ are Uniform are shown in Table 3 and are omitted here.