Determining Sufficient Number of Imputations Using Variance of Imputation Variances: Data from 2012 NAMCS Physician Workflow Mail Survey*

How many imputations are sufficient in multiple imputations? The answer given by different researchers varies from as few as 2 - 3 to as many as hundreds. Perhaps no single number of imputations would fit all situations. In this study, η, the minimally sufficient number of imputations, was determined based on the relationship between m, the number of imputations, and ω, the standard error of imputation variances using the 2012 National Ambulatory Medical Care Survey (NAMCS) Physician Workflow mail survey. Five variables of various value ranges, variances, and missing data percentages were tested. For all variables tested, ω decreased as m increased. The m value above which the cost of further increase in m would outweigh the benefit of reducing ω was recognized as the η. This method has a potential to be used by anyone to determine η that fits his or her own data situation.