title: Fraction of Missing Information (γ) at Different Missing Data Fractions in the 2012 NAMCS Physician Workflow Mail Survey.
abstract: In his 1987 classic book on multiple imputation (MI), Rubin used the fraction of missing information,γ, to define the relative efficiency (RE) of MI as RE = (1 +γ/m)-1/2, wheremis the number of imputations, leading to the conclusion that a smallm(≤5) would be sufficient for MI. However, evidence has been accumulating that many more imputations are needed. Why would the apparently sufficientmdeduced from the RE be actually too small? The answer may lie withγ. In this research,γwas determined at the fractions of missing data (δ) of 4%, 10%, 20%, and 29% using the 2012 Physician Workflow Mail Survey of the National Ambulatory Medical Care Survey (NAMCS). Theγvalues were strikingly small, ranging in the order of 10-6to 0.01. Asδincreased,γusually increased but sometimes decreased. How the data were analysed had the dominating effects onγ, overshadowing the effect ofδ. The results suggest that it is impossible to predictγusingδand that it may not be appropriate to use theγ-based RE to determine sufficientm.
authors.affiliation: National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, USA.
authors.forename: Qiyuan
authors.initials: Q
authors.lastname: Pan
authors.affiliation: National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, USA.
authors.forename: Rong
authors.initials: R
authors.lastname: Wei
keywords: Fraction of Missing Information (γ); Missing Data; Multiple Imputation; NAMCS; Sufficient Number of Imputations