TITLE:
Fraction of Missing Information (γ) at Different Missing Data Fractions in the 2012 NAMCS Physician Workflow Mail Survey
AUTHORS:
Qiyuan Pan, Rong Wei
KEYWORDS:
Multiple Imputation, Fraction of Missing Information (γ), Sufficient Number of Imputations, Missing Data, NAMCS
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.10,
June
15,
2016
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, where m is the number
of imputations, leading to the conclusion that a small m (≤5) would be
sufficient for MI. However, evidence has been accumulating that many more
imputations are needed. Why would the apparently sufficient m deduced from the
RE be actually too small? The answer may lie with γ. In this research, γ was
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). The γ values were strikingly small, ranging in the order of
10?6 to 0.01. As δ increased, γ usually increased but sometimes decreased. How
the data were analysed had the dominating effects on γ, overshadowing the
effect of δ. The results suggest that it is impossible to predict γ using δ and
that it may not be appropriate to use the γ-based RE to determine sufficient m.