The MI Procedure

Multiple Imputation Efficiency

The relative efficiency (RE) of using the finite m imputation estimator, rather than using an infinite number for the fully efficient imputation, in units of variance, is approximately a function of m and (Rubin 1987, p. 114):

where mis the number of imputations and is the fraction of missing information.

Table 76.7 shows relative efficiencies with different values of m and .

Table 76.7: Relative Efficiencies


m	10%	20%	30%	50%	70%
3	0.9677	0.9375	0.9091	0.8571	0.8108
5	0.9804	0.9615	0.9434	0.9091	0.8772
10	0.9901	0.9804	0.9709	0.9524	0.9346
20	0.9950	0.9901	0.9852	0.9756	0.9662

The table shows that if the fraction of missing information is modest, only a small number of imputations are needed. For example, if , only three imputations are needed to have a 91% efficiency and five imputations are needed to have a 94% efficiency.