PROC MI: Multiple Imputation Efficiency :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The MI Procedure

Multiple Imputation Efficiency

The relative efficiency (RE) of using the finite $\text{[math]}$ imputation estimator, rather than using an infinite number for the fully efficient imputation, in units of variance, is approximately a function of $\text{[math]}$ and $\text{[math]}$ (Rubin 1987, p. 114):

$\text{[math]}$

Table 54.5 shows relative efficiencies with different values of $\text{[math]}$ and $\text{[math]}$ .

Table 54.5 Relative Efficiencies
$\text{[math]}$
$\text{[math]}$	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 for situations with little missing information, only a small number of imputations are necessary. In practice, the number of imputations needed can be informally verified by replicating sets of $\text{[math]}$ imputations and checking whether the estimates are stable between sets (Horton and Lipsitz 2001, p. 246).

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