The MIANALYZE 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 ${\lambda }$ (Rubin, 1987, p. 114):

$\mr {RE} = (1 + \frac{\lambda }{m})^{-1}$

Table 58.2 shows relative efficiencies with different values of m and ${\lambda }$ .

Table 58.2: Relative Efficiencies

	$\blambda$
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 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 m imputations and checking whether the estimates are stable between sets (Horton and Lipsitz, 2001, p. 246).