IMPUTE: number imputations recommended by Hershberger and Fisher

[Howells, William]

I came across a note from Hershberger and Fisher on the number of imputations (citation below), where they conclude that a much larger number of imputations is required (over 500 in some cases) than the usual rule of thumb that a relatively small number of imputations is needed (say 5 to 20 per Rubin 1987, Schafer 1997).  They argue that the traditional rules of thumb are based on simulations rather than sampling theory.  Their calculations assume that the number of imputations is a random variable from a uniform distribution and use a formula from Levy and Lemeshow (1999) n >= (z**2)(V**2)/e**2, where n is the number of imputations, z is a standard normal variable, V**2 is the squared coefficient of variation (~1.33) and e is the “amount of error, or the degree to which the predicted number of imputations differs from the optimal or “true” number of imputations”.  For example, with z=1.96 and e=.10, n=511 imputations are required.    I’m having difficulty conceiving of the number of imputations as a random variable.  What does “true” number of imputations mean?  Is this argument legitimate?  Should I be using 500 imputations instead of 5?    Bill Howells, MS Behavioral Medicine Center Washington University School of Medicine St Louis, MO   Hershberger SL, Fisher DG (2003), Note on determining the number of imputations for missing data, Structural Equation Modeling, 10(4): 648-650.    http://www.leaonline.com/loi/sem