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When using multiple imputation, users often want to know how many imputationsthey need. An old answer is that 2 to 10 imputations usually suffice, but thisrecommendation only addresses the efficiency of point estimates. You may needmore imputations if, in addition to efficient point estimates, you also wantstandard error (SE) estimates that would not change (much) if you imputed thedata again. For replicable SE estimates, the required number of imputationsincreases quadratically with the fraction of missing information (not linearly,as previous studies have suggested). I recommend a two-stage procedure in whichyou conduct a pilot analysis using a small-to-moderate number of imputations,then use the results to calculate the number of imputations that are needed fora final analysis whose SE estimates will have the desired level ofreplicability. I implement the two-stage procedure using a new Stata commandcalled how_many_imputations (available from SSC) and a new SAS macro called%mi_combine (available from the website missingdata.org).

How many imputations do you need? A two-stage calculation using a quadratic rule