# Missing rates and multiple imputation

Is there a limit which is the least acceptable when using multiple imputation (MI)?

For example can I use MI if the missing values in a variable are the 20% of the cases while and other variables have missing values but not to such a high level?

• I wouldn't consider 20% very high, so I'm sure the answer to your second question is yes, although I don't have a rigorous justification. My gut feeling is that the only limit is that which prevents the algorithm from working at all. I vaguely remember seeing a table in Rubin's book showing results for very high rates of missingness. Whether it's worthwhile (as opposed to valid) doing MI with very high rates of missingness is another question. – mark999 Mar 9 '12 at 19:35
• A lot will depend on how much you can assume your missings are missing completely at random. If there is a high percentage of missings and they're not missing at random, you may get biased estimates for the imputation. Because it has to be done on cases present in the data (by definition), where there is a systematic bias in the missing cases the present cases may not be very informative from an accuracy perspective. – Michelle Mar 9 '12 at 21:36
• @mark999 - Thanks for the answer. When the rate of missingness for one variable can be considered as high? Regarding your last question do you have any answer? – Nick Mar 10 '12 at 17:33
• @Michelle - Thank you. Fortunately the hypothesis MAR is quite plausible (and even the MCAR could be considered plausible) – Nick Mar 10 '12 at 17:50
• @Nick: I don't know what should be considered a very high rate, and I don't think it's necessary to put a specific number on it. I don't have an answer to the last question. – mark999 Mar 10 '12 at 21:12

From the comments, you're confident that your in a MAR or MCAR situation. Then multiple imputation is at least reasonable. So how much missingness is tractable? Think of it this way:

Basically, multiple imputation makes all your model parameter estimates less certain as a function of the accuracy with which the missing data can be predicted with your imputation model, which will depend, among other things, on the amount of missing that needs imputing, and the number of imputations you use.

How much is 'too much' missingness therefore depends on how much added variance/uncertainty you are willing to put up with. A useful quantity for you might be the relative efficiency ($RE$) of an MI analysis. This depends on the 'fraction of missing information' (not the simple rate of missingness), usually called $\lambda$, and the number of imputations, usually called $m$, as $RE \approx 1/(1+\lambda/m)$.

Rather than generate the definitions of missing information etc. here, you might simply read the MI FAQ which puts things very clearly. From there you'll know whether you want to tackle the original sources: Rubin etc.

Practically speaking you should probably just try an imputation analysis and see how it works out.

• the FAQ link is broken. Any chance you might have a current one? (it looks useful) – drstevok Apr 4 '17 at 21:31
• Added. Not sure how official it is though. – conjugateprior Apr 4 '17 at 22:18

You might find

Rubin, Donald B. and Nathaniel Schenker. 1986. “Multiple Imputation for Interval Estimation from Simple Random Samples with Ignorable Nonresponse.” Journal of the American Statistical Association 81(394):366–374.