# Multiple imputations via MICE package: is there an upper limit for number of imputations?

When performing mulitple imputations with the MICE package in R, I found some resources (http://www.statisticalhorizons.com/more-imputations) that recommend around 10 imputations. I was wondering if there is any drawback of e.g. performing 1000 or 10000 imputations as it should lead to more precise results and is computationally easily feasible?

The governing equation is $$T_m = (1 + \frac{\gamma}{m})T_{\infty}$$ where $T_m$ is the variance estimate for the imputation with m imputed datasets, $T_\infty$ is the theoretical optimal case of an infinite number of different imputations and $\gamma$ is the rate of missing information. In the case of a single variable without covariates $\gamma$ is actually equal to the fraction of missing values. With covariates and missing values in more than one variable it is a bit more complicated.
Now, for a $\gamma$ of say 30% you get $$T_{10}=1.03T_{\infty}$$ which is already quite close. Since this is the variance your confidence interval for your estimates would then be larger than the theoretical optimal case by a factor of $\sqrt{1.03}$. This additional error is very small and shows that it is not often worth imputing many more times.