Difference between "within" and "between" variance in multiple imputation What do is within-variance and between-variance  mean in multiple imputation?
I need some illustration.
 A: You can think of the within-variance $W$ and between-variance $B$ in multiple imputation as the between and within groups variation in ANOVA but the total variance $T$ is NOT equal to the sum of the within-variance and between-variance( $T \neq W+B$ )that would be correct only if we have infinite number of imputations $m$ i.e ($T_{\infty} = W_{\infty}+B_{\infty}$)so that we have to modify the latter equation to let the multiple imputation work with low values of $m$ and since in multiple imputation our estimate $\bar\theta$ is a combined estimate of the estimates stem from the $m's$ repeated imputation and the imputed values are sampled form a distribution reflect our uncertainty about the missing values which is the posterior predictive distribution this implies we can add a simulation variance term such that $T = W+B+B/{\infty}$ so that $B$ approximate $B_{\infty}$ so in summary we have three sources of variance :


*

*Within variance which is the conventional statistical measure of variability

*Between variance  caused by the missing values 

*$B/{\infty}$ simulation variance .

