The mice package provides an alternative approach to imputation, being based on a Bayesian procedure without assuming multivariate normality. The approach used by mice relies upon a procedure known as "chained equations". The basic operation goes as follows:
Some preliminary starting imputation values are filled in for all missing data.
The imputation starts for some particular variable, which we will call X. Starting imputation values are removed from X and missing data in X is, once again, treated as missing. Preliminary imputations are left in place of all other variables. Observed elements of X are regressed on, or somehow matched to the other variables (values of these other variables may be observed or imputed). Based on this regression or matching, the missing values of X are filled in.
Step 2 is then repeated for the next variable in line Y. Step 2 is then repeated for variable Z, and this goes on until the imputation has been done for all variables.
Steps 2 and 3 are...