From where is initial value drawn in Multivariate Imputation by Chained Equations (_mice_)? Based on documentation on mice from Van Buuren & Groothuis-Oudshoorn (2011)--
 Starting from an initial imputation representing a value from observed data, the mice algorithm draws imputations by iterating over conditional densities.
My question: does this initial value come from any variable in the dataset? Or does it come from observed data from the variable to be imputed?
 A: The documentation for the mice() function in the mice package says the following for the data.init argument:

data.init
  A data frame of the same size and type as data, without
  missing data, used to initialize imputations before the start of the
  iterative process. The default NULL implies that starting imputation
  are created by a simple random draw from the data. Note that
  specification of data.init will start all m Gibbs sampling streams
  from the same imputation.

So it seems that the user can supply the initial values themself, or the algorithm will take a random draw from the observed data. 
The documentation doesn't actually answer your question because you're asking whether the random draw for a missing value for a given variable can come from any observed value of any variable in the dataset. Clearly that would make no sense. If you have income in $ and age in years in the data and they both have missing values, the algorithm will not use a random draw from the income variable to initialize a missing value for the age variable because the income values are wildly out of the range of the age variable. The only thing that makes any sense is for the initialization value to come from the same variable. 
Indeed, digging through the source code of mice indicates this. When data.init is NULL, mice uses mice.impute.sample() to initialize the imputation. This takes a simple random sample of the variable to be imputed.
