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Is the missForest package a special case of MICE using Random Forest as imputation (for just a single imputation)?

The missForest algorithm is described here: https://academic.oup.com/bioinformatics/article/28/1/112/219101 (chapter 2) The MICE algorithm here: https://stefvanbuuren.name/fimd/sec-FCS.html (chapter 4.5.2)

To me both approaches look pretty similar (or even the same?). missForest does a sorting of the variables to be imputed by amount of missings first and (as far as a i know) MICE uses the order in which variables are supplied to the function, but other than that i can't see any differences?

It would be great if somebody could confirm or disprove my thoughts (and point out the differences of the two approaches in case).

This is just a question of interest. I am not having a usecase for data imputation in mind yet.

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