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I've been looking into missing data imputation via multiple imputation chained equations (MICE) and I've yet to come across a discussion of when to use MICE rather than regression to impute data.

Until now, whenever I've needed to impute data, I've been able to create a regression that explains 75-90% of explained variance in variable that I want to impute observations for and predict observations for the missing data.

My predicament now is that I have a variable that I need to impute missing data for and the best model I can come up with only explains 35% of the variance in the available observations.

My question is how can imputation via MICE perform better than just using regression since MICE is based on "chained" regression techniques of the variables within the data set? In other words, isn't the accuracy of MICE based on the predictive power of the variables used in the chained equations? Is it simply better because it does many simulations?

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  • $\begingroup$ Imagibe a scenario with two missing values per line, randomly scattered over columns. How do you want to fill the gaps by multiple regressions when there are no complete observations left to train the models? That's e.g. where chaining may provide useful results. $\endgroup$ – Michael M Jul 26 '16 at 15:38
  • $\begingroup$ OK, so is it fair to say that MICE wouldn't produce better results than using a regression in the example I laid out above? $\endgroup$ – RTrain3K Jul 27 '16 at 0:43
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    $\begingroup$ If you don't care much about too small variance in your imputed column, I'd say yes. But you could easily try to fix the variance problem by adding a predictive mean matching step after your regession. $\endgroup$ – Michael M Jul 27 '16 at 5:13

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