Uncertainty in random forest imputations from R missForest package I am in the process of imputing missing values for my data set that contains approximately 20 variables and 3,000 observations. Most of the missing data values are contained in 2 of the variables (one has about 20% missing data, and the other 40%). 
I have already explored using MICE for the imputations. However, my main analytical model has extensive non-linearity and I will ultimately be using generalized additive models in my analysis so that I can fit non-parametric smooth terms. Unfortunately MICE does not lend itself to using GAMs. 
I have thus decided upon using random forest imputations, which seem to produce valid imputations. The missForest package in R seems relatively straightforward and easy to use. I was able to get my imputations and the out of bag error was relatively low. However, it only produces one imputed data set. 
Is it now valid to perform all of my subsequent analyses on this one data set? My concern is that the subsequent analyses will not take into account the uncertainty in the imputations. Is this a legitimate concern? If so, is there anything I can do about it? I have not had much luck finding papers about how people analyzed their data after successfully using missForest.
 A: You're correct that understatements of imputation uncertainty is the reason that people use multiple imputation packages like MICE. I can't answer this question for the missForest example in particular, except to observe that by the same token that one might use multiple imputation in estimating a model, I see no reason to not use multiple missForest runs: the trees and bootstrap samples will be different (provided different random seeds), so you can quantify the uncertainty in your imputed data set this way.
It sounds as though you have some strong notions of where and how the variables are related to each other, though, so perhaps a fully Bayesian approach is in order, wherein the modeling of missing data and the estimation of model parameters happens at the same time. One advantage to this approach is that uncertainty at all levels of the model -- parameter estimates and missing data imputation -- are all simultaneously accounted for, whereas in the standard imputation model, missing data is imputed and then models are estimated. The standard "two-stage" approach to imputation and modeling is what gives rise to the understatement of imputation uncertainty in the first place, so the Bayesian method avoids that entirely.
A: Using the mice package, you can conduct multiple imputation using random forest as the underlying modeling method. Modifying the example shown in the mice documentation:
imp <- mice(nhanes,defaultMethod=c("rf","rf","rf"))

This would create 5 imputed datasets, with all missing data, whether continuous or categorical, filled-in via random forest. The problem is how to pool the gam objects with smoothed terms fitted on each imputed dataset. From scanning the mice documentation, it seems that package has functions to pool results from lm, glm, lme, and lmer objects. So for other objects such as gam, the pooling would have to be done by hand, if feasible. So no advantage in this case. It would be the same as generating 5 imputed datasets with missForest and pooling results by hand. 
A: In the paper presenting the missForest package (see Ref below), it is mentioned in the abstract that: "By averaging over many unpruned classification or regression trees, random forest intrinsically constitutes a multiple imputation scheme."
...followed by:"Using the built-in out-of-bag error estimates of random forest, we are able to estimate the imputation error without the need of a test set."
If I understand this right, the OOBerror represent the error accross multiple imputations (so it would include the error of imputed vs observed for individual trees AND the error across different trees ?).
Still, I am not an expert and I think that previous answers for your questions provide a safe way to address your question (by using multiple missForest runs). Depending on the exact meaning of what the authors said in the abstract, I think you should obtain, accross your multiple missForest runs, an error close to the OOBerror of a single run ?
Ref:
Stekhoven, Daniel J., and Peter Bühlmann. "MissForest—non-parametric missing value imputation for mixed-type data." Bioinformatics 28.1 (2011): 112-118.
