Looking for More Information on Imputation During Model Fitting

I want to learn more about imputation during model fitting after reading the vignette “Handle Missing Values with brms” by @paul.buerkner . I’ve been brainstorming strategies for specifying a type of multilevel model that is not yet offered as an imputation model option in standard software, and it sounds like imputation during model fitting may be the answer I’ve been looking for.

Does anyone know where I can find more information on imputation during model fitting? I’m hoping for scholarly articles and ideally a simulation study comparing multiple imputation to this so-called “‘one-step’ approach”, but I don’t know what to search for since this is the first time I’m hearing of imputation during model fitting.

Thank you for taking the time to read this topic!

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Hi, a good read would be the 2nd edition of Statistical Rethinking by Richard McElreath (Chapter 15). Not only does he cover imputation during model fitting, he also discusses imputation of binary data (0/1).


That was great. Thank you for the recommendation. Would you say that you’ve seen imputation during model fitting referred to as “Bayesian imputation”? That’s what McElreath seems to refer to it as, but searching for “Bayesian imputation” in the literature just pulls up examples of multiple imputation, which of course make sense given that multiple imputation is Bayesian.

Yes, he calls it Bayesian imputation. I would argue that multiple imputation is not needed nor wanted when doing Bayesian modeling.

Bayesian imputation appeals to me because I’m not quite as limited in the type of imputation model I can specify (like I am with standard MI software options).

I noticed in the comments of another topic that you mention one may have to choose MI over Bayesian imputation when values are missing for discrete variables and when computation power is lacking.

My follow-up questions are:
(1) Do you know of other times when MI may be desirable over Bayesian imputation (when doing Bayesian modeling)?
(2) Do you have any thoughts on what the best strategy is for specifying imputation models unavailable in standard MI software options when Bayesian imputation is infeasible?

Thank you for taking the time to chat with me. I’ve already learned a lot.

No. And I would say that even with discrete variables MI is not needed.

Build a Directed Acyclic Graph encoding your assumptions regarding the missingness. McElreath has great examples regarding this in Chapter 15.