How does combine in BRMS work?


Just wondering, how does combine_models work? Is it pooling the models, according to Reuben’s rule?

Many thanks

The samples from the posterior distributions from each fit to each imputed dataset are simply pooled - that is, all the samples from the separate models are just extracted and combined together. The combined posteriors are then subsequently summarised or processed asusual. There is no need for Rubin’s rules, which are only relevant when summarising multiply imputed results from frequentists stats where a point estimate and SE is the result from each fit to each imputed dataset

From the brms vignette on missing data (Handle Missing Values with brms): “While pooling across models is not necessarily straightforward in classical statistics, it is trivial in a Bayesian framework. Here, pooling results of multiple imputed data sets is simply achieved by combining the posterior samples of the submodels.”

Please also see my response to your previous post (How to pool BRMSfit imputed data, Mice not appropriate - #2 by AGranholm).

(Of note, using Rubin’s rule on summary statistics from the posteriors - i.e. means and SDs - would probably work OK as an approximation if the posteriors are normally distributed, but there is no need for an approximation that may not always be correct, as directly pooling the samples is easier).

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