stan_lmer prints out its summary giving the means and sd for the parameters rather than medians and mads as may be more frequent in Bayesian analysis. The documentation notes that the printed sds are estimated from the mads to produce a “robust” estimate of the sd. I assume that this print out is designed to look as much as possible like the output of lme4::lmer to reassure frequentists using a Bayesian procedure. But as discussed by CDEager at https://github.com/stan-dev/rstanarm/issues/189, there is some inconsistency in mixing means and medians. (While a weighted mean of subset means is a mean of the whole set, a median of subset medians is not necessarily a median of the whole set.) Of course, since the entire set of draws is available following run of stan_lmer, it is pretty trivial to obtain either means/sds or medians/mads of whatever one wants.
Is there a strong argument for preference for median/mad over mean/sd in Bayesian analyses? Would it be better simply to use the set of draws to compute exactly what I want?
Thanks in advance for any comments/discussion by Bayesians that are more experienced than I.
Larry Hunsicker
I don’t know about a strong argument, but the median always exists in the analytical posterior distribution whereas the mean and / or standard deviation might not. Also, I get the impression that when frequentists see a point estimate they tend to rationalize that “there is an equal chance that the true population parameter is below / above this” even though that is not justified.
But definitely calculate whatever you want from the raw draws.
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