I’d like to incorporate the standard errors for the response/outcome variable into the analysis through rstanarm, but I could not find any information as to how to do that in stan_lmer(). Could someone point me to the right direction? Thanks!

My guess is that it is not currently possible. You mean that the outcome variable is measured with error whose standard deviations are known?

Yes, it’s pretty much like meta analysis. Any possibility to implement it in the future?

Some. But meta-analysis isn’t very Bayesian when you only have estimates of the means and standard deviations and have to treat them as knowns.

It would be ideal if the analysis can be performed on the original data. However, sometimes the original data are not directly available, and we would have to deal with the summarized data. Even the famous eight-school data frequently mentioned in the Bayesian community is such a scenario, isn’t it?

Yes, 8 schools is an example of that but it still isn’t good.

I agree with this, but it does raise the question of what exactly we want to recommend to people who are in this situation (I think it’s a pretty common situation, unfortunately). When only the estimates from previous studies are available, I would think that an 8-schools style model using Stan would at least be better than the alternatives.

I would say they have to do it in Stan directly or maybe `brms::brm`

. Basically, you have to model the estimation process in the underlying studies and that would generally be hard to do with pre-compiled functions.

And yet Andrew continues to use 8 schools, which has exactly this meta-analytic flavor, as the standard example of Bayesian hierarchical modeling (which always confuses me and I think makes a terrible first example precisely becuase of the meta-analytic flavor making it hard to understand for non-statisticians). Of course, getting the originl data is preferable when avaialble, because then you can model it directly, including measurement error processes.