New vignette on MAP priors

[wlandau]

This PR adds a new vignette on MAP priors. vigntettes/map.Rmd.source is the true source, and vignettes/map.Rmd is entirely pre-rendered for efficiency.

RBesT makes univariate MAP priors super easy, and thanks to the smooth integration with brms, they're easy to use with brms.mmrm. @andrew-bean and @weberse2, thanks for the example code.

At the end, I added a section on robust multivariate mixture priors. I'm wondering if there's an easier way to do this using gMAP() + automixfit() + robustify() as in the univariate case.

[chstock]

Thank you very much for this vignette, @wlandau, and others for the inspiration and the basis, especially in RBesT. It is excellent that (multivariate) mixture priors can now be used here, and the technical implementation even appears quite straightforward.

[weberse2]

Really nice to see this going into brms.mmrm... the RBesT::mixstanvar magic is a bit under the radar of people, but it is quite powerful from my view - so it is great to see this landing here. Just two points: Can you update the tau.prior=1 to follow the recommendations from RBesT vignetts (https://opensource.nibr.com/RBesT/articles/introduction.html). Specifically, one needs to make the scale proportional to sigma (taken usually to be the pooled sampling sd as estimated from the data). The conservative choice is sigma/2, but whenever data is somewhat homogeneous to a level common when selecting data sets for meta-analysis sigma/4 is better, I think.

For the multivariate case you could point out to use brms directly with multiple random effects, for example as demonstrated here: https://opensource.nibr.com/bamdd/src/02ad_meta_analysis_covariate.html#sec-impl-complete-only ... not sure if you want to link that section directly... but a link to https://opensource.nibr.com/bamdd/ and hist data with a covariate you could consider.

The robust component for the multi variate normal should also be a unit information prior... so using sigma here again. The choice of the robust component is a topic (if you make the sigma too large in comparison of the sampling sd, then the robustification is never kicking in).

Last point: The mixstanvar has been written so that the brms function prior can be used; I see that you make people specify the actual code for the prior... fine... I did like the priors functions more, but both works.

Great work!

[weberse2]

Two more small things:

• please do not use sigma = mean(data_historical_visit4$sd), but rather average variances instead
• also ensure that the color code is consistent for the different fits in the two plots (the diffuse fit changes color)

[wlandau]

I really appreciate your comments, @weberse2. Sorry for the long delay in responding. I am starting to look at your comments now.

[wlandau]

please do not use sigma = mean(data_historical_visit4$sd), but rather average variances instead

Fixed in ed2ab34. I used the pooled standard deviation.

[wlandau]

also ensure that the color code is consistent for the different fits in the two plots (the diffuse fit changes color)

Fixed in 855e26a

[wlandau]

Can you update the tau.prior=1 to follow the recommendations from RBesT vignetts (https://opensource.nibr.com/RBesT/articles/introduction.html). Specifically, one needs to make the scale proportional to sigma (taken usually to be the pooled sampling sd as estimated from the data). The conservative choice is sigma/2, but whenever data is somewhat homogeneous to a level common when selecting data sets for meta-analysis sigma/4 is better, I think.

423ee1b sets tau.prior in gMAP() to pooled_external_data_sd / 4 (at most "substantial" study-to-study heterogeneity according to https://opensource.nibr.com/RBesT/reference/gMAP.html#details, which was a really helpful read). The external data I made up for the univariate MAP prior (data_historical_visit4) seems relatively homogeneous.

[wlandau]

For the multivariate case you could point out to use brms directly with multiple random effects, for example as demonstrated here: https://opensource.nibr.com/bamdd/src/02ad_meta_analysis_covariate.html#sec-impl-complete-only ... not sure if you want to link that section directly... but a link to https://opensource.nibr.com/bamdd/ and hist data with a covariate you could consider.

Yes, the evidence synthesis piece is really important here. Referenced in b8ea816.

[wlandau]

The robust component for the multi variate normal should also be a unit information prior... so using sigma here again. The choice of the robust component is a topic (if you make the sigma too large in comparison of the sampling sd, then the robustification is never kicking in).

Since that section doesn't conduct any data synthesis, I'm not sure we have access to to sigma (unless we're constructing a MAP prior from a single historical study). But b96fdf7 does restate the general recommendation.

[wlandau]

Last point: The mixstanvar has been written so that the brms function prior can be used; I see that you make people specify the actual code for the prior... fine... I did like the priors functions more, but both works.

I mildly prefer the consistency and predictability of having a single input type for the code argument of brm_prior_label(), but we could weigh the pros and cons in another thread if you decide you have strong feelings about this.

[wlandau]

Thanks again @chstock and @weberse2 for your insightful feedback. I believe I have addressed your comments so far. Please let me know if you have more.

It would be great to merge this on April 15 when the brms.mmrm team next meets.