Lognormal brms model: looking correlations between its re-parametrized estimates (median and SD)?

[StaffanBetner]

@martinmodrak

When speaking about “reparametrization” we usually don’t mean transforming estimates. We mean changing the model internals to work on a different scale - e.g. when you transform your estimates as above, the priors still work on the log scale. You could use the custom_family feature to make the model (priors, predictors, …) work on the natural scale (Define Custom Response Distributions with brms • brms). Although in this specific case I don’t think this would be worth the effort.

A custom family for brms with natural scale reparametrization is available here: Modelling sigma - #6 by StaffanBetner

The only that is missing in that comment is the init = "0" statement, which seems to be needed.

@martinmodrak

If you only need the estimates for the median/sd/… those can be extracted directly from the brms fit: you can use posterior_linpred to get mu estimates for each row in your dataset (or use newdata to only include cases you care about). You can then use posterior_linpred( ..., dpar = "sigma") to get samples for the sigma parameters. You can then apply any transformations you need to get posterior samples of the desired quantities. If I understand correctly what you are showing in the “auto correlation” plot (is each dot a region?), this is IMHO not an issue - you have let each region has its own distribution, so the model has all the flexibility it needs, so the plot really shows just what your data include (i.e. I believe the plot would look very similar if you used the raw data to calculate it).

One alternative might be to use random intercepts with correlation between mu and sigma, to estimate the correlation within the model.