Using brms, I have fitted 2 linear Bayesian regression models of a response variable A with each 4 binary and one real valued (standardized) parameters (i.e. A ~ b_1 + b_2 + b_3 + b_4 + r). One of the models includes a population level effect (1|user_id). The models are fitted each on a different data set, but both using a log-normal distribution family. I haven’t specified priors, i.e. non-informative default priors were used. Using brms::pp_check, the models seem to (optically) fit well to the data.
My objective is now to quantify for each of the models, how the response A changes when a certain binary variable is true/false. An example is presented here: https://bayesat.github.io/lund2018/slides/andrey_anikin_slides.pdf (from page 29), where contrasts between corpora are estimated from MCMC samples. I basically want to do the same but for each of my parameters, i.e. “What change can be expected in A when p_1 is true/false”.
My idea was to use the MCMC samples, i.e. the posterior distribution, from brms::posterior_samples. For each sample, I get estimates of the log-normal distribution parameters for intercept and the binary variable I am interested in. However, I am interested in the real value of A, which could be the mean/median/mode of the log-normal distribution, calculated from the distribution parameters. What I tried at first is to estimate the median of the log-normal distribution, i.e. med = exp(mu), for the certain binary parameter at every MCMC sample, and then plot a histogram of all the values. The distribution looks reasonable but I am not sure if taking the median of each sample is valid, or taking mean/mode would be a better choice.
How would you recommend to do that? Does this sound like a common procedure that I am not yet aware of?
I noticed a similar output when using brms::pp_check with stat type “_grouped”, and specifying the binary variable which I want to show the contrast for. The resulting plot shows what I am trying to reconstruct, however, for fitted/predicted samples.
- Operating System: Ubuntu 16.04 LTS
- brms Version: 2.6.0