Great, thank you, also for the nice example.
I haven’t really gotten behind what this is actually doing (am not very familiar with stan yet). Looking at the complete stan code, it seems that J_1 contains which subject is associated to row n (‘grouping indicator per observation’). r_1_1 I assume is then the equivalent of the \mathbf{u} vector, but what is Z_1_1 then (‘group-level predictor values’)?
Also, checking brm_model$fit, it seems that there are some individual intercepts (r_subject[1,Intercept] etc.):
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
b_Intercept -0.07 0.13 2.33 -5.15 -1.15 -0.09 1.00 5.04 313 1.01
b_b1 -0.07 0.03 0.86 -1.99 -0.50 -0.07 0.39 1.62 1116 1.00
b_b2 0.66 0.05 1.97 -3.56 -0.34 0.68 1.74 4.61 1316 1.00
b_b3 0.78 0.04 1.59 -2.57 -0.04 0.78 1.68 3.73 1292 1.00
sd_subject__Intercept 3.25 0.19 3.19 0.11 1.07 2.24 4.33 11.30 289 1.01
sigma 2.45 0.05 1.30 1.08 1.61 2.12 2.90 5.91 670 1.01
Intercept 0.28 0.14 2.23 -4.26 -0.69 0.25 1.21 5.17 264 1.02
r_subject[1,Intercept] -0.76 0.16 2.67 -6.80 -1.86 -0.46 0.34 4.40 287 1.01
r_subject[2,Intercept] -0.20 0.13 2.48 -6.30 -1.14 -0.03 0.83 4.83 344 1.01
r_subject[3,Intercept] 0.78 0.13 2.65 -5.20 -0.37 0.41 1.90 6.75 388 1.01
lp__ -32.53 0.15 3.33 -40.15 -34.45 -32.07 -30.18 -26.97 519 1.02
Do you know how to interpret those and how they are related to sd_subject__Intercept, and should they be included in the equation?