I just have a quick question to check that I am correctly interpreting the output of a multilevel model I have run using BRMS. The formula for the model is:

Outcome ~ 1 + Session + Session:Condition + (1 + Session | gr(PPN, by = Condition))

With this model, I obtain the following output (the precise numbers are not relevant):

Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat

sd(Intercept:Condition1) 0.48 0.11 0.31 0.73 2731 1.00

sd(sessions2:Condition1) 0.62 0.12 0.43 0.89 2525 1.00

sd(sessions3:Condition1) 0.71 0.14 0.48 1.04 2986 1.00

sd(sessions4:Condition1) 0.77 0.15 0.53 1.10 3070 1.00

sd(Intercept:Condition2) 0.42 0.06 0.31 0.57 2695 1.00

sd(sessions2:Condition2) 0.55 0.08 0.41 0.72 2778 1.00

sd(sessions3:Condition2) 0.57 0.08 0.44 0.74 2674 1.00

sd(sessions4:Condition2) 0.61 0.08 0.47 0.79 2915 1.00

What I wanted to check is that the sd terms for sessions2, sessions3, and sessions4 are not themselves sd terms, but rather deviations from the intercept sd. Is that correct?

For example, in order to calculate the sd for sessions2 in Condition 1, I would not just take the estimate sd(sessions2:Condition1). Instead, I should add together the posterior distributions of the intercept sd(Intercept:Condition1) and sd(sessions2:Condition1), and then make an estimate from the result.

This is quite important to understand, because if the values of the sd parameters must be combined, then it seems clear that the sds for the later sessions are higher than for the intercept (which makes sense, as people respond differently to a treatment, but are quite similar to one another at the start). On the other hand, if the sds for the later sessions are just direct estimates of the the session sds (rather than deviations from the intercept sd), the interpretation is quite different.

Have I understood the sd parameters correctly?

All the best,

Jamie

Please also provide the following information in addition to your question:

- Operating System: MacOS 10.12.06
- brms Version: 2.8.0