Discussing Estimates from the brms summary table

In the summary() table of a brms model, are all Estimates directly relative to the Intercept (reference levels) or do we need to add higher-order effects (i.e., interactions) to their base? I believe it’s the former, but I’m curious to check that.

For example, there is a simple model with two factors, two levels each: F1 (A, B) and F2(I, K). The summary table could look like this (and I’ve added the full specification of the respective level combinations):

Effects Full Specs Estimate Est.Error
Intercept [F1(A), F2(I)] 0.00 0.10
F1(B) [F1(B), F2(I)] 0.40 0.26
F2(K) [F1(A), F2(K)] 0.19 0.06
F1(B):F2(K) [F1(B), F2(K)] 0.22 0.20

One does not need to add 0.22 and 0.40 for the F1(B):F2(K) combination? That would not make sense to me.


Hi @striatum, I am not sure with your example because I don’t know how you specified the model. However, the estimated quantities are interpreted exactly as one would with lm()/glm() etc: it all depends on how you specified the contrasts for your categorical variables.

Hi @matti and thanks for pointing that out – correcting. I did not specify contrasts, which means they are default (contr.treatment). Does this help?

And what would happen if I would redefine them to sum coding (contr.sum)?


That’s right treatment contrasts are the default. Maybe something here will help: Contrasts