`brms`

is one of the best ways of fitting multi membership, multi-level models. I have a multi membership, multi-level problem that I’m trying to tackle, but could do with a second opinion on best practice when it comes to including random slopes.

Imagine a case where we want to estimate the following model in `brms`

:

```
y ~ 1 + x + (1 + mmc(x1, x2, x3) | mm(g1, g2, g3, weights = cbind(w1, w2, w3), scale = F))
```

Here, we have some outcome, `y`

, that we expect to vary according to `x1`

, `x2`

, `x3`

, but we also expect their effect to vary over the three multi-membership groups (`g1`

, `g2`

, `g3`

), which we in turn assume to be weighted according to weights `w1`

, `w2`

, `w3`

and for these groups *not* to be scaled to sum to 1 within each case.

My question is, in this case, how do we include the main effect of `x`

when we in fact have only the variables `x1`

, `x2`

, and `x3`

in the data?

I have discussed this in the past with @paul.buerkner and his recommendation was to create a new variable, `x`

, that is the mean of `x1`

, `x2`

, `x3`

. But that was in the context of equal weights and `scale = T`

. Am I right in thinking that where the data *are not* scaled and *are* weighted, one should compute the weighted average of `x1`

, `x2`

, and `x3`

to include as the main effect instead?