## Summary

- I’d like to model the group-level variance of a random coefficient as a function of other group-level variables.
- I know I can model
`sigma`

as a function of other variables. But cannot see how to model the random slope as well.

Adapting the `fit_rent2`

example from Bürkner (2018), suppose we have a model:

```
library(brms)
data("rent99", package = "gamlss.data")
bform <- bf(rentsqm ~ area + (area | district),
sigma ~ area + (1 | district))
m1 <- brm(bform,
data = rent99,
chains = 4, cores = 4)
```

What I’d like is something like:

```
bform <- bf(rentsqm ~ area + (area | district),
sigma ~ (1 | district),
---> sigma[area] ~ district) <---
m2 <- brm(bform,
data = rent99,
chains = 4, cores = 4)
```

`sigma`

allows modelling of the group-level intercept. In theory, ** sigma[area]** would allow modelling of the random slope for

`area`

.Is anything like this possible?

## Motivation

I may be confusing things, so to explain the motivation:

- We have a continuous outcome
`y`

that we relate to a binary covariate`x1`

. - We allow a group-level intercept for
`y`

and a group-level coefficient for`x1`

. - The effect of
`x1`

on`y`

is larger for some individuals than others. - We want to consider what other variables explain this variation (e.g.
`x2`

).

So, the thinking was to model predictors of the group-level coefficient for `x1`

, as suggested above (`sigma[x1] ~ x2`

). A positive coefficient for for `sigma[x1]_x2`

would mean that the effect of `x1`

on `y`

is larger for individuals with greater `x2`

.

It’s entirely possible I’m missing something obvious, have the wrong approach and/or question. Any suggestions would be gratefully received.

- Operating System: Arch Linux x86_64
- brms Version: 2.16.1