# Modelling group-level variance of random slope/coefficient

## 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:

1. We have a continuous outcome `y` that we relate to a binary covariate `x1`.
2. We allow a group-level intercept for `y` and a group-level coefficient for `x1`.
3. The effect of `x1` on `y` is larger for some individuals than others.
4. 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

It sounds like maybe you are asking something similar as on this post?