Question about coding of the variation in a BRMS model:

I have built a hierarchical model; the data format is that for each participant I have about 50 measurements. I want to allow their mean and variation to vary for each participant (and the mean also to vary between groups).

I have coded it like this:

```
bf(y ~ 1+ group + (1|ID), sigma ~ group + (1|ID)
```

I hope this looks ok.

I am a bit unsure what the equivalent model for a single subject would be? I’ve tried two options:

```
[1] bf(y ~ 1, sigma ~1)
```

or:

```
[2] y ~ 1
```

I thought that these models would be equivalent for a single subject. But I don’t think they are. For example, for one participant I get as outputs

for model [1]:

Population-level effects:

Intercept - estimate: 4.75

sigma_intercept - estimate: 0.91

for model [2]:

Population level effects

Intercept - estimate: 4.75

family specific parameters:

sigma: 2.51

→ So, the intercept is the same, but I’m not sure how to map the two sigma values onto each other?

When I simulated the ‘y’ values to test my model (in fact they are parameters that then get used in a more complicated decision-making model), I use:

```
rnorm(mean=subject.mean, sd= subject.sd); I’m assuming this is equivalent to model [2]?
```

I would be very grateful for any pointers

Jacquie