Below is my model specified through `brms`

with a `log-normal`

likelihood:

```
m <- brm(bf(y ~ 1+(0+groupA | id) + (0+groupB | id),
sigma ~ 0+group),
data=mydata, family=lognormal, chains = 4, iter=1000)
```

The output of `summary(m)`

is shown below:

```
Family: lognormal
Links: mu = identity; sigma = log
Formula: y ~ 1 + (0 + condition | id)
sigma ~ 0 + condition
...
Group-Level Effects:
~id (Number of levels: 6917)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(groupA) 0.08 0.00 0.08 0.08 1.01 560 999
sd(groupB) 0.11 0.00 0.11 0.11 1.00 655 1075
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 3.19 0.00 3.19 3.19 1.00 1982 1679
sigma_groupA -2.19 0.01 -2.21 -2.16 1.00 730 1324
sigma_groupB -2.54 0.02 -2.58 -2.50 1.00 647 1492
```

To understand the output above, I want to convert the values back to the original scale. For the population-level intercept below, I think I should exponentiate the result:

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 3.19 0.00 3.19 3.19 1.00 1982 1679
```

However, I’m not sure about the following two population-level standard errors:

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma_groupA -2.19 0.01 -2.21 -2.16 1.00 730 1324
sigma_groupB -2.54 0.02 -2.58 -2.50 1.00 647 1492
```

Should I double-exponentiate them like below?

```
exp(exp(-2.19))=1.12
exp(exp(-2.54))=1.08
```

Similarly, I’m not sure how to convert two group-level standard errors either:

```
Group-Level Effects:
~id (Number of levels: 6917)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(groupA) 0.08 0.00 0.08 0.08 1.01 560 999
sd(groupB) 0.11 0.00 0.11 0.11 1.00 655 1075
```