set.seed(0)
data <- brm_data(
  data = brm_simulate_simple()$data,
  outcome = "response",
  role = "response",
  group = "group",
  time = "time",
  patient = "patient",
  reference_group = "group_1",
  reference_time = "time_1"
)

brm_formula_sigma(data) # heterogeneous
# sigma ~ 0 + AVISIT
# attr(,"brm_allow_effect_size")
# [1] TRUE
# <environment: 0x144d60588>
brm_formula_sigma(data, time = FALSE, intercept = TRUE) # homogeneous
# sigma ~ 1
# attr(,"brm_allow_effect_size")
# [1] TRUE
# <environment: 0x16f95e5f8>
brm_formula_sigma(
  data,
  time = TRUE,
  group = TRUE,
  subgroup = TRUE,
  covariates = TRUE
)
# sigma ~ 0 + ARMCD + SEX + AVISIT + RACE
# attr(,"brm_allow_effect_size")
# [1] FALSE
# <environment: 0x145407fe0>

brm_formula(
  data = data,
  sigma = brm_formula_sigma(
    data,
    time = TRUE,
    group = TRUE,
    subgroup = TRUE,
    covariates = TRUE
  )
)
#> FEV1 ~ ARMCD + ARMCD:SEX + ARMCD:SEX:AVISIT + ARMCD:AVISIT + SEX + SEX:AVISIT + AVISIT + RACE + unstr(time = AVISIT, gr = USUBJID) 
#> sigma ~ 0 + ARMCD + SEX + AVISIT + RACE