Hey! I’m also no `brms`

expert.

However, I think conceptually, you’d want to do something like this:

```
bf(
cum_cases ~ logA - exp(-(exp(logk) * (day_norm - exp(logdelay)))),
logA ~ 1 + (1 | ID | Country.Region),
logk ~ 1 + (1 | ID | Country.Region),
logdelay ~ 1 + (1 | ID | Country.Region),
nl = TRUE
)
```

In the model above there are 2 problems, I think:

- You’ve put a lognormal prior on the common mean of
`A`

, `k`

, and `delay`

. This ensures that the common mean is positive, however, the parameters could still be negative due to the random effect structure. To ensure positivity on the varying parameters, I think you have to wrap them in `exp`

and define everything on the log scale.
- The lognormal “identity” link is essentially a log-link. So i think you
*do* have to take the log of the mean formula if you’re using `family = lognormal()`

.

```
case_counts$Country.Region <- as.factor(case_counts$Country.Region)
case_counts$day_norm <- case_counts$day/max(case_counts$day)
form_mult2 <-
bf(
cum_cases ~ logA - exp(-(exp(logk) * (day_norm - exp(logdelay)))),
logA ~ 1 + (1 | ID | Country.Region),
logk ~ 1 + (1 | ID | Country.Region),
logdelay ~ 1 + (1 | ID | Country.Region),
nl = TRUE
)
mult_priors2 <- c(
prior(normal(0, 1), nlpar = "logA", lb = 0),
prior(normal(0, 0.5), nlpar = "logk", lb = 0),
prior(normal(0, 0.5), nlpar = "logdelay", lb = 0),
prior(normal(0, 1), class = "sigma"),
prior(
normal(0, 2.5),
class = "sd",
group = "Country.Region",
nlpar = "logA"
),
prior(
normal(0, 1),
class = "sd",
group = "Country.Region",
nlpar = "logk"
),
prior(
normal(0, 1),
class = "sd",
group = "Country.Region",
nlpar = "logdelay"
)
)
modmult2 <- brm(
form_mult2,
data = case_counts,
prior = mult_priors2,
seed = 1234,
family = lognormal(),
chains = 4,
cores = 4,
sample_prior = "no",
control = list(adapt_delta = 0.95, max_treedepth = 15)
)
conditions <- make_conditions(case_counts, "Country.Region")
plot(
conditional_effects(
modmult2,
conditions = conditions,
re_formula = NULL
),
points = TRUE,
facet_arg = list(scales = "free")
)
```

This runs with only a couple of divergences for me (around ~3 divergences; the model runs slooooooow, though). However, the fit seems not so different from what you have posted. The parameters are obviously fairly correlated – especially, `logk`

and `logdelay`

. I’m afraid the (unsatisfactory) answer here could be that the folk theorem of statistical computing comes into play here: the model is probably not so great… :/ But maybe I’m missing something…