I would like to explore a non-linear transformation \frac{Emax*X}{EC50+X} of my predictor X in a logistic regression problem. I tried the below but something seems off when I plot the model. Happy for any assistance.

```
set.seed(666)
pk = seq(0,100, length.out = 50)
data <- tibble('pk' = pk,"pd" = response) %>%
mutate(response = ifelse(pk >50, rbinom(n(), c(0,1), c(0.1,0.9)),
rbinom(n(), c(0,1), c(0.7,0.3))))
inv_logit <- function(x) 1 / (1 + exp(-x))
fit_1 <- brm(
bf(response ~ inv_logit(int + Emax*pk/(EC50 + pk)) ,
int~1, Emax ~ 1,EC50 ~1, nl = TRUE),
data = data, family = bernoulli("identity"),
prior = c(
prior(beta(1, 1), nlpar = "int", lb = 0, ub = 1),
prior(normal(0.8, 0.1), nlpar = "Emax"),
prior(normal(50, 10), nlpar = "EC50")
)
)
```

Now the output of this model looks reasonable

```
Family: bernoulli
Links: mu = identity
Formula: response ~ inv_logit(int + Emax * pk/(EC50 + pk))
int ~ 1
Emax ~ 1
EC50 ~ 1
Data: data (Number of observations: 50)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 4000
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
int_Intercept 0.07 0.07 0.00 0.25 1.00 3024 1746
Emax_Intercept 0.74 0.10 0.55 0.94 1.00 3493 2716
EC50_Intercept 54.30 9.44 36.45 73.02 1.00 3514 2758
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
```

But when I plot the model

```
plot(conditional_effects(fit_1), points = TRUE)
```

It looks off. Am I missing something?