Hello,

I am implementing a GLM with a monotonic link growth function, because for my data a generalised sigmoid function, includes all the possible dynamics interesting to me.

( @Bob_Carpenter this is a dummy example that isolates the issue, on real data I am trying applying this link function in the multinomial framework )

( I realise I should use beta prior on data, however I believe that for this dummy example does not make the difference )

```
data {
int<lower = 0> G; // all genes
int<lower = 0> T; // tube
int<lower=0> R; //covariate
vector<lower = 0>[G] y[T]; // RNA-seq counts
matrix[T,R] X; // design matrix
}
parameters {
matrix[R, G] beta; //design matrix
vector<lower=1>[G] k; // amplitude
real<lower=0> sigma; //standard deviation
real<lower=0> k_mu; // prior of amplitude
real<lower=0> k_sigma; // prior amplitude
}
model {
for (t in 1:T)
y[t] ~ normal( inv_logit( X[t] * beta ) .* to_row_vector(k), sigma );
for(r in 1:R) beta[r] ~ normal(0, 5);
k ~ normal(k_mu,k_sigma);
sigma ~ cauchy(0,2.5);
k_mu ~ normal(0,2);
k_sigma ~ normal(0,2);
}
```

**In the case I have a slope != 0**

I have good inference

**In the case I have a slope == 0** the formula

```
inv_logit( X[t] * beta ) .* to_row_vector(k),
```

has multiplicative indeterminability between beta[1] (intercept) and k. Because for a flat line the intercept is confounded with the amplitude k

Is there a good way to avoid this? For xample

- constrain parameters to avoid banana shaped posterior
- use another growth function more stable for Bayesian inference.

Thanks a lot.