GLM with growth function - problem of indetermiinability when slope = 0

[stemangiola]

I tried to convert your model to my case (simplified).

I assume from your documentation and discourse reply:

• your targets == my genes
• your regulators == my covariates (I just have one in this example)
• if you have 1 regulator/covariate: relative_weights == [1, 1, …, 1], so we can ignore
• if the sign of the slope is not supposed to not cause non-identifiability issues, regulation_signs is omitted and sd_regulatory_input must exist in the domain -(Inf, Inf)

My basic link function with equation is

inv_logit( intercept + X * beta ) * k

Given all this my model is

data {
	      int<lower = 0> T;                   // tube colleciton of genes for a patient
	      vector<lower = 0>[T] y;          // RNA-seq counts
				vector[T] X;                      // design matrix
	}
	parameters {
	real mean_regulatory_input;
	real sd_regulatory_input;
	real<lower=0> sigma;
	real mean_observed_value;
	}
	transformed parameters {
	  real observed_sd_input = sd(X);
	  real observed_mean_input = mean(X);
		real slope = sd_regulatory_input / observed_sd_input;
		real intercept = mean_regulatory_input - slope * observed_mean_input;
		real k = mean_observed_value / mean(inv_logit(intercept + X * slope));
	}
	
	model {
	  for (t in 1:T) y[t] ~ normal( inv_logit( intercept + X[t] * slope ) * k, sigma );
	
	  mean_regulatory_input ~ normal(0,5);
		sd_regulatory_input ~ normal(0,5);
		sigma ~ cauchy(0,2.5);
		mean_observed_value ~ normal(0,5);
	}

it does not converge so well although tends to predict reasonable values for parameters.

My questions are: it is correct in your opinion? Am I missing something on the prior usage?

Slope == 0

Slope == 5