ERROR: Negative initial value for lognormal prior

Modeling
1

I am running advi on a simple mixed effects model where random effects are lognormally distributed as in

model <- 'data {
          int<lower=0> N;// Number of observations
          vector[N] time; //predictor
          vector[N] concentration;  //response
          
          real beta1_pop;
          real beta2_pop;
          real beta3_pop;
          real<lower=0> omega_beta1;
          real<lower=0> omega_beta2;
          real<lower=0> omega_beta3;
          real<lower=0>  pres;
        }
        parameters {
          vector[3] beta;
        }
        model {
          //Priors
          beta[1] ~ lognormal( beta1_pop , omega_beta1);
          beta[2] ~ lognormal( beta2_pop , omega_beta2);
          beta[3] ~ lognormal( beta3_pop , omega_beta3);
          concentration ~ normal(100*beta[1]/(beta[2]*(beta[1]-beta[3]))*(exp(-beta[3]*time)-exp(-beta[1]*time)), pres);
        }'


modelstan <- stan_model(model_name = "warfarin",model_code = model)

and then running advi

stan_data <- list(N = length(obs),concentration = obs
					,time = time,
					beta1_pop=beta1,beta2_pop=beta2,beta3_pop=beta3,
			    omega_beta1=omega.eta1,omega_beta2=omega.eta1,omega_beta3=omega.eta3,
					pres=pres)

fit <- vb(modelstan, data = stan_data, iter = 10000)

beta1, beta2 ad beta3 are positive, yet running vb method returns

Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: lognormal_lpdf: Random variable is -0.214347, but must be >= 0! (in ‘model14f6567ff8b9_warfarin’ at line 19)

Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: lognormal_lpdf: Random variable is -1.97402, but must be >= 0! (in ‘model14f6567ff8b9_warfarin’ at line 19)

Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: lognormal_lpdf: Random variable is -0.498263, but must be >= 0! (in ‘model14f6567ff8b9_warfarin’ at line 19)

Any thoughts? Is the model not defined correctly?
Thanks

2

Declare a lower bound of 0 on beta, i.e.: vector<lower=0>[3] beta;

3

Yes, worked.

Thanks!