Rstan, censored model, no convergence

Modeling
1

Hi,
I am trying to fit the following model, however it doesn’t converge

data {
int N;
real Y[N]; //Explanatory variable
real PRICE[N];
real com1[N];
real com2[N];
real com3[N];
real com4[N];
real com5[N];
real com6[N];
int<lower=0, upper=1> diabetes[N];
int<lower=0, upper=1> bloodpress[N];
int<lower=0, upper=1> overweight[N];
int<lower=0, upper=1> cholesterol[N];
int hhinc[N];
int age[N];
int<lower=0, upper=1> gender[N];
int y[N];
real L; //Left hand side. zero consumption
int M; //the Number of consumers
int<lower=1, upper=M> MID[N]; //Individual identification variable
}

parameters {
real b1_r[M];
real b2_r[M];
real b3;
real b4;
real b5;
real b6;
real b7;
real b8;
real b9;
real b10;
real b11;
real b12;
real b13;
real b14;
real b15;
real b18_r[M];
real mean_b1;
real mean_b2;
real mean_b18;
real<lower=0> sd_b1;
real<lower=0> sd_b2;
real<lower=0> sd_b18;
real<lower=0> sigma;
}

//reparametrisation
transformed parameters{
real b1[M];
real b2[M];
real b18[M];
for (m in 1:M){
b1[m] = mean_b1+sd_b1b1_r[m];
b2[m] = mean_b2+sd_b2b2_r[m];
b18[m] = mean_b18+sd_b18*b18_r[m];
}
}

model{
for (m in 1:M){
b1_r[m]~normal(0,1);
b2_r[m]~normal(0,1);
b18_r[m]~normal(0,1);
}
for(n in 1:N){
if(Y[n] == 0){
target += normal_lcdf(L | b1[MID[n]]+ b2[MID[n]]PRICE[n] + b18[MID[n]]y[n]+b3com1[n]+b4com2[n]+b5com3[n]+b6com4[n]+b7com5[n]+b8com6[n]+b9age[n]+b10gender[n]+b11hhinc[n], sigma);
}else{
target += normal_lpdf(Y[n] |b1[MID[n]]+ b2[MID[n]]PRICE[n] + b18[MID[n]]y[n]+b3com1[n]+b4com2[n]+b5com3[n]+b6com4[n]+b7com5[n]+b8com6[n]+b9age[n]+b10gender[n]+b11hhinc[n], sigma);
}
}
}

I get this warning message

Warning messages:
1: There were 6254 divergent transitions after warmup. Increasing adapt_delta above 0.99 may help. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
2: There were 620 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 15. See
http://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded
3: There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
http://mc-stan.org/misc/warnings.html#bfmi-low
4: Examine the pairs() plot to diagnose sampling problems

I can’t find the source of the problem. Any help would be much appreciated

2

With a quick look I would suggest to put sensible (even non informative) priors to every parameter you have

real b1_r[M];
real b2_r[M];
real b3;
real b4;
real b5;
real b6;
real b7;
real b8;
real b9;
real b10;
real b11;
real b12;
real b13;
real b14;
real b15;
real b18_r[M];
real mean_b1;
real mean_b2;
real mean_b18;
real<lower=0> sd_b1;
real<lower=0> sd_b2;
real<lower=0> sd_b18;
real<lower=0> sigma;

Still you could have some other pathology

3

Thank you.