Help with Stan modeling using Mixture model

Modeling
1

I am quite new to the Stan. I am trying to use the following Stan code to simulate the distribution of some sentence length and word place for each sentence in some corpus.

functions {
  real genpoiss_truncated_lpmf(int y, real theta, real lambda, int truncation) {
    
    if (y > truncation) {
      return -1000; // Probability is zero outside the truncation
    }
    if ((theta * pow(theta + lambda * y, y-1) * exp(-theta - lambda * y)) / tgamma(y + 1) == 0) {
      return -1000;
    }
    return log((theta * pow(theta + lambda * y, y-1) * exp(-theta - lambda * y)) / tgamma(y + 1));
  }
}


data {
  int<lower=1> N;  // total number of observations
  int place[N];  
  int unit_length[N];
}

transformed data {
  int back_place[N];
  for (i in 1:N) {
    back_place[i] = unit_length[i] - place[i];
  }
}
parameters {
  real<lower = 0> theta1;
  real<lower = -1, upper = 1> lambda1;
  real<lower = 0> theta2;
  real<lower = -1, upper = 1> lambda2;
  real<lower = 0> mu1; 
  real<lower = 0> phi1;  
  real<lower = 0, upper = 1> psi;
}

transformed parameters {
  real lprior = 0;
  lprior += gamma_lpdf(theta1 | 2, 0.5); 
  lprior += gamma_lpdf(lambda1 | 1, 1);
  lprior += gamma_lpdf(theta2 | 2, 0.5); 
  lprior += gamma_lpdf(lambda2 | 1, 1);
  lprior += gamma_lpdf(mu1 | 1, 1);
  lprior += gamma_lpdf(phi1 | 1, 1);
}
model {
  target += lprior;
  
  for (i in 1:N) {
  target += log_sum_exp(log(psi) + genpoiss_truncated_lpmf(place[i] | theta1, lambda1, unit_length[i]) 
                  + neg_binomial_2_lpmf(unit_length[i] | mu1, phi1),
                  log1m(psi) + genpoiss_truncated_lpmf(back_place[i] | theta2, lambda2, unit_length[i]) 
                  + neg_binomial_2_lpmf(unit_length[i] | mu1, phi1)); //change to the same negative binomial 
  }
}

generated quantities {
  real log_lik[N];
  for (i in 1:N){
    log_lik[i] = psi*(neg_binomial_2_lpmf(unit_length[i] | mu1, phi1)
    + genpoiss_truncated_lpmf(place[i] | theta1, lambda1, unit_length[i]));
    log_lik[i] += (1-psi)*(neg_binomial_2_lpmf(unit_length[i] | mu1, phi1)
    + genpoiss_truncated_lpmf(back_place[i] | theta2, lambda2, unit_length[i]));
  }
}

But it gives the following error like this:

Chain 1: Rejecting initial value:
Chain 1:   Log probability evaluates to log(0), i.e. negative infinity.
Chain 1:   Stan can't start sampling from this initial value.

Warning: There were 3445 divergent transitions after warmup. See
https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
to find out why this is a problem and how to eliminate them.Warning: Examine the pairs() plot to diagnose sampling problems
Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
https://mc-stan.org/misc/warnings.html#tail-ess

I would be really grateful if someone can help with this. Thank you.

2

Have you tried following the provided link and tried any of the offered help there?

Generally for mixture models I found that you have to help the model identify the components via the priors, otherwise the chains can separate. There are a few threads in my comment history regarding such problems. You might find them there or with the search function. This is an example where narrower (and more distinct) priors helped with convergence: Convergence issues with brms mixture models

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