# Initialization between (-2, 2) failed after 100 attempts

**URL:** <https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474>\
**Category:** Modeling\
**Tags:** specification\
**Created:** [May 22, 2023, 8:38am UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474 "2023-05-22T08:38:03Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![dmp](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/dmp/32/16409_2.png) [@dmp](https://discourse.mc-stan.org/u/dmp)\
**Post date:** [May 22, 2023, 8:38am UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474/1 "2023-05-22T08:38:03Z")

</div>

Hi I am new to Stan. I am trying to estimate a model and to start, I run ‘model0$optimize(data = data\_m0,algorithm = ‘lbfgs’)’. However, it returns the following error message:

**Rejecting initial value:**  
Error evaluating the log probability at the initial value.  
Exception: lkj\_corr\_lpdf: Correlation matrix is not positive definite. (in ‘/tmp/RtmpU01otz/model-2e799e29da4e1b.stan’, line 43, column 2 to column 22)  
Rejecting initial value:  
…  
Initialization between (-2, 2) failed after 100 attempts.  
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model. "

How should I fix the intial values? Would really appreciate any help!! Thanks

```stan
model{
  matrix[n_par,n_par] Sigma;
  //vector[N] delta; //individual_habit derperacion rate
  
  Omega ~ lkj_corr(2);
  tau ~ cauchy(0,2.5);
  
  Sigma = quad_form_diag(Omega,tau);
  //equivalent to diag(tau)*Omega*diag(tau)
  
  mu ~ normal(0,5);
  
  for (i in 1:N){
    beta[,i] ~ multi_normal(mu,Sigma);
  }
  
  for (ob in 1:nobs){
    real habit_stock;
    vector[2] utils;
    int id = ids[ob];
    vector[n_par] b = beta[1:n_par,id];
    
    if (t_0[ob]==1){
      habit_stock = b[1];
    } 
    
    utils[1] = b[n_par_h+1]*habit_stock + b[n_par_h+2]*habit_stock^2 + b[n_par_h+3] + dot_product(b[(n_par_h+5):(n_par_h+4+k_use)],to_vector(x_use[ob])) + dot_product(b[(n_par_h+k_use+5):(n_par_h+k_use+4+k_context)],to_vector(x_context[ob])) + dot_product(b[(n_par_h+k_use+5+k_context):n_par],to_vector(x_indi[id,]));
    y_out[ob,1] ~ bernoulli_logit(utils[1]);
    

    utils[2] = b[(n_par_h+4)];
    y_out[ob,2] ~ bernoulli_logit(utils[2]+utils[1]);
    
    
    habit_stock = habit_stock*b[1]+dot_product(b[2:n_par_h],to_vector(x_use[ob]));
  }
  
  }

```

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<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [May 22, 2023, 2:20pm UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474/2 "2023-05-22T14:20:16Z")

</div>

To address this question, we need to see the entire Stan file, including the `data` and especially the `parameters` blocks, as well as `transformed data` and `transformed parameters` if those exist.

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<div class="post-metadata">

**Author:** ![dmp](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/dmp/32/16409_2.png) [@dmp](https://discourse.mc-stan.org/u/dmp)\
**Post date:** [May 22, 2023, 2:29pm UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474/3 "2023-05-22T14:29:48Z")

</div>

hi here is the full code.

Regading the data, should I share the whole data/a small sample or a snapshot would be enough?

```plaintext
data{
  int<lower=1> nobs;
  int<lower=1> N;
  int<lower=1> n_out;
  array[nobs] int<lower=1> ids;
  
  int<lower=1> k_use;
  array[nobs,n_out] int<lower=0,upper=1> y_out;
  
  array[nobs,k_use] int<lower=0,upper=1> x_use;
  array[nobs] int<lower=1> t_0;
}

transformed data{
  int<lower=1> n_par_h = 1+n_out; //how does different activity contribute to habit stock = 3
  int<lower=1> n_par_r = n_out + 2 + k_use; //9;
  int<lower=1> n_par = n_par_h + n_par_r;
}

parameters{
  matrix[n_par,N] beta;
  
  corr_matrix[n_par] Omega;
  
  vector[n_par] mu;
  vector<lower=0>[n_par] tau;
}

model{
  matrix[n_par,n_par]Sigma;
  Omega ~ lkj_corr(2);
  tau ~ cauchy(0,2.5);
  
  Sigma = quad_form_diag(Omega,tau);
  
  mu ~ normal(0,5);
  
  for (i in 1:N){
    beta[,i] ~ multi_normal(mu,Sigma);
  }
  
  real habit_stock = beta[1,1]*dot_product(beta[2:(k_use+1),1],to_vector(x_use[1]));
  for (ob in 1:nobs){
    vector[2] utils;
    int id = ids[ob];
    vector[n_par] b = beta[1:n_par,id];
    
    
    utils[1] = b[n_par_h+1]*habit_stock + b[n_par_h+2]*habit_stock^2 + b[n_par_h+3] + dot_product(b[(n_par_h+5):(n_par)],to_vector(x_use[ob]));
    
    utils[2] = b[(n_par_h+4)] + utils[1];
    
    y_out[ob,1] ~ bernoulli_logit(utils[1]);
    y_out[ob,2] ~ bernoulli_logit(utils[2]);
    
    if(t_0[ob]==1){
      habit_stock = b[1]*dot_product(b[2:(k_use+1)],to_vector(x_use[1]));
    } else{
      habit_stock = habit_stock * b[1] + dot_product(b[2:(k_use+1)],to_vector(x_use[ob]));
    }
  }
  
  
}

```

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<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [May 22, 2023, 2:46pm UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474/4 "2023-05-22T14:46:13Z")

</div>

I actually just meant sharing the `data` block of your code, but a quick glance at your full Stan model wasn’t enough for me to spot the problem. Maybe @spinkney’s discerning eye can do better.

If you’re able to provide your full data, or any dataset that reproduces the problem, that could help lubricate things.

Also, if you can provide the details of your Stan version that might help.

---

<div class="post-metadata">

**Author:** ![dmp](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/dmp/32/16409_2.png) [@dmp](https://discourse.mc-stan.org/u/dmp)\
**Post date:** [May 22, 2023, 3:34pm UTC](https://discourse.mc-stan.org/t/initialization-between-2-2-failed-after-100-attempts/31474/5 "2023-05-22T15:34:19Z")

</div>

I actually just found another post discussing a similar problem. It seems that my dimension is too big to use the corr\_matrix method. So I am tried the solution in their post, using the ‘lkj\_corr\_cholesky’ instead ‘lkj\_corr’.  
There is no longer the non positive definite problem poping up..  
However, it shows a different error.

* * *

## Initial log joint probability = -3.63009e+12 Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes 1 -3.63009e+12 0 1.49699e+13 0.001 0.001 12 Error evaluating model log probability: Non-finite gradient. Error evaluating model log probability: Non-finite gradient.

I am sharing the modified code below. I suspect I should also change the way I generate the Sigma if I am using the ‘multi\_normal\_cholesky’ for beta priors.

Could you help take another look please?

```no-highlight
data{
  int<lower=1> nobs;
  int<lower=1> N;
  int<lower=1> n_out;
  array[nobs] int<lower=1> ids;
  
  int<lower=1> k_use;
  array[nobs,n_out] int<lower=0,upper=1> y_out;
  
  array[nobs,k_use] int<lower=0,upper=1> x_use;
  array[nobs] int<lower=1> t_0;
}

transformed data{
  int<lower=1> n_par_h = 1+n_out; //how does different activity contribute to habit stock = 3
  int<lower=1> n_par_r = n_out + 2 + k_use; //9;
  int<lower=1> n_par = n_par_h + n_par_r;
}

parameters{
  matrix[n_par,N] beta;
  
  cholesky_factor_corr[n_par] Omega;
  
  vector[n_par] mu;
  vector<lower=0>[n_par] tau;
}

model{
  matrix[n_par,n_par]Sigma;
  Omega ~ lkj_corr_cholesky(1);
  tau ~ cauchy(0,2.5);
  
  Sigma = quad_form_diag(Omega,tau);
  
  mu ~ normal(0,5);
  
  for (i in 1:N){
    beta[,i] ~ multi_normal_cholesky(mu,Sigma);
  }
  
  real habit_stock = beta[1,1]*dot_product(beta[2:(k_use+1),1],to_vector(x_use[1]));
  for (ob in 1:nobs){
    vector[2] utils;
    int id = ids[ob];
    vector[n_par] b = beta[1:n_par,id];
    
    
    utils[1] = b[n_par_h+1]*habit_stock + b[n_par_h+2]*habit_stock^2 + b[n_par_h+3] + dot_product(b[(n_par_h+5):(n_par)],to_vector(x_use[ob]));
    
    utils[2] = b[(n_par_h+4)] + utils[1];
    
    y_out[ob,1] ~ bernoulli_logit(utils[1]);
    y_out[ob,2] ~ bernoulli_logit(utils[2]);
    
    if(t_0[ob]==1){
      habit_stock = b[1]*dot_product(b[2:(k_use+1)],to_vector(x_use[1]));
    } else{
      habit_stock = habit_stock * b[1] + dot_product(b[2:(k_use+1)],to_vector(x_use[ob]));
    }
  }
  
  
}

```