Ill-typed arguments to '~' statement. No distribution 'bernoulli_logit' was found with the correct signature

Modeling
1

Dear Stan community,

I have a problem fitting the bernoulli_logit model. I am trying to combine the linear predictors and inputting into a longitudinal binary model using bernoulli_logit. I have two matrices X (predictor) and Y (outcome), where the row represented subjects and column represented the visits. In the Y matrix, some cells are “NA” because for some subjects, they have missing outcomes at some visits, for others their outcome are 0/1.

I searched and found that the Y should be integer type using bernoulli_logit(). I am not sure how to indicate the matrix to be integer, or does the missing data affect?

Please see code below:

// Binary long model for PA+
  
  data {
    // Define variables in data
    // Number of observations (an integer)
    int<lower=0> M;
    // Number of c parameters
    int<lower=0> p;
    // Number of timepoints
    int k[M];

    // Covariates
    int N;
    matrix[M, N] X;
    
    // Count outcome
    matrix[M, N] Y;
  }
  
  parameters {
    // Define parameters to estimate
    real c0;
    real c[p];
    real sig[p];
    real cp;
    real s[M];
    real u[M];
    real ga;
  }
  
  transformed parameters  {
    //
    matrix[M, N] p2;
    for(i in 1:M){ 
         for(j in 1:k[i]){
             p2[i,j] <-  c0 + c[1] * (X[i,j]-cp) + c[2] * (X[i,j]-cp) * step(X[i,j]-cp) + ga*s[i] + u[i];
         } 
     }
  }
  
  model {
    // Prior part of Bayesian inference
    c0 ~ normal(0,10000);
    c[1] ~ normal(0,10000);
    c[2] ~ normal(0,10000);
    sig[1] ~ uniform(0,100);
    sig[2] ~ uniform(0,100);
    for(i in 1:M){ 
         u[i] ~ normal(0,sig[1]);
         s[i] ~ normal(0,sig[2]);
     }
    ga ~ normal(0,10000);
    cp ~ uniform(0.07,21.45);
    
   // Likelihood part of Bayesian inference
	Y ~ bernoulli_logit(p2);
  }

I got the error below:

Error in stanc(file = file, model_code = model_code, model_name = model_name,  : 
  0

Semantic error in 'string', line 43, column 1 to column 25:

Ill-typed arguments to '~' statement. No distribution 'bernoulli_logit' was found with the correct signature.

After I change the matrix to vector using to_vector(), the error becomes,

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Info: assignment operator <- deprecated in the Stan language; use = instead.
No matches for: 

  vector ~ bernoulli_logit(vector)

Available argument signatures for bernoulli_logit:

  int ~ bernoulli_logit(real)
  int ~ bernoulli_logit(real[ ])
  int ~ bernoulli_logit(vector)
  int ~ bernoulli_logit(row_vector)
  int[ ] ~ bernoulli_logit(real)
  int[ ] ~ bernoulli_logit(real[ ])
  int[ ] ~ bernoulli_logit(vector)
  int[ ] ~ bernoulli_logit(row_vector)

Real return type required for probability function.
 error in 'model1ea0b972b7c_50a1805149e3235b326959a4870349ac' at line 56, column 50
  -------------------------------------------------
    54:     
    55:    // Likelihood part of Bayesian inference
    56: 	to_vector(Y) ~ bernoulli_logit(to_vector(p2));
                                                         ^
    57:   }
  -------------------------------------------------

Error in stanc(file = file, model_code = model_code, model_name = model_name,  : 
  failed to parse Stan model '50a1805149e3235b326959a4870349ac' due to the above error.

Thank you for your help!

2

Is that the full error message? The lpdf function does not accept matrices (besides the multivariate ones). You can fix this with

to_vector(Y) ~ bernoulli_logit(to_vector(p2));
4

I reinstall the package and rerun the file, now the error becomes,

SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Info: assignment operator <- deprecated in the Stan language; use = instead.
No matches for: 

  vector ~ bernoulli_logit(vector)

Available argument signatures for bernoulli_logit:

  int ~ bernoulli_logit(real)
  int ~ bernoulli_logit(real[ ])
  int ~ bernoulli_logit(vector)
  int ~ bernoulli_logit(row_vector)
  int[ ] ~ bernoulli_logit(real)
  int[ ] ~ bernoulli_logit(real[ ])
  int[ ] ~ bernoulli_logit(vector)
  int[ ] ~ bernoulli_logit(row_vector)

Real return type required for probability function.
 error in 'model1ea0b972b7c_50a1805149e3235b326959a4870349ac' at line 56, column 50
  -------------------------------------------------
    54:     
    55:    // Likelihood part of Bayesian inference
    56: 	to_vector(Y) ~ bernoulli_logit(to_vector(p2));
                                                         ^
    57:   }
  -------------------------------------------------

Error in stanc(file = file, model_code = model_code, model_name = model_name,  : 
  failed to parse Stan model '50a1805149e3235b326959a4870349ac' due to the above error.

Do you know how can I convert the vector to integer?

5

You’ll need to declare Y as a two-dimensional array of integers:

data {
  ...
  array[M, N] Y;
}

Then because bernoulli_logit() is only defined for a single-dimensional array of integers as an outcome, you’ll then use a loop in your model {} block:

model {
  ...
  for (m in 1:M) {
    Y[m] ~ bernoulli_logit(p2[m]);
  }
}
7

If we declare Y` is a two-dimensional array of integers, why in the model we only use the single-dimensional array from 1:M? No need for N?

8

If we declare Y` is a two-dimensional array of integers, why in the model we only use the single-dimensional array from 1:M? No need for N?

Because it’s a two-dimensional array, when you use Y[m] you’re requesting all N elements from the m-th array. This is equivalent to how you would index rows in a matrix

9

Thank you for your response. There is something wrong with my rstan package and I reload it these days before I could try the code you mentioned above.

After removing and installing the package, I still have an error below, do you know what happened? Thanks!

> resStan <- stan_model(model_code = stan_code, data = data_stan,
+                 chains = 1, iter = 1000, warmup = 1000)
Error in stan_model(model_code = stan_code, data = data_stan, chains = 1,  : 
  unused arguments (data = data_stan, chains = 1, iter = 1000, warmup = 1000)
10

Use the stan() function, not stan_model()