Hierarchical polynomial regression, data type errors

hello all,
I am trying to create a hierarchical second-order polynomial model on the logit scale, using cmdstanr. I thought that this would be fairly straightforward if I adapted the example code in the user guide for hierarchical logistic regression to this slightly more complex model structure. But it won’t compile because of a data type incompatibility error that I can’t figure out the cause of.

For reference, the non-hierarchical version of the model I am trying to fit looks like this in R’s stats package:

glm( y ~ poly(x, 2),  data=df, family=binomial) 

The following code for a hierarchical logistic regression compiles without a problem:

data {
  int<lower=1> D;
  int<lower=0> N;
  int<lower=1> L;
  array[N] int<lower=0, upper=1> y;
  array[N] int<lower=1, upper=L> ll;
  array[N] row_vector[D] x;
parameters {
  array[D] real mu;
  array[D] real<lower=0> sigma;
  array[L] vector[D] beta;
model {
  for (d in 1:D) {
    mu[d] ~ normal(0, 100);
    for (l in 1:L) {
      beta[l, d] ~ normal(mu[d], sigma[d]);
  for (n in 1:N) {
    y[n] ~ bernoulli(inv_logit(x[n] * beta[ll[n]]));

but when I simply expand the model formula from beta * x to A + B * x + C * x^2, like I do below, I get an error telling me one of my parameters is in an inappropriate data type (A, B, and C are coded as pA, pB, and pC).

  int <lower=1> D;   
  int <lower=0> N;    
  int <lower=1> L; 

  array[N] int<lower=0, upper=1> y;
  array[N] int<lower=1, upper=L> ll;
  array[N] row_vector[D] x;

 array [D] real prior_pA;
 array [D] real prior_pB;
 array [D] real prior_pC;
 array [D] real <lower=0> sigma_pA;
 array [D] real <lower=0> sigma_pB;
 array [D] real <lower=0> sigma_pC;
 array [L] vector[D] pA;
 array [L] vector[D] pB;
 array [L] vector[D] pC;

model {
   for (d in 1:D) {
     prior_pA[d] ~ normal(0, 100);
     prior_pB[d] ~ normal(0, 100);
     prior_pC[d] ~ normal(0, 100);
     for (l in 1:L) {
        pA[l, d] ~ normal(prior_pA[d], sigma_pA[d]);
        pB[l, d] ~ normal(prior_pB[d], sigma_pB[d]);
        pC[l, d] ~ normal(prior_pC[d], sigma_pC[d]);
   for (n in 1:N) {
     y[n] ~ bernoulli_logit(pA[n] + pB[ll[n]] * x[n] + pC[ll[n]] * x[n]^2);

The error:

Semantic error in '/var/folders/k7/2gf32r911sgfpf0pld60jb780000gn/T/RtmpVMTXH5/model-12d67652ed1e4.stan', line 35, column 28 to column 52:
    33:     }
    34:     for (n in 1:N) {
    35:       y[n] ~ bernoulli_logit(pA[n] + pB[ll[n]] * x[n] + pC[ll[n]] * x[n]^2);
    36:     }
    37:  }

Ill-typed arguments supplied to infix operator +. Available signatures: 
(int, int) => int
(real, real) => real
(real, vector) => vector
(vector, real) => vector
(vector, vector) => vector
(complex, complex) => complex
(real, row_vector) => row_vector
(row_vector, real) => row_vector
(row_vector, row_vector) => row_vector
(real, matrix) => matrix
(matrix, real) => matrix
(matrix, matrix) => matrix
(complex, complex_vector) => complex_vector
(complex_vector, complex) => complex_vector
(complex_vector, complex_vector) => complex_vector
(complex, complex_row_vector) => complex_row_vector
(complex_row_vector, complex) => complex_row_vector
(complex_row_vector, complex_row_vector) => complex_row_vector
(complex, complex_matrix) => complex_matrix
(complex_matrix, complex) => complex_matrix
(complex_matrix, complex_matrix) => complex_matrix
Instead supplied arguments of incompatible type: vector, matrix.

I don’t think I defined any variables as a matrix, and I adapted the code as directly as possible. I’d be grateful for any help figuring out what exactly is going on here.

thanks in advance