  int<lower=0> num_non_zero;         // number of non-zero elements in the Z matrix
  vector[num_non_zero] w;            // non-zero elements in the implicit Z matrix
  int<lower=0> v[num_non_zero];      // column indices for w
  int<lower=0> u[t > 0 ? N + 1 : 0]; // where the non-zeros start in each row
  int<lower=0,upper=1> special_case; // is the only term (1|group)
