binomial_logit_glm_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_BINOMIAL_LOGIT_GLM_LPMF_HPP
#define STAN_MATH_PRIM_PROB_BINOMIAL_LOGIT_GLM_LPMF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/multiply.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/dot_product.hpp>
#include <stan/math/prim/fun/isfinite.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/max.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/as_value_column_vector_or_scalar.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_n, typename T_N, typename T_x,
          typename T_alpha, typename T_beta, require_matrix_t<T_x>* = nullptr>
inline return_type_t<T_x, T_alpha, T_beta> binomial_logit_glm_lpmf(
    const T_n& n, const T_N& N, const T_x& x, const T_alpha& alpha,
    const T_beta& beta) {
  constexpr int T_x_rows = T_x::RowsAtCompileTime;
  using T_partials_return = partials_return_t<T_x, T_alpha, T_beta>;
  using T_n_ref = ref_type_if_t<is_autodiff_v<T_n>, T_n>;
  using T_N_ref = ref_type_if_t<is_autodiff_v<T_N>, T_N>;
  using T_x_ref = ref_type_if_t<is_autodiff_v<T_x>, T_x>;
  using T_alpha_ref = ref_type_if_t<is_autodiff_v<T_alpha>, T_alpha>;
  using T_beta_ref = ref_type_if_t<is_autodiff_v<T_beta>, T_beta>;
 
  T_n_ref n_ref = n;
  T_N_ref N_ref = N;
  T_x_ref x_ref = x;
  T_alpha_ref alpha_ref = alpha;
  T_beta_ref beta_ref = beta;
 
  if (size_zero(n, N, alpha, beta, x)) {
    return 0;
  }
 
  if constexpr (!include_summand<propto, T_x, T_alpha, T_beta>::value) {
    return 0;
  }
 
  const size_t N_instances = max_size(n, N, x.col(0), alpha);
  const size_t N_attributes = x.cols();
 
  static const char* function = "binomial_logit_glm_lpmf";
  check_consistent_sizes(function, "Successes variable", n,
                         "Population size parameter", N);
  check_consistent_size(function, "Successes variable", n, N_instances);
  check_consistent_size(function, "Population size parameter", N, N_instances);
  check_consistent_size(function, "Weight vector", beta, N_attributes);
  check_consistent_size(function, "Vector of intercepts", alpha, N_instances);
 
  auto&& n_val = as_value_column_array_or_scalar(n_ref);
  auto&& N_val = as_value_column_array_or_scalar(N_ref);
 
  check_bounded(function, "Successes variable", n_val, 0, N_val);
  check_nonnegative(function, "Population size parameter", N_val);
 
  auto&& alpha_val = as_value_column_array_or_scalar(alpha_ref);
  auto&& beta_val = as_value_column_vector_or_scalar(beta_ref);
  auto&& x_val = value_of(x_ref);
  Eigen::Array<T_partials_return, -1, 1> theta(N_instances);
  if constexpr (T_x_rows == 1) {
    theta = (x_val * beta_val)(0, 0) + alpha_val;
  } else {
    theta = multiply(x_val, beta_val).array() + alpha_val;
  }
 
  constexpr bool gradients_calc = is_any_autodiff_v<T_beta, T_x, T_alpha>;
  auto&& log_inv_logit_theta = to_ref_if<gradients_calc>(log_inv_logit(theta));
 
  T_partials_return logp = sum(n_val * log_inv_logit_theta
                               + (N_val - n_val) * log1m_inv_logit(theta));
 
  using std::isfinite;
  if (!isfinite(logp)) {
    check_finite(function, "Weight vector", beta);
    check_finite(function, "Intercept", alpha);
    check_finite(function, "Matrix of independent variables", x);
  }
 
  if constexpr (include_summand<propto, T_n, T_N>::value) {
    size_t broadcast_n = max_size(N, n) == N_instances ? 1 : N_instances;
    logp += sum(binomial_coefficient_log(N_val, n_val)) * broadcast_n;
  }
 
  auto ops_partials = make_partials_propagator(x_ref, alpha_ref, beta_ref);
  if constexpr (gradients_calc) {
    Eigen::Matrix<T_partials_return, -1, 1> theta_derivative
        = n_val - N_val * exp(log_inv_logit_theta);
 
    if constexpr (is_autodiff_v<T_beta>) {
      if constexpr (T_x_rows == 1) {
        edge<2>(ops_partials).partials_ = theta_derivative.sum() * x_val;
      } else if constexpr (T_x::ColsAtCompileTime == 1) {
        partials<2>(ops_partials)[0] = dot_product(x_val, theta_derivative);
      } else {
        partials<2>(ops_partials)
            = multiply(x_val.transpose(), theta_derivative);
      }
    }
 
    if constexpr (is_autodiff_v<T_x>) {
      if constexpr (T_x_rows == 1) {
        edge<0>(ops_partials).partials_ = beta_val * theta_derivative.sum();
      } else {
        edge<0>(ops_partials).partials_
            = (beta_val * theta_derivative.transpose()).transpose();
      }
    }
    if constexpr (is_autodiff_v<T_alpha>) {
      partials<1>(ops_partials) = theta_derivative;
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_n, typename T_N, typename T_x, typename T_alpha,
          typename T_beta>
inline return_type_t<T_x, T_beta, T_alpha> binomial_logit_glm_lpmf(
    const T_n& n, const T_N& N, const T_x& x, const T_alpha& alpha,
    const T_beta& beta) {
  return binomial_logit_glm_lpmf<false>(n, N, x, alpha, beta);
}
}  // namespace math
}  // namespace stan
#endif