groupedpaneldatamodels.models.ando_bai

Functions

grouped_interactive_effects(y, x, G[, GF, ...])

Estimates the Grouped Interactive Fixed Effects (GIFE) model with homogeneous slopes.

grouped_interactive_effects_hetrogeneous(y, x, G)

Estimates the Grouped Interactive Fixed Effects (GIFE) model with heterogeneous slopes.
groupedpaneldatamodels.models.ando_bai.grouped_interactive_effects(y, x, G, GF=None, kappa=0.0, gamma=3.7, tol=1e-06, gife_iterations=100, max_iterations=1000)[source]

Estimates the Grouped Interactive Fixed Effects (GIFE) model with homogeneous slopes.

This function performs the GIFE estimation process across multiple random initializations and returns the solution with the lowest objective value. The model assumes that slope coefficients are shared across groups (homogeneous).

Parameters:

  • y (np.ndarray) – A 3D array of shape (N, T, 1) containing the dependent variable.

  • x (np.ndarray) – A 3D array of shape (N, T, K) containing the independent variables.

  • G (int) – The number of groups.

  • GF (array-like, optional) – The number of factors per group. If None, defaults to one factor per group.

  • kappa (float, optional) – Regularization strength for SCAD penalty. Default is 0.0 (no penalty).

  • gamma (float, optional) – SCAD parameter. Default is 3.7.

  • tol (float, optional) – Convergence tolerance. Default is 1e-6.

  • gife_iterations (int, optional) – Number of initializations for the GIFE estimator. Default is 100.

  • max_iterations (int, optional) – Maximum number of iterations within each GIFE run. Default is 1000.

Returns:

  • best_beta: Estimated homogeneous coefficients, shape (K, 1)

  • best_g: Group assignments for each unit, shape (N,)

  • best_F: Estimated common factors, shape (T, sum(GF))

  • best_Lambda: Estimated factor loadings, shape (sum(GF), N)

  • best_objective_value: Final value of the objective function

  • resid: Residuals of the model, shape (N, T)

Return type:

tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, float, np.ndarray]

groupedpaneldatamodels.models.ando_bai.grouped_interactive_effects_hetrogeneous(y: ndarray, x: ndarray, G: int, GF=None, kappa: float = 0.0, gamma: float = 3.7, tol: float = 1e-06, gife_iterations: int = 100, max_iter: int = 1000)[source]

Estimates the Grouped Interactive Fixed Effects (GIFE) model with heterogeneous slopes.

This function runs the GIFE estimation procedure multiple times and selects the best solution based on the objective value. The model allows for heterogeneous slope coefficients across groups.

Parameters:

  • y (np.ndarray) – A 3D array of shape (N, T, 1) containing the dependent variable.

  • x (np.ndarray) – A 3D array of shape (N, T, K) containing the independent variables.

  • G (int) – The number of groups.

  • GF (ArrayLike, optional) – The number of factors per group. If None, defaults to one factor per group.

  • kappa (float, optional) – Regularization strength for SCAD penalty. Default is 0.0 (no penalty).

  • gamma (float, optional) – SCAD parameter. Default is 3.7.

  • tol (float, optional) – Convergence tolerance. Default is 1e-6.

  • gife_iterations (int, optional) – Number of initializations for the GIFE estimator. Default is 100.

  • max_iter (int, optional) – Maximum number of iterations within each GIFE run. Default is 1000.

Returns:

  • ordered_beta: Estimated heterogeneous coefficients, shape (K, G)

  • ordered_g: Group assignments for each unit, shape (N,)

  • ordered_F: Estimated common factors, shape (T, sum(GF))

  • best_Lambda: Estimated factor loadings, shape (sum(GF), N)

  • best_objective_value: Final value of the objective function

  • resid: Residuals of the model, shape (N, T)

Return type:

tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, float, np.ndarray]