pyblp.OptimizationProgress¶

class pyblp.OptimizationProgress¶

Information about the current progress of optimization.

They key attributes of this class needed to define a custom optimization routine are objective and gradient. Many other attributes of ProblemResults are also included, and can be used to help define an alternative optimization routine (e.g., Gauss-Newton), to debug issues, or to add custom ad-hoc moments to the configured problem.

problem¶

Problem that created this progress.

Type: Problem

fp_converged¶

Flags for convergence of the iteration routine used to compute \(\delta(\theta)\) in each market. Values are in the same order as Problem.unique_market_ids.

Type: ndarray

fp_iterations¶

Number of major iterations completed by the iteration routine used to compute \(\delta(\theta)\) in each market. Values are in the same order as Problem.unique_market_ids.

Type: ndarray

contraction_evaluations¶

Number of times the contraction used to compute \(\delta(\theta)\) was evaluated in each market. Values are in the same order as Problem.unique_market_ids.

Type: ndarray

theta¶

Unfixed parameters, \(\theta\), in the following order: \(\Sigma\), \(\Pi\), \(\rho\), non-concentrated out elements from \(\beta\), and non-concentrated out elements from \(\gamma\).

Type: ndarray

sigma¶

Cholesky root of the covariance matrix for unobserved taste heterogeneity, \(\Sigma\).

Type: ndarray

sigma_squared¶

Covariance matrix for unobserved taste heterogeneity, \(\Sigma\Sigma'\).

Type: ndarray

pi¶

Parameters that measures how agent tastes vary with demographics, \(\Pi\).

Type: ndarray

rho¶

Parameters that measure within nesting group correlations, \(\rho\).

Type: ndarray

beta¶

Demand-side linear parameters, \(\beta\).

Type: ndarray

gamma¶

Supply-side linear parameters, \(\gamma\).

Type: ndarray

sigma_bounds¶

Bounds for \(\Sigma\) that were used during optimization, which are of the form (lb, ub).

Type: tuple

pi_bounds¶

Bounds for \(\Pi\) that were used during optimization, which are of the form (lb, ub).

Type: tuple

rho_bounds¶

Bounds for \(\rho\) that were used during optimization, which are of the form (lb, ub).

Type: tuple

beta_bounds¶

Bounds for \(\beta\) that were used during optimization, which are of the form (lb, ub).

Type: tuple

gamma_bounds¶

Bounds for \(\gamma\) that were used during optimization, which are of the form (lb, ub).

Type: tuple

sigma_labels¶

Variable labels for rows and columns of \(\Sigma\), which are derived from the formulation for \(X_2\).

Type: list of str

pi_labels¶

Variable labels for columns of \(\Pi\), which are derived from the formulation for demographics.

Type: list of str

rho_labels¶

Variable labels for \(\rho\). If \(\rho\) is not a scalar, this is Problem.unique_nesting_ids.

Type: list of str

beta_labels¶

Variable labels for \(\beta\), which are derived from the formulation for \(X_1\).

Type: list of str

gamma_labels¶

Variable labels for \(\gamma\), which are derived from the formulation for \(X_3\).

Type: list of str

theta_labels¶

Variable labels for \(\theta\), which are derived from the above labels.

Type: list of str

delta¶

Mean utility, \(\delta(\theta)\).

Type: ndarray

clipped_shares¶

Vector of booleans indicating whether the associated simulated shares were clipped during the last fixed point iteration to compute \(\delta(\theta)\). All elements will be False if shares_bounds in Problem.solve() is disabled (by default shares are bounded from below by a small number to alleviate issues with underflow and negative shares).

Type: ndarray

tilde_costs¶

Estimated transformed marginal costs, \(\tilde{c}(\theta)\) from (9). If costs_bounds were specified in Problem.solve(), \(c\) may have been clipped.

Type: ndarray

clipped_costs¶

Vector of booleans indicating whether the associated marginal costs were clipped. All elements will be False if costs_bounds in Problem.solve() was not specified.

Type: ndarray

xi¶

Unobserved demand-side product characteristics, \(\xi(\theta)\), or equivalently, the demand-side structural error term. When there are demand-side fixed effects, this is \(\Delta\xi(\theta)\) in (32). That is, fixed effects are not included.

Type: ndarray

omega¶

Unobserved supply-side product characteristics, \(\omega(\theta)\), or equivalently, the supply-side structural error term. When there are supply-side fixed effects, this is \(\Delta\omega(\theta)\) in (32). That is, fixed effects are not included.

Type: ndarray

micro¶

Micro moments, \(\bar{g}_M\), in (34).

Type: ndarray

micro_values¶

Micro moment values, \(f_m(v)\). Rows are in the same order as ProblemResults.micro.

Type: ndarray

objective¶

GMM objective value, \(q(\theta)\), defined in (10). If scale_objective was True in Problem.solve() (which is the default), this value was scaled by \(N\) so that objective values are more comparable across different problem sizes. Note that in some of the BLP literature (and earlier versions of this package), this expression was previously scaled by \(N^2\).

Type: float

xi_by_theta_jacobian¶

\(\frac{\partial\xi}{\partial\theta} = \frac{\partial\delta}{\partial\theta}\).

Type: ndarray

omega_by_theta_jacobian¶

\(\frac{\partial\omega}{\partial\theta} = \frac{\partial\tilde{c}}{\partial\theta}\).

Type: ndarray

micro_by_theta_jacobian¶

\(\frac{\partial\bar{g}_M}{\partial\theta}\).

Type: ndarray

gradient¶

Gradient of the GMM objective, \(\nabla q(\theta)\), defined in (18).

Type: ndarray

projected_gradient¶

Projected gradient of the GMM objective. When there are no parameter bounds, this will always be equal to ProblemResults.gradient. Otherwise, if an element in \(\hat{\theta}\) is equal to its lower (upper) bound, the corresponding projected gradient value will be truncated at a maximum (minimum) of zero.

Type: ndarray

projected_gradient_norm¶

Infinity norm of ProblemResults.projected_gradient.

Type: ndarray

W¶

Weighting matrix, \(W\), used to compute these results.

Type: ndarray

Methods