biogeme.mdcev.generalized module

Implementation of the “generalized translated utility function” MDCEV model. See the technical report.

Michel Bierlaire Tue Apr 9 08:44:12 2024

class biogeme.mdcev.generalized.Generalized(model_name, baseline_utilities, gamma_parameters, alpha_parameters=None, scale_parameter=None, prices=None, weights=None)

Bases: Mdcev

Implementation of the MDCEV model with generalized translated utility function.

Parameters:

• model_name (str)

• baseline_utilities (dict[int, Expression])

• gamma_parameters (dict[int, Expression | None])

• alpha_parameters (dict[int, Expression] | None)

• scale_parameter (Expression | None)

• prices (dict[int, Expression] | None)

• weights (Expression | None)

calculate_inverse_of_determinant_one_alternative(the_id, consumption)

Calculate the inverse of the entries for the determinant. For

the outside good, gamma is equal to 0.

Parameters:

• the_id (int) – identifier of the good.

• consumption (Expression) – expression for the consumption.

Return type:

Expression

calculate_log_determinant_one_alternative(the_id, consumption)

Calculate the log of the entries for the determinant. For

the outside good, gamma is equal to 0.

Parameters:

• the_id (int) – identifier of the good.

• consumption (Expression) – expression for the consumption.

Return type:

Expression

derivative_utility_one_alternative(the_id, the_consumption, epsilon, one_observation)

Used in the optimization problem solved for forecasting tp calculate the dual variable.

Return type:

float

Parameters:

• the_id (int)

• the_consumption (float)

• epsilon (float)

• one_observation (Database)

lower_bound_dual_variable(chosen_alternatives, one_observation, epsilon)

Method providing model specific bounds on the dual variable. It not overloaded, default values are used.

Parameters:

• chosen_alternatives (set[int]) – list of alternatives that are chosen at the optimal solution

• one_observation (Database) – data for one observation.

• epsilon (ndarray) – draws from the error term.

Return type:

float

Returns:

a lower bound on the dual variable, such that the expenditure calculated for any larger value is

well-defined and non negative.

optimal_consumption_one_alternative(the_id, dual_variable, epsilon, one_observation)

Analytical calculation of the optimal consumption if the dual variable is known.

Return type:

float

Parameters:

• the_id (int)

• dual_variable (float)

• epsilon (float)

• one_observation (Database)

sorting_utility_one_alternative(alternative_id, epsilon, one_observation)

Utility used to sort the alternatives. Used in the forecasting algorithm to identify chosen and non chpsen alternatives

Return type:

float

Parameters:

• alternative_id (int)

• epsilon (float)

• one_observation (Database)

transformed_utility(the_id, the_consumption)

Calculates the utility for one alternative.

Return type:

Expression

Parameters:

• the_id (int)

• the_consumption (Expression)

utility_expression_one_alternative(the_id, the_consumption, unscaled_epsilon)

Utility expression. Used only for code validation.

Return type:

Expression

Parameters:

• the_id (int)

• the_consumption (Expression)

• unscaled_epsilon (Expression)

utility_one_alternative(the_id, the_consumption, epsilon, one_observation)

Utility needed for forecasting

Return type:

float

Parameters:

• the_id (int)

• the_consumption (float)

• epsilon (float)

• one_observation (Database)