biogeme.models.mev module

Implements the Multivariate Extreme Value models.

author:

Michel Bierlaire

date:

Wed Oct 25 11:35:34 2023

biogeme.models.mev.logmev(util, log_gi, av, choice)[source]

Log of the choice probability for a MEV model.

Parameters:

  • util (dict[int, Expression | float | int | bool]) – dict of objects representing the utility functions of each alternative, indexed by numerical ids.

  • log_gi (dict[int, Expression | float | int | bool]) –

    a dictionary mapping each alternative id with the function

    \[\ln \frac{\partial G}{\partial y_i} (e^{V_1},\ldots,e^{V_J})\]

    where \(G\) is the MEV generating function. If an alternative \(i\) is not available, then \(G_i = 0\).

  • av (dict[int, Expression | float | int | bool]) – dict of objects representing the availability of each alternative (\(a_i\) in the above formula), indexed by numerical ids. Must be consistent with util, or None. In this case, all alternatives are supposed to be always available.

  • choice (Expression | float | int | bool) – id of the alternative for which the probability must be calculated.

Return type:

Expression

Returns:

log of the choice probability of the MEV model, given by

\[V_i + \ln G_i(e^{V_1},\ldots,e^{V_J}) - \ln\left(\sum_j e^{V_j + \ln G_j(e^{V_1}, \ldots,e^{V_J})}\right)\]
biogeme.models.mev.logmev_endogenousSampling(util, log_gi, av, correction, choice)[source]

Warning

This function is deprecated. Use logmev_endogenous_sampling() instead.

Parameters:
biogeme.models.mev.logmev_endogenous_sampling(util, log_gi, av, correction, choice)[source]

Log of choice probability for a MEV model, including the correction for endogenous sampling as proposed by Bierlaire, Bolduc and McFadden (2008).

Parameters:

  • util (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the utility functions of each alternative, indexed by numerical ids.

  • log_gi (dict(int:biogeme.expressions.expr.Expression)) –

    a dictionary mapping each alternative id with the function

    \[\ln \frac{\partial G}{\partial y_i} (e^{V_1}, \ldots, e^{V_J})\]

    where \(G\) is the MEV generating function. If an alternative \(i\) is not available, then \(G_i = 0\).

  • av (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the availability of each alternative (\(a_i\) in the above formula), indexed by numerical ids. Must be consistent with util, or None. In this case, all alternatives are supposed to be always available.

  • correction (dict(int:biogeme.expressions.expr.Expression)) – a dict of expressions for the correstion terms of each alternative.

  • choice (biogeme.expressions.expr.Expression) – id of the alternative for which the probability must be calculated.

Returns:

log of the choice probability of the MEV model, given by

\[V_i + \ln G_i(e^{V_1}, \ldots,e^{V_J}) + \omega_i - \ln\left(\sum_j e^{V_j + \ln G_j(e^{V_1}, \ldots, e^{V_J})+ \omega_j}\right)\]

where \(\omega_i\) is the correction term for alternative \(i\).

Return type:

biogeme.expressions.expr.Expression

Parameters:
biogeme.models.mev.mev(util, log_gi, av, choice)[source]

Choice probability for a MEV model.

Parameters:

  • util (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the utility functions of each alternative, indexed by numerical ids.

  • log_gi (dict(int:biogeme.expressions.expr.Expression)) –

    a dictionary mapping each alternative id with the function

    \[\ln \frac{\partial G}{\partial y_i} (e^{V_1}, \ldots, e^{V_J})\]

    where \(G\) is the MEV generating function. If an alternative \(i\) is not available, then \(G_i = 0\).

  • av (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the availability of each alternative (\(a_i\) in the above formula), indexed by numerical ids. Must be consistent with util, or None. In this case, all alternatives are supposed to be always available.

  • choice (biogeme.expressions.expr.Expression) – id of the alternative for which the probability must be calculated.

Returns:

Choice probability of the MEV model, given by

\[\frac{e^{V_i + \ln G_i(e^{V_1}, \ldots,e^{V_J})}}{\sum_j e^{V_j + \ln G_j(e^{V_1},\ldots,e^{V_J})}}\]
Return type:

biogeme.expressions.expr.Expression

Parameters:
biogeme.models.mev.mev_endogenousSampling(util, log_gi, av, correction, choice)[source]

Warning

This function is deprecated. Use mev_endogenous_sampling() instead.

Parameters:
biogeme.models.mev.mev_endogenous_sampling(util, log_gi, av, correction, choice)[source]

Choice probability for a MEV model, including the correction for endogenous sampling as proposed by Bierlaire, Bolduc and McFadden (2008).

Parameters:

  • util (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the utility functions of each alternative, indexed by numerical ids.

  • log_gi (dict(int:biogeme.expressions.expr.Expression)) –

    a dictionary mapping each alternative id with the function

    \[\ln \frac{\partial G}{\partial y_i} (e^{V_1}, \ldots, e^{V_J})\]

    where \(G\) is the MEV generating function. If an alternative \(i\) is not available, then \(G_i = 0\).

  • av (dict(int:biogeme.expressions.expr.Expression)) – dict of objects representing the availability of each alternative (\(a_i\) in the above formula), indexed by numerical ids. Must be consistent with util, or None. In this case, all alternatives are supposed to be always available.

  • correction (dict(int:biogeme.expressions.expr.Expression)) – a dict of expressions for the correstion terms of each alternative.

  • choice (biogeme.expressions.expr.Expression) – id of the alternative for which the probability must be calculated.

Returns:

log of the choice probability of the MEV model, given by

\[V_i + \ln G_i(e^{V_1}, \ldots, e^{V_J}) + \omega_i - \ln\left(\sum_j e^{V_j + \ln G_j(e^{V_1},\ldots,e^{V_J})+ \omega_j}\right)\]

where \(\omega_i\) is the correction term for alternative \(i\).

Return type:

biogeme.expressions.expr.Expression

Parameters: