Different formulations for nested Logit models

There are different formulations for hierarchical nested Logit models. ABM Nested Demand follows the formulation in Ben-Akiva 1985. Transformations are given below for alternative formulations.

For the sake of clarity, we will concentrate on the case destination choice - mode choice. The letters d and m stand for destination and mode.

ABM Nested Demand

The following applies:

where

Vdm

Base utility

lD

Location choice lambda

lM

Mode choice lambda

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Attraction factor of destination d

Transformation according to Ben-Akiva

The following applies:

where

Vd

Utility of destination d (systematic part)

Vm

Uility of mode m (systematic part)

Vdm

Utility of mode m in combination with destination d (systematic part)

μD

Scale parameter destination

μM

Scale parameter mode

Transformation according to ABM Nested Demand

ABM Nested Demand

Ben-Akiva

Vdm

Vd + Vm + Vdm

lM

μM

lM

μD

AM

1

Transformation according to the tour-based model

The following applies:

where

Vd

Utility of destination d

Vdm

Mode choice utility

θ

LogSum parameter

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Attraction factor of destination d

Transformation according to ABM Nested Demand

ABM Nested Demand

Tour-based model

Vdm

Vd / θ + Vdm

lM

1

lD

θ

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Another variant

The following applies:

where

Vdm

Utility of mode m in combination with destination d (systematic part)

θ

LogSum parameter

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Attraction factor of destination d

Transformation according to ABM Nested Demand

ABM Nested Demand

Variant

Vdm

Vdm / θ

lM

1

lD

θ

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Web TAG

TAG essentially describes the case mode choice - destination choice.

  • ABM Nested Demand

For the mode choice - destination choice case, the ABM formulation is Nested Demand:

  • Web TAG

The following applies:

where

Gdm

Generalised cost

θmode

Mode parameter

ldist

Distribution parameter

Bd

Attraction factor

Transformation according to ABM Nested Demand

ABM Nested Demand

Web TAG

Vdm

Gdm

lM

θ...λdist

lD

-λdist

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Bd