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 |
Destination choice lambda |
|
lM |
Mode choice lambda |
|
Ad |
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 |
|
Ad |
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 |
|
Ad |
Ad |
Another variant
The following applies:
where
|
Vdm |
Utility of mode m in combination with destination d (systematic part) |
|
θ |
LogSum parameter |
|
Ad |
Attraction factor of destination d |
Transformation according to ABM Nested Demand
|
ABM Nested Demand |
Variant |
|
Vdm |
Vdm / θ |
|
lM |
1 |
|
lD |
θ |
|
Ad |
Ad |
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 |
|
Ad |
Bd |
