Introducing Destination Correlation Across Modes with Cross-Nested Logit
Neil Raha, Systra
Results from testing the introduction of destination correlation across modes within a UK WebTAG standard choice hierarchy transport demand model (mode choice less sensitive than destination) using a Cross-Nested Logit (CNL) formulation.
An extensively used standard approach for modelling the distribution and mode split of trip-makers is to employ a choice hierarchy where mode choice is at the upper level and destination choice is at the lower level. This is in keeping with the form proposed as the default hierarchy for a multi-stage transport model in the UK Department for Transport (DfT) Transport Analysis Guidance (TAG) Unit M2.
TAG Unit M2 notes that alternative hierarchies may be appropriate for different trip purposes where suitable local data exists to support the estimation of the relevant parameters and they in turn support such a hierarchy. Nevertheless, illustrative parameter values are provided which are predicated on the standard hierarchy and are derived from transport models which exemplified UK best practice in the mid-2000s and included major models in London, Birmingham and Scotland. These illustrative values for mode choice comprise “scaling parameters”, which determine mode choice sensitivity relative to that of destination choice, and are less than or equal to one as required to prevent perverse cross-elasticities of response to cost changes.
However, the mathematical nature of the hierarchical logit model form can give rise to counter-intuitive outcomes from policy testing. Consider the outcome of a policy to introduce a new or significantly improved orbital urban public transport (PT) service between two zones A and B in the outer area of a conurbation: a major objective and proposed benefit of such a policy may be congestion relief of highway traffic along the orbital corridor served by the PT scheme as many car trips along the corridor divert to PT, as well as increased demand for the new PT service.
Assume that we use a multi-stage transport model incorporating just car and PT modes and test the simple case where there is a significant reduction in PT costs between A and B and no change in any other PT costs or any car costs. Unfortunately, the initial response of a TAG standard (mode choice less sensitive than destination choice) hierarchical logit model for trip productions from zone A would be as follows:
1. significant increase in the weight of destination zone B in the PT distribution model (with no change in the weights of any other attraction zones);
2. correspondingly large increase in PT trips from A to B;
3. small and uniform percentage reduction in trips to all other attraction zones for PT;
4. small reduction in composite PT cost for travel to all destinations from A (passed upward to the mode choice model);
5. small increase in PT mode share for trip productions from A and therefore a small decrease in car mode share from A; and
6. correspondingly small uniform proportional decrease in car trips to all destination zones while retaining the original distributional pattern of car movements from A.
The model outcome for PT distribution is intuitively reasonable in that the greatest effect by far is to increase PT trips along the new route from A to B (although they are diverted uniformly from all other destinations and not preferentially from those proximate to B for which B may be a relatively more attractive alternative). However, for car the traffic reduction for trips from A applies uniformly to all destinations with no preference at all for the A to B corridor served by the new PT scheme. This is because there is no correlation between destinations in their entirely separate choice nests for the PT and car mode distribution models.
Bates (2014, private communication) proposed the use of a Cross-Nested Logit (CNL) model form to overcome this problem without reversing the standard choice hierarchy completely. The CNL is a generalisation of the standard nested logit model which allows alternatives to belong to more than one nest.
We report the results of applying the CNL approach to a transport demand model representing an urban area, and implemented in incremental form. The CNL formulation is applied to ensure that individual destination alternatives in the distribution models are correlated across modes. Tests are made for a number of alternative transport schemes (including provision of an orbital PT service) and policies, and for a range of values of destination correlation parameters. The responses are compared to those from the equivalent standard hierarchical model.
Conclusions are drawn regarding the efficacy of the CNL approach for different types of scheme and policy test and its impact on realism responses. We also comment on issues of estimation of the CNL model and computational requirements.
Association for European Transport