## Modeling Dominated Choice Alternatives Using the Constrained Multinomial Logit

### Authors

F Martinez, University of Chile, CL; E Cascetta, F Pagliara, University of Naples Federico II, IT, M Bierlaire, EPFL Lausanne, CH, K W Axhausen, ETH, Zurich, CH

### Description

The objective of this paper is to specify and estimate a Constrained Multinomial Logit model with dominance variables. Estimation results will be compared with a simple Multinomial Logit model including dominance variables as well.

### Abstract

Random utility models are widely used to analyze choice behaviour and predict choices among discrete alternatives in a given set. These models are based on the assumption that an individual?s preference for the available alternatives can be described with a utility function and that the individual selects the alternative with the highest utility (Ben-Akiva and Lerman, 1985; Cascetta, 2001). The traditional formulation of logit models applied to transport demand assumes compensatory (indirect) utilities based on the trade-off between attributes. Some authors have criticized this approach because it fails to recognize attribute thresholds in consumers? behavior, as for example the process of elimination-by-aspects (EBA) (Tversky, 1972), or a more generic feasible choices domain, including for example income and time constraints, where such compensatory strategy is contained.

A different strategy has been proposed by Cascetta and Papola (2001) and Martinez et al. (2005), which makes those choice alternatives out of the feasible domain, available but undesirable. This approach has the advantage that the model is applied to the entire set of choices, thus gaining on efficiency by avoiding the explicit identification of choice sets for every individual, and secondly, obtaining a model with better properties for the calculation of equilibrium or optimum conditions (Martinez et al., 2005). Based on this approach, the Constrained Multinomial Logit (CMNL) model was specified, which combines the multinomial logit model with a binomial logit factor that represents soft cut-offs.

The objective of this paper is to apply the CMNL to reproduce a principle of rationality: transferability of preferences. Under this principle some feasible alternatives may not be considered because they are dominated by another alternative. Conceptually, an alternative d is dominated by another alternative d* if d is ?worse? than d*, with respect to one or more characteristics, without being better with respect to any characteristic.

We consider the general approach proposed by Cascetta and Papola (2005) and Cascetta et al. (2007) that extends and applies these concepts of dominance to the random utility theory. They defined a set of criteria to identify dominated alternatives for the case of the trip destination choice in a closed spatial context. This leads the authors to propose two types of dominance of alternatives: i) global dominance, when another alternative is globally preferred, considering their higher attractiveness and travel costs equal or lower; ii) spatial dominance, where in addition of the previous criterion the dominating alternative is along the path from the individual?s trip origin to the dominated alternative.

The proposed approach is applied using the revealed preference survey conducted in 2005 in the canton of Zurich in Switzerland (Cascetta et al., 2007), covering the mobility and moving biography of the respondents. The estimation results (Bierlaire, 2007) of the proposed model will be compared with the ones reported in Cascetta et al. (2007) to derive some conclusions about both the specification of dominance variables in the CMNL model and the calibration procedure of this model. Conclusions are also obtained on the data required for the application of CMNL on other similar contexts.

References

Ben-Akiva, M. and Lerman, (1985) Discrete Choice Analysis: Theory and Application to Travel Demand, MIT Press, Cambridge, Mass.

Bierlaire, M. (2007) An introduction to BIOGEME (Version 1.4), EPF Lausanne, Lausanne 2007) http://transp-or2.epfl.ch/biogeme/doc/tutorial.pdf.

Cascetta, E. (2001) Transportation systems engineering: theory and methods, Kluwer Academic Publisher, Boston.

Cascetta E., Pagliara F. and Axhausen K. W.(2007) The use of dominance variables in spatial choice modelling. Proceedings of the 11th World Conference on Transport Research, University of California at Berkely, June.

Cascetta, E. and Papola, A. (2001) Random utility models with implicit availability/perception of choice alternatives for the simulation of travel demand. Transportation Research C 9, 249-263.

Cascetta, E. and Papola, A. (2005) Dominance among alternatives in random utility models: a general framework and an application to destination choice. Proceedings of the European Transport Conference, Strasbourg, October.

MartÃnez F., Aguila F. and Hurtubia R (2005) The Constrained Multinomial Logit Model: A Semi-Compensatory Choice Model. 8th International Conference on Computers in Urban Planning and Urban Management (CUPUM 2005), London.

Tversky A. (1972) Elimination by Aspect: a Theory of Choice. Psycological Review, 79, pp. 281-299.

#### Publisher

Association for European Transport