Nonlinearity and Taste Heterogeneity Influence on Discrete Choice Models Forecasts
A Orro, M Novales, University of La Coruňa, ES; F G Benitez, University of Sevilla, ES
Comparison and analysis of the predictions yielded by Multinomial Logit, Box-Cox Logit, Mixed Logit and Box-Cox Mixed Logit with several sets of synthetic data of mode transport choices.
Discrete choice models are used in transport to study the travel behaviour. They are employed to predict mode choices and, less often, destination choices. In current practice, the most usual models are the Multinomial Logit and the Nested Logit. These are linear in the parameters and use a fixed coefficients specification.
Nevertheless, these assumptions could not be in accordance with reality. There are models, like the Box-Cox Logit (Gaudry and Wills, 1978), that can accommodate nonlinearity in parameters through the employment of the Box-Cox transformation. The Mixed Logit model, that are established since the late 70?s as Hedonic Demand Model (Cardell, Dobson and Dunbar, 1978), has achieved great popularity in the research community in last years, after contributions like Ben-Akiva and Bolduc (1996), Bhat (1998) or Brownstone and Train (1999). McFadden and Train (2000) proved that this model can approximate any random utility model. By means of this model, random coefficients can be specified in a more flexible and simple way than through the classic probit scheme.
In this communication we present a Box-Cox Mixed Logit model. It includes the estimation of the Box-Cox exponents in addition to the parameters of the random coefficients distribution. In the authors? knowledge of the literature, this kind of model has not been estimated hitherto, although Lapparent (2003) suggests a model like this.
The differences between the predictions yielded by models that are not consistent with the real behaviour has been studied, using series of synthetic data sets with known characteristics, in the framework of simulation experiments suggested by Williams and Ortúzar (1982). These data sets simulate the behaviour of a population in transport mode choices that follow the assumptions of the random utility maximization theory. The data sets are generated in several situations, with presence or absence of taste heterogeneity and/or nonlinearity in the attribute influence. Four different model specifications are estimated with each data set for several sample sizes: Multinomial Logit, Box-Cox Logit, Mixed Logit and Box-Cox Mixed Logit.
In order to investigate the consequences of the use of these models in real practice, several ?policy changes? in the variables are applied, based on the policies proposed by Munizaga, Heydecker and Ortúzar (2000) and Cantillo and Ortúzar (2004). Comparisons are made among the simulated response of the population, the forecasts of the real model used for the generation of the synthetic data set and with the forecasts of the different estimated models. Several statistical tests are calculated to analyze the results and to investigate how the available tests allow us to identify the most correct model.
All the models have been estimated with a Gauss code. This code has been developed using the well know ?Mixed Logit Estimation Routine for Cross-Sectional Data? (Kenneth Train, David Revelt and Paul Ruud, 1996) as a basis. And it has been modified in order to incorporate new capabilities, as the estimation of Box-Cox exponents, the application of the policy changes and the evaluation of several statistical test in addition to those included in the original code. A classical estimation with maximum simulated likelihood is used.
Association for European Transport