Ben-Elia, E. , Toledo, T. and Prashker, J. N.
On negative correlations and the consistency of GEV-based discrete choice models.
Seventh Triennial Symposium on Transportation Analysis, Tromso, Norway, 20-25 June 2010.
- Published Version
The science of choice modelling has flourished in the last years as more and more studies are made in order to better understand human decision making. Discrete choice models form a major part in econometric studies in general and travel based studies in particular. Econometric random utility based discrete-choice models are still regarded as the main workhorse for most travel related behavioural modelling. Consequently, random utility models (RUM) have been developed considerably in the past three decades . The wide RUM family includes three main sub-family types: The Multinomial Logit Model (MNL) and its applications, The GEV (General Extreme Value) models and the different mixed models. Despite the improvements in more sophisticated
modelling specifications, MNL and the family of GEV models are still those most frequently applied in practical
applications involving planning, forecasting and feasibility assessments. However, GEV models are based on a
set of specific mathematical properties one of which is non-negativity in unobserved correlations. In reality, there is no fundamental reason why non-positive correlations should not occur.
The generalized extreme value (GEV) theory was, developed by  to accommodate these deficiencies of MNL. This general theorem consists of a large family of pecifications that includes in addition to MNL itself, also the different nest-based logit models: nested logit (NL), pair combinatorial logit (PCL), cross-nested logit (CNL) and generalized nested logit (GNL) models. GEV models are derived under a set of several restricting assumptions. These conditions are sufficient to observe a continuous multivariate extreme value distribution function. However, as noted by , these constraints also imply that the correlations in unobserved factors (or error terms) reproduced by a GEV model are necessarily always positive.
The inherited assumption of non-negative correlations is brought about by mathematical necessities. However, from a behavioural perspective, within elaborate nested structures, there is no apparent reason why this
assumption must always hold. Therefore, we decided to put this to the test by creating artificial correlation structures by generating synthetic data and estimating GEV models – NL (Experiment I) and CNL (Experiment II) to measure the obtained bias between estimated parameters and true parameters. In this context it is appropriate to use synthetic data generated with a postulated model, since the true parameter values are known in advance. As explained in the next subsection, in order to validate the results, the same models were also estimated using a Multinomial Probit (MNP) specification.
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