Modeling Inter-And Intra- Alternative Heteroscedasticity in Travel Choice Behavior: A Heteroscedastic Extreme Value Webit Model Approach

Abstract

The aim of this study is to develop a heteroscedastic extreme value weibit (HEV-Weibit) model to simultaneously account for inter-alternative heteroscedasticity (non-identical errors across alternatives) and intra-alternative heteroscedasticity (non-identical errors within an alternative) in travel choice behavior. In particular, the alternative-specific Weibull distributed random error deals with a different error variance for each alternative, and the error variance within an alternative depends on the observed utilities. As a result, the proposed model does not suffer from the 'independence of irrelevant alternatives' (IIA) property, and it represents the varying perception variance. The proposed model is applied to synthetic data and also to empirical data to compare its performance against existing models. Our results with synthetic data show that the use of existing models that do not simultaneously account for inter-alternative and intra-alternative heteroscedasticity leads to estimation bias when both heteroscedasticities are present in the choice observations. Only the proposed model accounted for alternative heteroscedasticity well in the estimation. In addition, the results of empirical data reveal that mode choice behavior could include inter-alternative and intra-alternative heteroscedasticities, and the advantageous properties of the proposed model are significant in the description and prediction of the choice behavior.

Keywords: Discrete choice model, Heteroscedastic extreme value, Inter- and Intra-alternative heteroscedasticities, Intercity mode choice