Testing the Theoretical Accuracy of Travel Choice Models Using Monte Carlo Simulation.

In recent years a considerable advance has been made in the construction of micro-travel demand models from choice theoretic principles. Within random utility theory, the structure of models may be shown to relate to the perceived similarity between discrete choice alternatives, and this aspect may be interpreted mathematically in terms of the correlation between the components of random utility functions. Several possible model structures have now been proposed, varying from the multinomial logit model (uncorrelated) through the partly correlated structures (hierarchical and cross-correlated logit kctions) to the most general form of probit model which allows an arbitrary variance-covariance matrix. In this paper, these model structures are discussed using a geometric interpretation of random utility theory, and the possibility of invoking transformations on the general probit model is examined. Monte Carlo simulation methods are then used to investigate some aspects of the trade-off between the generality and accuracy of correlated structures (the cross-correlated logit model in particular) and the greater ease with which less consistent structures may be implemented. In this way, the theoretical accuracy of the multinomial logit model is assessed. It is concluded that where the general probit model is too complex to implement, the practice of comparing the multinomial logit model with alternative hierarchical logit structures is unlikely to lead to significant errors in forecasting.