Discrete choice models with multiplicative stochasticity in choice environment variables: Application to accommodating perception errors in driver behaviour models

This paper presents a mixed multinomial logit-based discrete choice modelling framework to accommodate decision-makers' errors in perceiving choice environment variables that do not vary across choice alternatives. An analysis is undertaken to evaluate two different ways of specifying errors in the choice environment variables in discrete choice models - (a) the additive specification and (b) the multiplicative specification. Between these two approaches, the multi-plicative error specification is consistent with psychophysical theories of human perception of physical quantities in that the variability in perception tends to be greater for quantities of greater magnitude. Further, it is shown that models with an additive error specification run into parameter (un)identifiability problems if the analyst attempts to accommodate errors in several variables. In contrast, models with multiplicative errors in variables allow separate identification of stochasticity in as many variables as needed, as long as those variables have a significant in-fluence on the choice outcome.The usefulness of the proposed framework with multiplicative errors is demonstrated through simulation experiments and an empirical application for analysing driver behaviour while considering drivers' errors in perceiving traffic environment variables. The empirical analysis is carried out using space-time trajectories of vehicles from a heterogeneous, disorderly (HD) traffic stream in Chennai, India. Results suggest that the proposed model, with power lognormal distributed multiplicative errors in traffic environment variables, outperformed the typically used mixed logit models with random coefficients (uncorrelated and correlated) or error components. Further, allowing for perception errors in traffic environment variables was found to be more important than allowing unobserved heterogeneity in the drivers' sensitivity to those variables. In addition, the empirical model offers interesting insights into the extent of variability due to perception errors in different traffic environment variables.