Estimation of gap acceptance parameters within and across the population from direct roadside observation

This paper explores the feasibility of maximum likelihood as an approach to determine the parameters of gap acceptance functions when these functions vary from individual to individual. Specifically, it is shown that it is theoretically possible to estimate the average critical gap of a population of drivers (or pedestrians) and its variance, within and across individuals, from direct roadside observations. Although the Multinomial Probit Model provides a natural theoretical framework for the estimation of these parameters, the model seems not to be statistically estimable for this particular problem. It was shown, however, that if one of the parameters is known, the other two become estimable and a two-stage estimation process that takes into account this phenomenon can be utilized. The technique is demonstrated with the 203-driver data set included in Appendix A. The Multinomial Probit Model can also be used to determine simultaneously the mean critical gap, the mean critical lag (the first gap considered by a driver), and the variances of these. For the data set in Appendix A, the mean critical gap was significantly smaller than the mean critical lag, as one might expect. The techniques proposed in this paper have the further advantage of being statistically efficient with large data sets and of not requiring a panel of individuals to be observed under controlled conditions.