Estimating travel mode choice, including rail in regional area, based on a new family of regression models

In this paper, we model mode choice with the new specification of generalized linear models proposed by Peyardi et al. (2015). In logit models used by economists, the link function can be decomposed into the reference ratio of probabilities and a cumulative distribution function (cdf). Alternative cdfs (Student, Cauchy, Gumbel, Gompertz, Laplace, Normal) can be used. These cdfs differ in their symmetry (symetric or asymetric distributions) and in their tails (heavy or thin tails), each allowing a different distribution of behaviors. We test the statistic and economic implications of changing the cdf. First, we investigate the goodness-of-fit indicators (AIC, BIC, Mc-Fadden R2). Then, we compare estimated parameters in terms of sign and significativity. And finally, we look at behavioural outputs such as value of time and demand elasticities. We use a recent stated preferences survey conducted by the author in the Rhône-Alpes Région (France). Its specificity is to specifically address the question of mode choice (rail, coach and car) in a regional context. Attributes include travel time, cost and comfort. We also investigate the cross effect of travel time and comfort. Comparisons between cdfs are made on the basis of three models, including only attributes variables or only individual variables or both. Our results show that the different cdfs provide quite similar results. But, in our estimations, the logistic cdf never ranks among the best options. In terms of significance and sign of coefficients, parameters' estimation are globally the same even if some special features can be noticed. Looking at time equivalence of comfort, we notice that in the model without individual variables, the cdf has a major influence on outputs. In particular, the Student cdf provides very consistent results while some other cdfs (e.g. Gompertz, Logistic, Normal) are extreme.