An alternative closed-form crash severity model with the non-identical, heavy-tailed, and asymmetric properties

Crash severity model is a classical topic in road safety research. The multinomial logit (MNL) model, as a basic discrete outcome method, is widely applied to measure the association between crash severity and possible risk factors. However, the MNL model has several assumptions and properties that are possibly not consistent with the actual crash mechanism, and therefore with the association measure for crash severity. One significant attribute is the variation in drivers' safety perception. Risk-taking drivers tends to drive at a higher speed, which increases the likelihood of severe crashes. However, the variations in speed and other driving performance lead to the error in the utility function more profound. This violates the assumption of identical error distributions between different crash severity outcomes. In this paper, we propose a multinomial multiplicative (MNM) model, as an alternative for crash severity model. There are two possible formulations for the proposed MNM model: (1) Weibull and (2) Fréchet, according to the distributions of random propensities and subject to the signs of the systematic parts of the regression equation. The two heavy-tailed distributions can capture the effect of unobserved contributory factors on crash injury severity. Additionally, the MNM model can incorporate the effects of the non-identical, heavy-tailed, and asymmetric properties of the distribution, whereas the conventional MNL model cannot. Several operational considerations are also attempted in this study, including the specifications of the systematic parts and the interpretations of the parameters. The MNM model is further extended to the mixed MNM (MMNM) model by considering unobserved heterogeneities using random coefficients, while the mixed MNL (MMNL) model is used as the benchmark model. The proposed MMNM model is calibrated using the crash dataset obtained from the Guangdong Province, China. Results indicated that the proposed MMNM model outperformed the MMNL model in this case. Also, the results of parameter estimates are indicative to impact factors on crash severity as well as the design and implementation of policies. This justified the use of MMNM model as an alternative for crash severity model in practice. This is the first application of MMNM model in the traffic safety literature, it is worth exploring the application of other advanced multiplicative models for safety analysis in the future.