A joint econometric framework for modeling crash counts by severity

ABSTRACT

This paper proposes an innovative joint econometric framework for examining total crash count and crash proportion by different crash severity. In our proposed approach, irrespective of the number of crash frequency variables the dimensions to be investigated is ‘two’, offering substantial benefits in terms of parameter stability and computational time as opposed to the traditional multivariate approaches. The proposed model is demonstrated by employing a joint negative binomial-ordered logit fractional split model framework. The empirical analysis is conducted using zonal level crash count data for different crash severity levels from Florida for the year 2015. The results clearly highlight the superiority of the joint model in terms of data fit compared to independent model. The applicability of the proposed framework is demonstrated by generating spatial distribution of predicted motor vehicle crash frequency and predicted crash counts by severity levels.

KEYWORDS:

• Count model
• crash count by severity
• negative binomial model
• ordered fractional split model
• joint model
• crash prediction model

Acknowledgements

The authors would also like to gratefully acknowledge Signal Four Analytics (S4A) for providing access to Florida crash data.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Naveen Eluru http://orcid.org/0000-0003-1221-4113

Notes

1. In some cases, a parametric multivariate distributional assumption might result in closed form approaches such as the copula-based approach (see Nashad et al. 2016).

2. The reader would note that there might be other approaches to combining counts and severity. For example, see Pei, Wong, and Sze (2011) for an approach that employs MCMC-based joint model estimation of crash counts and crash counts by severity. Also, Wang, Quddus, and Ison (2011) and Xu, Wong, and Choi (2014) developed a two-stage model by incorporating a sequential estimation of the Poisson-mixed multinomial and bivariate logistic-Tobit model, respectively.

3. It is worthwhile to recognize that the proposed approach can also be implemented with unordered or generalized ordered fractional split approaches. Moreover, the approach can be employed in developing both macro- and micro-level count models.

4. STAZ areas under consideration vary from 10⁻⁷ to 885.321 mile² with a mean of 6.472 mile². Given the wide range in STAZ areas, we allow the area associated with STAZs as an offset variable in order to account for different sizes of STAZs in our model specification. The coefficient of the offset variable is restricted to be one in estimating the model to normalize for the number crash events by STAZ area.

5. Dependence is defined as the ratio of youth (15 years or younger) and elderly (65 years or more) to working age persons.

6. Estimation results of independent NB-OLFS and joint NB-OLFS without correlation parameterization are presented in Table A1 and A2, respectively, in Appendix section.

7. These measures can be computed as and where, and are the predicted and observed values across different study units n (n = 1,1,2, … 8518).