Multivariate Model of Road Crashes for Vulnerable Users
DOI:
https://doi.org/10.15517/akz5sc87Keywords:
pedestrian, motorcyclist, bicyclist, Area-wide, CorrelationAbstract
Different authors have analyzed the occurrence of crashes involving vulnerable users, but most studies focus on pedestrians and cyclists. Few have explored the correlation between crash types and neglected another vulnerable user: motorcyclist. This article investigates the correlation between crashes involving pedestrians, cyclists, and motorcyclists at the area level in Costa Rica. Univariate and multivariate models using the Full Bayesian hierarchical approach were developed to relate crashes in the 489 districts between 2016 and 2022 with sociodemographic and exposure variables. Results showed that the multivariate model was more parsimonious, exhibiting lower posterior deviance and DIC compared to the univariate model, also the inclusion of multivariate random errors impacted both model fit and parameter estimates. Key variables like vehicle-kilometers, population, and proportion of households with vehicles showed significant improvements in their estimation parameters. Additionally, the multivariate model was better suited for estimating excess crash frequency. These findings can be very useful for future research exploring the correlation between these crash types, particularly at smaller scales like intersections or highway segments.
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References
[1] WHO, Global Status Report on Road Safety 2018: Supporting a Decade of Action, Geneva, Switzerland: World Health Organization, 2018.
[2] INEC, "Sistema de consulta en línea de estadísticas de defunciones 2000-2022," Unidad de Estadísticas Demográficas, Instituto Nacional de Estadística y Censos, 2023. [En línea]. Disponible en: http://sistemas.inec.cr:8080/bininec/RpWebEngine.exe/Portal?BASE=VITDEF&lang=esp
[3] S. Heydari, L. Fu, L. F. Miranda-Moreno, and L. Joseph, "Using a flexible multivariate latent class approach to model correlated outcomes: A joint analysis of pedestrian and cyclist injuries," Analytic Methods in Accident Research, vol. 13, pp. 16–27, Mar. 2017.
[4] H. Huang, H. Zhou, J. Wang, F. Chang, and M. Ma, "A multivariate spatial model of crash frequency by transportation modes for urban intersections," Analytic Methods in Accident Research, vol. 14, pp. 10–21, Jun. 2017.
[5] J. Lee, M. Abdel-Aty, and X. Jiang, "Multivariate crash modeling for motor vehicle and non-motorized modes at the macroscopic level," Accident Analysis & Prevention, vol. 78, pp. 146–154, May 2015.
[6] T. Nashad, S. Yasmin, N. Eluru, J. Lee, and M. A. Abdel- Aty, "Joint modeling of pedestrian and bicycle crashes: Copula-based approach," Transportation Research Record, vol. 2601, no. 1, pp. 119–127, Jan. 2016.
[7] J. Aguero-Valverde, K. F. Wu, and E. T. Donnell, "A multivariate spatial crash frequency model for identifying sites with promise based on crash types," Accident Analysis & Prevention, vol. 87, pp. 8–16, Feb. 2016.
[8] A. Osama and Safwat Sayed, "Investigating the effect of spatial and mode correlations on active transportation safety modeling," Analytic Methods in Accident Research, vol. 16, pp. 60–74, Dec. 2017.
[9] M. Singh, Y. Zhang, W. Cheng, Y. Li, and E. Clay, "Effect of transit-oriented design on pedestrian and cyclist safety using bivariate spatial models," Journal of Safety Research, vol. 83, pp. 152–162, Dec. 2022.
[10] P. Wu, X. Meng, and L. Song, "Bayesian space–time modeling of bicycle and pedestrian crash risk by injury severity levels to explore the long-term spatiotemporal effects," Physica A: Statistical Mechanics and its Applications, vol. 581, Art. no. 126171, Nov. 2021.
[11] A. Jimenez, J. P. Bocarejo, R. Zarama, and J. Yerpez, "A case study analysis to examine motorcycle crashes in Bogota, Colombia," Journal of Safety Research, vol. 52, pp. 29–38, Feb. 2015.
[12] J. H. Salum, A. E. Kitali, H. Bwire, T. Sando, and P. Alluri, "Severity of motorcycle crashes in Dar es Salaam, Tanzania,"
Traffic Injury Prevention, vol. 20, no. 2, pp. 189–195, Feb. 2019.
[13] F. J. Cunto and S. Ferreira, "An analysis of the injury severity of motorcycle crashes in Brazil using mixed ordered response models," Journal of Transportation Safety & Security, vol. 9, no. sup1, pp. 33–46, Jan. 2017.
[14] L. Wahab and H. Jiang, "A comparative study on machine learning based algorithms for prediction of motorcycle crash severity," PLoS ONE, vol. 14, no. 4, Art. no. e0214966, Apr. 2019.
[15] S. K. Sivasankaran, H. Rangam, and V. Balasubramanian, "Investigation of factors contributing to injury severity in single vehicle motorcycle crashes in India," International Journal of Injury Control and Safety Promotion, vol. 28, no. 2, pp. 243–254, Jun. 2021.
[16] J. Aguero-Valverde and P. P. Jovanis, "Spatial analysis of fatal and injury crashes in Pennsylvania," Accident Analysis & Prevention, vol. 38, no. 3, pp. 618–625, May 2006.
[17] J. Aguero-Valverde, "Multivariate spatial models of excess crash frequency at area level: Case of Costa Rica," Accident Analysis & Prevention, vol. 59, pp. 365–373, Oct. 2013.
[18] H. Huang, A. L. Darwiche, and M. A. Abdel-Aty, "County- level crash risk analysis in Florida: Bayesian spatial modeling," Transportation Research Record, vol. 2148, pp. 27–37, Jan. 2010.
[19] S. P. Miaou, J. J. Song, and B. K. Mallick, "Roadway traffic crash mapping: A space-time modeling approach," Journal of Transportation and Statistics, vol. 6, pp. 33–58, 2003.
[20] M. A. Quddus, "Modeling area-wide count outcomes with spatial correlation and heterogeneity: An analysis of London crash data," Accident Analysis & Prevention, vol. 40, no. 4, pp. 1486–1497, Jul. 2008.
[21] I. Tasic, R. Elvik, and S. Brewer, "Exploring the safety in numbers effect for vulnerable road users on a macroscopic scale," Accident Analysis & Prevention, vol. 109, pp. 36–46, Dec. 2017.
[22] Y. Wang and K. M. Kockelman, "A Poisson-lognormal conditional-autoregressive model for multivariate spatial analysis of pedestrian crash counts across neighborhoods," Accident Analysis & Prevention, vol. 60, pp. 71–84, Nov. 2013.
[23] M. Abdel-Aty, J. Lee, C. Siddiqui, and K. Choi, "Geographical unit based analysis in the context of transportation safety planning," Transportation Research Part A: Policy and Practice, vol. 49, pp. 62–75, Mar. 2013.
[24] F. J. Al-Mahameed, X. Qin, R. J. Schneider, and M. R. R. Shaon, "Analyzing pedestrian and bicyclist crashes at the corridor level: Structural equation modeling approach,"Transportation Research Record, vol. 2673, no. 7, pp. 308–318, Jul. 2019.
[25] H. Ding and N. N. Sze, "Effects of road network characteristics on bicycle safety: A multivariate Poisson-lognormal model," Multimodal Transportation, vol. 1, no. 2, Art. no.100020, Jun. 2022.
[26] H. Huang, B. Song, P. Xu, Q. Zeng, J. Lee, and M. Abdel- Aty, "Macro and micro models for zonal crash prediction with application in hot zones identification," Journal of Transport Geography, vol. 54, pp. 248–256, Jun. 2016.
[27] C. A. S. Machado, M. A. Giannotti, F. C. Neto, A. Tripodi, L. Persia, and J. A. Quintanilha, "Characterization of black spot zones for vulnerable road users in São Paulo (Brazil) and Rome (Italy)," ISPRS International Journal of Geo-Information, vol. 4, no. 2, pp. 858–882, Jun. 2015.
[28] S. Narayanamoorthy, R. Paleti, and C. R. Bhat, "On accommodating spatial dependence in bicycle and pedestrian injury counts by severity level," Transportation Research Part B: Methodological, vol. 55, pp. 245–264, Sep. 2013.
[29] A. Rampinelli, J. F. Calderón, C. A. Blazquez, K. Sauer-Brand, N. Hamann, and J. I. Nazif-Munoz, "Investigating the risk factors associated with injury severity in pedestrian crashes in Santiago, Chile," International Journal of Environmental Research and Public Health, vol. 19, no. 17, Art. no. 11126, Aug. 2022.
[30] S. M. Rifaat, R. Tay, and A. De Barros, "Effect of street pattern on the severity of crashes involving vulnerable road users," Accident Analysis & Prevention, vol. 43, no. 1, pp. 276–283, Jan. 2011.
[31] J. Aguero-Valverde and P. P. Jovanis, "Analysis of road crash frequency with spatial models," Transportation Research
Record, vol. 2061, no. 1, pp. 55–63, Jan. 2008.
[32] J. Ma and K. M. Kockelman, "Bayesian multivariate Poisson regression for models of injury count, by severity," Transportation Research Record, vol. 1950, no. 1, pp. 24–34, Jan. 2006.
[33] J. Ma, K. M. Kockelman, and P. Damien, "A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods," Accident Analysis & Prevention, vol. 40, no. 3, pp. 964–975, May 2008.
[34] X. Ma, S. Chen, and F. Chen, "Multivariate space-time modeling of crash frequencies by injury severity levels," Analytic Methods in Accident Research, vol. 15, pp. 29–40, Sep. 2017.
[35] A. Chandran, T. R. V. Sousa, Y. Guo, D. Bishai, F. Pechansky, and Vida No Transito Evaluation Team, "Road traffic deaths in Brazil: Rising trends in pedestrian and motorcycle occupant deaths," Traffic Injury Prevention, vol. 13, no. sup1, pp. 11–16, Mar. 2012.
[36] R. Amoh-Gyimah, M. Saberi, and M. Sarvi, "Macroscopic modeling of pedestrian and bicycle crashes: A cross-comparison
of estimation methods," Accident Analysis & Prevention, vol. 93, pp. 147–159, Aug. 2016.
[37] W. Cheng, G. S. Gill, J. L. Ensch, J. Kwong, and X. Jia, "Multimodal crash frequency modeling: Multivariate spacetime models with alternate spatiotemporal interactions," Accident Analysis & Prevention, vol. 113, pp. 159–170, Apr. 2018.
[38] J. Aguero-Valverde and P. P. Jovanis, "Bayesian multivariate Poisson lognormal models for crash severity modeling
and site ranking," Transportation Research Record, vol. 2136, no. 1, pp. 82–91, Jan. 2009.
[39] D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. Van Der Linde, "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 64, no. 4, pp. 583–639, Oct. 2002.
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