Modeling unobserved heterogeneity using finite mixture random parameters for spatially correlated discrete count data

Transportation Research Part B: Methodological

Volumn 91, Issue , 2016, Pages 492-510

  Buddhavarapu, Prasad ^a   Scott, James G ^b   Prozzi, Jorge A ^b  

^a CISCO SYSTEMS   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Data augmentation; Finite mixture multivariate normal prior; Intrinsic Conditional Auto Regressive (ICAR) priors; Negative binomial model; Polya Gamma random variables; Road condition; Spatial dependence; Unobserved heterogeneity

Indexed keywords

BAYESIAN NETWORKS; INFERENCE ENGINES; MIXTURES; SPECIFICATIONS;

AUTO-REGRESSIVE; DATA AUGMENTATION; GAMMA RANDOM VARIABLES; MULTIVARIATE NORMAL; NEGATIVE BINOMIAL MODELS; ROAD CONDITION; SPATIAL DEPENDENCE; UNOBSERVED HETEROGENEITY;

ROADS AND STREETS;

BAYESIAN ANALYSIS; CORRELATION; HETEROGENEITY; MODELING; NUMERICAL MODEL; PARAMETERIZATION; PLANNING METHOD; ROAD; SAMPLING; SPATIAL ANALYSIS; TRANSPORTATION SAFETY;

EID: 84976298045     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2016.06.005     Document Type: Article

References (53)

1. Aguero-Valverde, J., Jovanis, P., Analysis of Road Crash Frequency with Spatial Models. Transp. Res. Record 2061 (2008), 55–63, 10.3141/2061-07.
2. Ahmed, M., Huang, H., Abdel-Aty, M., Guevara, B., Exploring a Bayesian hierarchical approach for developing safety performance functions for a mountainous freeway. Accid. Anal. Prev. 43:4 (2011), 1581–1589, 10.1016/j.aap.2011.03.021.
3. Albert, J.H., Chib, S., Bayesian Analysis of Binary and Polychotomous Response Data. J. Am. Stat. Assoc. 88:422 (1993), 669–679, 10.2307/2290350.
4. Anastasopoulos, P.C., Mannering, F.L., A note on modeling vehicle accident frequencies with random-parameters count models. Accid. Anal. Prev. 41:1 (2009), 153–159, 10.1016/j.aap.2008.10.005.
5. Anastasopoulos, P.C., Mannering, F.L., Shankar, V.N., Haddock, J.E., A study of factors affecting highway accident rates using the random-parameters tobit model. Accid. Anal. Prev. 45 (2012), 628–633, 10.1016/j.aap.2011.09.015.
6. Banerjee, S., Carlin, B.P., Gelfand, A.E., Hierarchical modeling and analysis for spatial data. Monographs on Statistics and Applied Probability, 2004, Chapman & Hall/CRC, Boca Raton, Fla 101.
7. Barua, S., El-Basyouny, K., Islam, M.T., Effects of spatial correlation in random parameters collision count-data models. Anal. Methods Accid. Res. 56 (2015), 28–42, 10.1016/j.amar.2015.02.001.
8. Barua, S., El-Basyouny, K., Islam, M.T., Multivariate random parameters collision count data models with spatial heterogeneity. Anal. Methods Accid. Res. 9 (2016), 1–15, 10.1016/j.amar.2015.11.002.
9. Besag, J., Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Stat. Soc. 36:Ser.B (1974), 192–236.
10. Bhat, C.R., Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences. Transp. Res. Part B 37:9 (2003), 837–855, 10.1016/S0191-2615(02)00090-5.
11. Bhat, C.R., The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models. Transp. Res. Part B 45:7 (2011), 923–939, 10.1016/j.trb.2011.04.005.
12. Blincoe, L., Miller, T., Zaloshnja, E., Lawrence, B., 2014. The Economic Impact of Motor Vehicle Crashes, 2000.
13. Bottolo, L., Consonni, G., Dellaportas, P., Lijoi, A., Bayesian Analysis of Extreme Values by Mixture Modeling. Extremes 6:1 (2003), 25–47, 10.1023/A:1026225113154.
14. Burda, M., Harding, M., Hausman, J., A Poisson mixture model of discrete choice. J. Econometrics 166:2 (2012), 184–203, 10.1016/j.jeconom.2011.09.001.
15. Chen, E., Tarko, A.P., Modeling safety of highway work zones with random parameters and random effects models. Anal. Methods Accid. Res. 1 (2014), 86–95, 10.1016/j.amar.2013.10.003.
16. Chin, H.C., Quddus, M.A., Applying the random effect negative binomial model to examine traffic accident occurrence at signalized intersections. Accid. Anal. Prev. 35:2 (2003), 253–259, 10.1016/S0001-4575(02)00003-9.
17. Coruh, E., Bilgic, A., Tortum, A., Accident analysis with aggregated data: The random parameters negative binomial panel count data model. Anal. Methods Accid. Res. 7 (2015), 37–49, 10.1016/j.amar.2015.07.001.
18. Deb, P., Trivedi, P.K., Demand for medical care by the elderly: a finite mixture approach. J. Appl. Econometrics 12:3 (1997), 313–336.
19. Dong, C., Clarke, D.B., Yan, X., Khattak, A., Huang, B., Multivariate random-parameters zero-inflated negative binomial regression model: An application to estimate crash frequencies at intersections. Accid. Anal. Prev. 70 (2014), 320–329, 10.1016/j.aap.2014.04.018.
20. Eddelbuettel, D., François, R., Rcpp: Seamless R and C++ Integration. J. Stat. Softw. 40:8 (2011), 1–18.
21. Frhwirth-Schnatter, S., Tchler, R., Otter, T., Bayesian Analysis of the Heterogeneity Model. J. Bus. Econ. Stat. 22:1 (2004), 2–15.
22. Gamerman, D., Lopes, H.F., Markov chain Monte Carlo: stochastic simulation for Bayesian inference. second ed. Texts in statistical science series, 2006, Taylor & Francis, Boca Raton 68.
23. Gelman, A., Rubin, D.B., Inference from Iterative Simulation Using Multiple Sequences. Stat. Sci. 7:4 (1992), 457–472, 10.1214/ss/1177011136.
24. Greene, W., Functional Form and Heterogeneity in Models for Count Data. Foundations Trends Econometrics 1:2 (2006), 113–218, 10.1561/0800000008.
25. Hauer, E., Observational before–after studies in road safety: estimating the effect of highway and traffic engineering measures on road safety. first ed., 1997, Pergamon, Oxford, OX, U.K. ; Tarrytown, N.Y., U.S.A.
26. Hausman, J., Hall, B., Griliches, Z., Econometric Models for Count Data with an Application to the Patents-R&D Relationship. Econometrica 52:4 (1984), pp.909–938.
27. Herbel, S., Laing, L., McGovern, C., 2010. Highway Safety Improvement Program (HSIP) Manual. Report No. FHWA-SA-09-029.
28. Jochmann, M., Len-Gonzlez, R., Estimating the demand for health care with panel data: a semiparametric Bayesian approach. Health Econ. 13:10 (2004), 1003–1014, 10.1002/hec.936.
29. Karlis, D., Xekalaki, E., Mixed Poisson Distributions. Int. Stat. Rev. / Revue Internationale de Statistique 73:1 (2005), 35–58.
30. Mannering, F.L., Bhat, C.R., Analytic methods in accident research: Methodological frontier and future directions. Anal. Methods Accid. Res. 1 (2014), 1–22, 10.1016/j.amar.2013.09.001.
31. Mannering, F.L., Shankar, V., Bhat, C.R., Unobserved heterogeneity and the statistical analysis of highway accident data. Anal. Methods Accid. Res. 11 (2016), 1–16, 10.1016/j.amar.2016.04.001.
32. Miaou, S.-P., Song, J.J., Bayesian ranking of sites for engineering safety improvements: Decision parameter, treatability concept, statistical criterion, and spatial dependence. Accid. Anal. Prev. 37:4 (2005), 699–720, 10.1016/j.aap.2005.03.012.
33. NHTSA, Traffic Safety Facts 2012. Technical Report. DOT HS 812 032, 2014, National Highway Traffic Safety Administration, Washington, DC.
34. Noland, R.B., Klein, N.J., Tulach, N.K., Do lower income areas have more pedestrian casualties?. Accid. Anal. Prev. 59 (2013), 337–345, 10.1016/j.aap.2013.06.009.
35. Otter, T., Tchler, R., Frhwirth-Schnatter, S., Capturing consumer heterogeneity in metric conjoint analysis using Bayesian mixture models. Int. J. Res. Market. 21:3 (2004), 285–297, 10.1016/j.ijresmar.2003.11.002.
36. Park, B.-J., Lord, D., Application of finite mixture models for vehicle crash data analysis. Accid. Anal. Prev. 41:4 (2009), 683–691, 10.1016/j.aap.2009.03.007.
37. Polson, N., Scott, J. G., Windle, J., 2012. BayesLogit. Explanation of the Polya-Gamma latent variable method.
38. Polson, N.G., Scott, J.G., Windle, J., Bayesian inference for logistic models using Plya-Gamma latent variables. J. Am. Stat. Assoc., 2013, 10.1080/01621459.2013.829001 130808174755007.
39. Quenouille, M., A Relation between the Logarithmic, Poisson, and Negative Binomial Series. Biometrics 5:2 (1949), 162–164.
40. R Core Team, R: A Language and Environment for Statistical Computing. 2013, R Foundation Stat. Comput., Vienna, Austria ISBN 3-900051-07-0.
41. Richardson, S., Green, P.J., On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion). J. Roy. Stat. Soc. 59:4 (1997), 731–792, 10.1111/1467-9868.00095.
42. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van Der Linde, A., Bayesian measures of model complexity and fit. J. Roy. Stat. Soc. 64:4 (2002), 583–639.
43. Ukkusuri, S., Hasan, S., Aziz, H.M.A., Random Parameter Model Used to Explain Effects of Built-Environment Characteristics on Pedestrian Crash Frequency. Transp. Res. Record 2237:-1 (2011), 98–106, 10.3141/2237-11.
44. Van Dyk, D.A., Meng, X.-L., The art of data augmentation. J. Comput. Graph. Stat., 10(1), 2001.
45. Venkataraman, N., Ulfarsson, G.F., Shankar, V.N., Random parameter models of interstate crash frequencies by severity, number of vehicles involved, collision and location type. Accid. Anal. Prev. 59 (2013), 309–318, 10.1016/j.aap.2013.06.021.
46. Wang, Y., Kockelman, K.M., A Poisson-lognormal conditional-autoregressive model for multivariate spatial analysis of pedestrian crash counts across neighborhoods. Accid. Anal. Prev. 60 (2013), 71–84.
47. Wedel, M., DeSarbo, W.S., Bult, J.R., Ramaswamy, V., A latent class Poisson regression model for heterogeneous count data. J. Appl. Econometrics 8:4 (1993), 397–411.
48. Wu, Z., Sharma, A., Mannering, F.L., Wang, S., Safety impacts of signal-warning flashers and speed control at high-speed signalized intersections. Accid. Anal. Prev. 54 (2013), 90–98, 10.1016/j.aap.2013.01.016.
49. Xie, K., Wang, X., Ozbay, K., Yang, H., Crash frequency modeling for signalized intersections in a high-density urban road network. Anal. Methods Accid. Res. 2 (2014), 39–51, 10.1016/j.amar.2014.06.001.
50. Xiong, Y., Mannering, F.L., The heterogeneous effects of guardian supervision on adolescent driver-injury severities: A finite-mixture random-parameters approach. Transp. Res. Part B 49 (2013), 39–54, 10.1016/j.trb.2013.01.002.
51. Zeng, Q., Huang, H., Bayesian spatial joint modeling of traffic crashes on an urban road network. Accid. Anal. Prev. 67 (2014), 105–112, 10.1016/j.aap.2014.02.018.
52. Zhou, M., Li, L., Dunson, D., Carin, L., 2012. Lognormal and gamma mixed negative binomial regression. arXiv preprint arXiv:1206.6456.
53. Zou, Y., Zhang, Y., Lord, D., Application of finite mixture of negative binomial regression models with varying weight parameters for vehicle crash data analysis. Accid. Anal. Prev. 50 (2013), 1042–1051, 10.1016/j.aap.2012.08.004.