A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

Accident Analysis and Prevention

Volumn 91, Issue , 2016, Pages 10-18

  Shirazi, Mohammadali ^a   Lord, Dominique ^a   Dhavala, Soma Sekhar ^b   Geedipally, Srinivas Reddy ^c  

^a Department of Electrical and Computer Engineering   (United States)

^b Perceptron Learning Solutions Pvt Ltd   (India)

^c TEXAS A AND M UNIVERSITY SYSTEM   (United States)

Author keywords

Crash data; Dirichlet process; Generalized linear model; Negative binomial

Indexed keywords

DISPERSIONS;

CRASH DATA; DEVELOPMENT AND APPLICATIONS; DIRICHLET PROCESS; GENERALIZED LINEAR MODEL; MULTI-PARAMETER MODELS; NEGATIVE BINOMIAL; RANDOMLY DISTRIBUTED; RESEARCH STUDIES;

BINS;

HUMAN; SAFETY; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA; TRAFFIC ACCIDENT;

ACCIDENTS, TRAFFIC; HUMANS; LINEAR MODELS; MODELS, STATISTICAL; SAFETY;

EID: 84959462804     PISSN: 00014575     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aap.2016.02.020     Document Type: Article

References (52)

1. P.C. Anastasopoulos, A.P. Tarko, and F.L. Mannering Tobit analysis of vehicle accident rates on interstate highways Accid. Anal. Prev. 40 2 2008 768 775
2. C.E. Antoniak Mixtures of dirichlet processes with applications to bayesian nonparametric problems Ann. Stat. 2 6 1974 1152 1174
3. R. Argiento, A. Guglielmi, C. Hsiao, F. Ruggeri, and C. Wang Modelling the association between clusters of snps and disease responses R. Mitra, P. Mueller, Nonparametric Bayesian Methods in Biostatistics and Bioinformatics 2015 Springer
4. C.R. Bhat The composite marginal likelihood (CML) inference approach with applications to discrete and mixed dependent variable models Found. Trends Econom. 7 1 2014 1 117
5. Bardenet, R., Doucet, A., Holmes, C., 2014. Towards scaling up markov chain monte carlo: An adaptive subsampling approach. In Proceedings of the 31st International Conference on Machine Learning, 405-413.
6. M.A. Beaumont, W.Y. Zhang, and D.J. Balding Approximate bayesian computation in population genetics Genetics 162 4 2002 2025 2035
7. D.M. Blei, and M.I. Jordan Variational inference for dirichlet process mixtures Bayesian Anal. 1 1 2006 121 143
8. J.G. Booth, G. Casella, H. Friedl, and J.P. Hobert Negative binomial loglinear mixed models Stat. Model. 3 3 2003 179 191
9. C. Carota, and G. Parmigiani Semiparametric regression for count data Biometrika 89 2 2002 265 281
10. S.S. Dhavala, S. Datta, B.K. Mallick, R.J. Carroll, S. Khare, S.D. Lawhon, and L.G. Adams Bayesian modeling of mpss data: gene expression analysis of bovine salmonella infection J. Am. Stat. Assoc. 105 491 2010 956 967
11. M.D. Escobar, and M. West Bayesian density-estimation and inference using mixtures J. Am. Stat. Assoc. 90 430 1995 577 588
12. M.D. Escobar, and M. West Computing nonparametric hierarchical models Pract. Nonparametric Semiparametric Bayesian Stat. 1998 1 22
13. T.S. Ferguson A bayesian analysis of some nonparametric problems Ann. Stat. 1973 209 230
14. T.S. Ferguson Prior distributions on spaces of probability measures Ann. Stat. 1974 615 629
15. S.R. Geedipally, D. Lord, and S.S. Dhavala The negative binomial-lindley generalized linear model: characteristics and application using crash data Accid. Anal. Prev. 45 2012 258 265
16. S.R. Geedipally, D. Lord, and S.S. Dhavala A caution about using deviance information criterion while modeling traffic crashes Saf. Sci. 62 2014 495 498
17. A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari, and D. Rubin Bayesian Data Analysis 2014 CRC Press
18. P. Ghosh, P. Gill, S. Muthukumarana, and T. Swartz A semiparametric bayesian approach to network modelling using dirichlet process prior distributions Aust. N. Z. J. Stat. 52 3 2010 289 302
19. J.E. Griffin, and S.G. Walker Posterior simulation of normalized random measure mixtures J. Comput. Graph.Stat. 20 1 2011 241 259
20. J.Q. Guo, and P.K. Trivedi Flexible parametric models for long-tailed patent count distributions∗ Oxford Bull. Econ. Stat. 64 1 2002 63 82
21. E. Hauer, and J. Bamfo Two tools for finding what function links the dependent variable to the explanatory variables Proceedings of the ICTCT 1997 Conference, Lund, Sweden 1997
22. F. Heinzl, and G. Tutz Clustering in linear mixed models with approximate dirichlet process mixtures using em algorithm Stat. Model. 13 1 2013 41 67
23. J. Hilbe Negative Binomial Regression 2nd ed. 2011 University Press Cambridge Cambridge
24. N. Hjort, C. Holmes, P. Muller, and S. Walker Bayesian Nonparametrics 2010 Cambridge University Press Cambridge, UK
25. H. Ishwaran, and L.F. James Gibbs sampling methods for stick-breaking priors J. Am. Stat. Assoc. 96 453 2001 161 173
26. H. Ishwaran, and M. Zarepour Exact and approximate representations for the sum dirichlet process Can. J. Stat. 30 2 2002 269 283
27. M. Kalli, J.E. Griffin, and S.G. Walker Slice sampling mixture models Stat. Comput. 21 1 2011 93 105
28. D. Lord, and F. Mannering The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives Transp. Res. Part A 44 5 2010 291 305
29. D. Lord, and S.R. Geedipally Safety Prediction with Datasets Characterized with Excess Zeros and Long Tails. 2016 Emerald Group Publishing Limited Bingley, UK Forthcoming chapter in Book
30. S.N. Maceachern, and P. Muller Estimating mixture of Dirichlet process models J. Comput. Graph. Stat. 7 2 1998 223 238
31. F.L. Mannering, and C.R. Bhat Analytic methods in accident research: methodological frontier and future directions Anal. Methods Accid. Res. 1 2014 1 22
32. M. Medvedovic, and S. Sivaganesan Bayesian infinite mixture model based clustering of gene expression profiles Bioinformatics 18 9 2002 1194 1206
33. S.P. Miaou, and D. Lord Modeling traffic crash flow relationships for intersections - dispersion parameter, functional form, and bayes versus empirical bayes methods Transp. Res. Rec. 1840 2003 31 40
34. R. Mitra, and P. Muller Nonparametric Bayesian Methods in Biostatistics and Bioinformatics 2015 Springer-Verlag New York
35. K. Miyazaki, and T. Hoshino A bayesian semiparametric item response model with dirichlet process priors Psychometrika 74 3 2009 375 393
36. S. Mukhopadhyay, and A.E. Gelfand Dirichlet process mixed generalized linear models J. Am. Stat. Assoc. 92 438 1997 633 639
37. Neiswanger, W., Wang, C., Xing, E., 2013. Asymptotically exact, embarrassingly parallel mcmc. stat 1050 (19).
38. J. Oh, C. Lyon, S. Washington, B. Persaud, and J. Bared Validation of fhwa crash models for rural intersections - lessons learned Transp. Res. Rec. 1840 2003 41 49
39. D.I. Ohlssen, L.D. Sharples, and D.J. Spiegelhalter Flexible random-effects models using bayesian semi-parametric models: applications to institutional comparisons Stat. Med. 26 9 2007 2088 2112
40. O. Papaspiliopoulos, and G.O. Roberts Retrospective markov chain monte carlo methods for dirichlet process hierarchical models Biometrika 95 1 2008 169 186
41. B.J. Park, and D. Lord Application of finite mixture models for vehicle crash data analysis Accid. Anal. Prev. 41 4 2009 683 691
42. Y. Peng, D. Lord, and Y. Zou Applying the generalized waring model for investigating sources of variance in motor vehicle crash analysis Accid. Anal. Prev. 73 2014 20 26
43. P. Pudlo, J.M. Marin, A. Estoup, J.M. Cornuet, M. Gautier, and C.P. Robert Abc Model Choice via Random forests 2014 Institut de Biologie Computationnelle (IBC) Montpellier, France Unpublished paper
44. X. Qin, J.N. Ivan, and N. Ravishanker Selecting exposure measures in crash rate prediction for two-lane highway segments Accid. Anal. Prev. 36 2 2004 183 191
45. M. Quiroz, M. Villani, and R. Kohn Speeding up mcmc by efficient data subsampling Riksbank Res. Paper Ser. 2015 121
46. J. Sethuraman A constructive definition of dirichlet priors Stat. Sin. 4 2 1994 639 650
47. D.J. Spiegelhalter, A. Thomas, N.G. Best, and D. Lun Winbugs Version 1 4.1 User Manual 2003 MRC Biostatistics Unit Cambridge
48. Y.W. Teh Dirichlet Processes. Encyclopedia of Machine Learning 2010 Springer
49. P. Vangala, D. Lord, and S.R. Geedipally Exploring the application of the negative binomial-generalized exponential model for analyzing traffic crash data with excess zeros Anal. Methods Accid. Res. 7 2015 29 36
50. S. Washington, M. Karlaftis, and F. Mannering Statistical and Econometric Methods for Transportation Data Analysis 2011 Chapman and Hall/CRC Boca Raton, FL
51. M.A. Yang, D.B. Dunson, and D. Baird Semiparametric bayes hierarchical models with mean and variance constraints Comput. Stat. Data Anal. 54 9 2010 2172 2186
52. Y. Zou, L. Wu, and D. Lord Modeling over-dispersed crash data with a long tail: examining the accuracy of the dispersion parameter in negative binomial models Anal. Methods Accid. Res. 5 2015 1 16