Adjustment for maximum likelihood estimate of negative binomial dispersion parameter

Transportation Research Record

Volumn , Issue 2061, 2008, Pages 9-19

  Park, Byung Jung ^a   Lord, Dominique ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HIGHWAY ACCIDENTS; HIGHWAY ENGINEERING; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; TRAFFIC CONTROL;

CONDITION; CRASH DATA; DISPERSION PARAMETERS; GAMMA MODELS; HIGHWAY SAFETY; MAXIMUM-LIKELIHOOD ESTIMATE; NEGATIVE BINOMIAL; POISSON GAMMAS; SAMPLE MEANS; SAMPLE SIZES;

DISPERSIONS;

EID: 56749184111     PISSN: 03611981     EISSN: None     Source Type: Journal    
DOI: 10.3141/2061-02     Document Type: Article

References (20)

1. Lord, D., S. P. Washington, and J. N. Ivan. Poisson, Poisson-Gamma and Zero Inflated Regression Models of Motor Vehicle Crashes: Balancing Statistical Fit and Theory. Accident Analysis and. Prevention, Vol. 37, No. 1,2005, pp. 35-46.
2. Hauer, E. Overdispersion in Modeling Accidents on Road Sections and in Empirical Bayes Estimation. Accident Analysis and Prevention, Vol. 33, No. 6, 2001, pp. 799-808.
3. Miaou, S. P. Measuring the Goodness-of-Fit of Accident Prediction Models. Publication FHWA-RD-96-040. FHWA, U.S. Department of Transportation, 1996.
4. Wood, G. R. Confidence and Prediction Intervals for Generalized Linear Accident Models. Accident Analysis and Prevention, Vol. 37, No. 2, 2005, pp. 267-273.
5. Piegorsch, W. W. Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter. Biometrics, Vol. 46, No. 3, 1990, pp. 863-867.
6. Dean, C. B. Modified Pseudo-Likelihood Estimator of the Overdispersion Parameter in Poisson Mixture Models. Journal of Applied Statistics, Vol. 21, No. 6, 1994, pp. 523-532.
7. Lord, D. Modeling Motor Vehicle Crashes Using Poisson-Gamma Models: Examining the Effects of Low Sample Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter. Accident Analysis and Prevention, Vol. 38, No. 4, 2006, pp. 751-766.
8. Lord, D., and J. A. Bonneson. Calibration of Predictive Models for Estimating Safety of Ramp Design Configurations. In Transportation Research Record: Journal of the Transportation Research Board, No. 1908, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 88-95.
9. Saha, K., and S. Paul. Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter. Biometrics, Vol. 61, No. 1,2005, pp. 179-185.
10. Ross, G. I. S., and D. A. Preece. The Negative Binomial Distribution. The Statistician, Vol. 34, No. 3, 1985, pp. 323-326.
11. Cameron, A. C., and P. K. Trivedi. Regression Analysis of Count Data. Cambridge University Press, Cambridge, U.K., 1998.
12. Myers, R. H., D. C. Montgomery, and G. G. Vining. Generalized Linear-Models: With Applications in Engineering and the Sciences. John Wiley & Sons, Inc., New York, 2002.
13. Morris, C. N. Fitting Hierarchical Models. Presented at Summer Program: Statistics and Epidemiology: Environment and Health, Institute for Mathematics and Its Application, University of Minnesota, Minn., 1997. http://www.ima.umn. edu/summerstat/week6.html#wk6tue. Accessed July 2007.
14. Lawless, J. F. Negative Binomial and Mixed Poisson Regression. Canadian Journal of Statistics, Vol. 15, No. 3, 1987, pp. 209-225.
15. Lloyd-Smith, J. O. Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases. PLoS ONE, Vol. 2, No. 2, 2007, p. e180. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1791715. Accessed July 2007.
16. Clark, S. J., and J. N. Perry. Estimation of the Negative Binomial Parameter K by Maximum Quasi-Likelihood. Biometrics, Vol. 45, No. 1, 1989, pp. 309-316.
17. Toft, N., G. T. Innocent, D. J. Mellor, and S. W. J. Reid. The Gamma-Poisson Model as a Statistical Method to Determine If Micro-Organisms Are Randomly Distributed in a Food Matrix. Food Microbiology, Vol. 23, No. 1, 2006, pp. 90-94.
18. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2006. ISBN 3-900051 -07-0. http://www.R-project.org. Accessed July 2007.
19. Bonneson, J. A., D. Lord, K. Zimmerman, K. Fitzpatrick, and M. Pratt. Development of Tools for Evaluating the Safety Implications of Highway Design Decisions. Publication FHWA/TX-07/0-4703-4. Texas Transportation Institute, College Station, 2007. http://tcd.tamu.edu/Documents/0-4703-4.pdf. Accessed July 2007.
20. Lord, D., and J. A. Bonneson. Development of Accident Modification Factors for Rural Frontage Road Segments in Texas. In Transportation Research Record: Journal of the Transportation Research Board, No. 2023, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 20-27.