Comparison of Poisson, Negative Binomial and Poisson-Lognormal RegressionModelsWith Application on Traffic Road Accident Count Data of Bauchi State

Abstract

Road Traffic Crash has been a serious problem on major roads in Nigeria. Different modelshave been used to predict accident on these roads but no unique model has been arrivedat. Inthis article, three statistical models: Poisson Regression, Negative Binomial and the PoissonLognormal were compared to determine the best fit on the road accident data obtainedfromfive major roads that link Bauchi metropolis from neighboring states. The roads are Bauchi-Jos, Bauchi-Gombe, Bauchi -Maiduguri, Bauchi-Kano and Bauchi-Dass roads. The dataforthe study spans a period of six years, (2010- 2015) consisting of the following variables: overtaking (OVT), over speeding  (OVS), Dangerous Driving (DGD) and Loss of Control (LOC). The analysis of data was carried out with the aid of R-statistical software. The  Poissonlog-normal Regression has the least AIC and BIC of 78.30 and 84.200 respectivelyforBauchi- Jos road, 76.000 and 81.900 for  Bauchi- Gombe road, 70.800 and 76.700 for Bauchi-Maiduguri road, 69.70 and 75.6 for Bauchi-Kano road and 66.00 and 60.100 for Bauchi- Dassroad. The Poisson Log-normal Regression is more robust than the Poisson RegressionandNegative Binomial Regression and  therefore recommended for modeling accident datainthearea of study.