Comparison of Poisson, Negative Binomial and Poisson-Lognormal Regression Models With 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 models have been used to predict accident on these roads but no unique model has been arrived at. In this article, three statistical models: Poisson Regression, Negative Binomial and the Poisson Lognormal were compared to determine the best fit on the road accident data obtained from five 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 data for the 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 Poisson log-normal Regression  has the least AIC and BIC of  78.30 and 84.200 respectively for Bauchi- 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-Dass road. The Poisson Log-normal Regression is more robust than the Poisson Regression and Negative Binomial Regression and therefore recommended for modeling accident data in the area of study.