Page 384 - Special Topic Session (STS) - Volume 3

STS551 Zamira Hasanah Zamzuri et al.

Estimating the proportion of unreported traffic
accidents using Bayesian Poisson lognormal
model with an adjusted mean
Zamira Hasanah Zamzuri, Nik Sarah Nik Zamri, Kamarulzaman Ibrahim
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan
Malaysia

Abstract
Typically, traffic accident count data is overdispersed and exhibit the presence
of extra zeros. This presence is commonly explained as a result due to the
under reporting scenario; in which the accident did occur but not reported.
Past research tend to use the zero adjusted or zero inflated models; however
these models may not explain the true situation of under reporting. This paper
intends to offer an alternative model for traffic accident count data. We
propose an adjustment being made to the mean of the Poisson lognormal
model by incorporating a parameter to estimate the proportion of unreported
accidents. The Poisson lognormal features cater for the overdispersion
characteristics whereas the proportion parameter explains the true situation
of extra zeros in the data set. Parameters in this model are estimated based
on the Bayesian approach. Simulation studies are conducted to compare the
performance of the proposed model with existing models in literature. It is
expected that this model will offer a satisfactory fit to the data and provides a
thorough explanation on the unreported accident count data.

Keywords
traffic accidents; Poisson lognormal; extra zeros

1. Introduction
In order to plan strategies for reducing the risk of traffic accidents, we need
to understand factors that contribute to their occurrence. Traffic flow, road
condition, weather and geographical location are among factors that
potentially influence the occurrence of accidents (Lord et al. 2004). Statistical
models have been developed in the traffic accident literature for this purpose.
The primary reason for using statistical models in practice is to estimate the
safety performance functions (SPFs), which are subsequently used to detect
traffic accident black spots, i.e. locations with high frequency of accidents.
Among the work that illustrated the use of SPFs in identifying black spots can
be found in Lu et al. (2013), Chen (2012) and Sims & Somenahaili (2010).

373 | I S I W S C 2 0 1 9