Page 386 - Special Topic Session (STS) - Volume 3

STS551 Zamira Hasanah Zamzuri et al.
single variance function, similar to the traditional NB distribution (Lord &
Geedipally 2011). A discussion on using a mixture of several count
distributions to explain the presence of extra zeros can be found in Zamzuri et
al. (2018).
Although the zero inflated model give new perspective to statistical modeling
of the frequency of accidents, but this model is likely to have difficulty in case
of undesirable phenomena (Jang et al 2010). Lord et. al. (2007) say that the
zero inflated model has a modeling error in highway accidents. Specifically, this
error is defined as that segment is said to be in safe condition although it is
likely to be involved in an accident even if no accident occurs for a long period.
According to Malyshkina and Mannering (2010), they noticed the phenomenon
of the segments based on previous data. However, this data has changed in
terms of data collection, the police and the traffic environment, in accordance
with the changing times. Hence, they used a Bayesian inference approach since
the conventional maximum likelihood estimate (MLE) cannot be used here.
This is due to the Markov switching models are difficult to estimate since the
state variable is unobservable. The Bayesian approach is a useful statistical
approach in which all forms of uncertainty are stated in terms of probability.
This paper intends to introduce a model that capture the presence of these
extra zeros based on a different specification. Since that these zeros are
hypothesised contributed due to the underreporting scenario, we propose that
a proportion parameter is introduced to the accident rate in the Bayesian
Poisson Lognormal model.

2. Methodology
Chib and Winkelmann (2002) explained in detail on implementation of the
Multivariate Poisson Lognormal (MPL). Park and Lord introduce the usage of
this model in traffic accident literature. Several critical elements on fitting the
MPL model are also discussed in Zamzuri (2015). The extension of this model
with addition of spatio-temporal component can be found in Zamzuri (2018).
The specification of this model is presented as an application to traffic accident
data, where observations are considered as recorded across intersections, with
each intersection having a number of levels of crash severity.
Let i represent the intersection and j the level of crash severity and let

be a column vector of reported crash counts for the ith intersection, =

( … ). We have N intersections and J levels of severity. Parameter =

2
1

( … ) is a vector of regression coefficients, while is the vector of

2
1
covariates. Parameter D is the covariance matrix for the random effects vector
= ( … ). When J=1, this model is reduced to the univariate setting.

1
2
We called the proposed model as the Adjusted Poisson Lognormal (APL)
model. In this model, we add two more parameters, π and τ. Parameter π
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