Accident Prediction by Using Poisson Regression for Unsignalised Junction in Khulna Metropolitan City, Bangladesh

Full text

Proceedings of International Conference on Planning, Architecture and Civil Engineering, 07 - 09 February 2019,
Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh
1
Accident Prediction by Using Poisson Regression for Unsignalised
Junction in Khulna Metropolitan City, Bangladesh
M. E. SHAIK1, Q. S. HOSSAIN2
1Department of Civil Engineering, KUET, Bangladesh (ebrahimkuet82@gmail.com)
2Department of Civil Engineering, KUET, Bangladesh (sazzad@ce.kuet.ac.bd)
Abstract
The Poisson regression models were used in the large area of application and likely to improve the quality and
important for the engineering aspects of accident prevention in Khulna Metropolitan City. A wide range of
accident data at each junction for the fifteen-year period (2000-2015) were used in the model development
process. In this model, numbers of accident were selected as an outcome variable and indicate the number of
accidents occurred at different types of junction in a year. Also total accident and junction types were selected as
a continuous predictor variable and categorical predictor variable respectively. It was found that the models
evaluated 2.19 times more variation in accidents at Not junctions and 1.80 times more variation at crossing
junctions than at T-junctions respectively. In absence of available dedicated left turning lane and traffic spot
speeds vehicle on the roads generally related with accident severity in each junction.
Keywords: Poisson Regression, Accident Prediction, Road, Unsignalised Junction, Variable.
1 Introduction
Road traffic accident is one of the most undesirable situations to occur to a road user resulting harmful to the people and
damages to the valuable properties. Now road traffic accident is the global phenomenon to the almost all countries of the
world. They are seriously concerned about the increasing number of people killed and injured on their highways. According
to the World Health Organization (WHO), more than 1.25 million people lives are cut short for the result of road traffic
accident every year. More people between 20 and 50 million suffer simple or non- fatal injuries, with many incurring a
disability as a result of their injury. For Bangladesh, accident severity and fatality in road accident is now an alarming issue.
In Bangladesh Khulna metropolitan city is the 3rd largest city with an area of 45.65 square kilometers and more than 1.022
million people live here. In this city, Total numbers of roads are 1215 with a total length of 356.65 kilometers (Khulna City
Corporation, 2015). Recently significant numbers of killed and injured people are increasing enormously in Khulna
metropolitan city (Ebrahim and Hossain, 2018).
For transportation safety, road traffic accident prediction models are very necessary tools given their effective for evaluating
both the frequency of accident frequency and the contributing factors that could then be determined by transportation
methods (Azad, 2017). To determine the accident frequency, accident severity level and different factors which are generally
responsible for road traffic accident, transportation authority and many research institute are often want to accident data and
factor to identify the most vulnerable road environment site. The different regression model including Poisson regression
model helps to explain the relationship between accident occurrence and responsible risk factor. Though multiple linear
regression models are widely used for prediction, it has been found that the Poisson regression model can often be better
fitted for prediction accident occurrence. The development of generalized theories concerning highway safety, road traffic
accident prediction models can also keep important contribution (Azad, 2017). Poisson regression has been often applied for
count road traffic and different transportation policies including frequency.
Generally Poisson regression has more advantages than other regression also related to different discrete distribution and
constraint to predicted value to non-negative integer number (Glenberg, 1996). In accident frequency analysis for different
platform, almost all the researcher has normally applied Poisson regression as a beginning point for analysis, they have often
found that the model data exhibit over and under dispersion that make the application of Poisson regression model
problematic (Lord and Mannering, 2010).As accidents are not occurred frequently, categorical style of accident data is more
efficient for expression of accident reaction and using this categorized accident data Poisson regression model make the taste
significance as fixed value (Sonia, 2012).

M. E. Shaik, Q. S. Hossain
ICPACE 2019
2
The situation of road accident in Khulna metropolitan city is actually frightful and the death of lives and infrastructure
damages are desired to continue if necessary corrective measures are not taken accordingly by applying proper engineering
measures through proper research. These situations for all metropolitan cities in Bangladesh are very dangerous. About 20
percent of road accident occurred in metropolitan cities viz. Dhaka, Chittagong, Khulna and Rajshahi (Hoque, M.M., 1991).
So, it is more important for Khulna city to predict road accident considering the basic factors including different types of
junctions.
2 Methodology
2.1 Data Collection
Five police stations were selected as study area namely Khulna sadar, Daulatpur, Khalishpur, Khanjahan Ali and
Sonadanga. The accident data from 2000 to 2015 were collected from the Khulna Metropolitan Police (KMP)
head quarter and Accident Research Institute (ARI), BUET.
2.2 Accidents Distribution
Figure 1 shows the yearly accident distribution.
Figure 1. Yearly accidents distribution.
Total 475 accidents were recorded within the year 2001 to 2015. Maximum 67 accidents and minimum 15
accidents were occurred in the year 2007 and 2004 respectively. Figure1 also showed that the accident rate
decreases in the last three years.
2.3 Model Development
IBM SPSS statistics 22 software was used for the development of Poisson regression model. In this study,
number of accidents, total number of accident and junction types were selected as model parameter where
number of accident was a outcome variable, total number of accident was a continuous predictor variable and
junction types is a categorical predictor variable.
The Poisson regression model is expressed as (Lord and Mannering, 2010):
!)exp(
)P(knn
k
nn
k
n



(1)
Where,
n = kn accidents per some time period,
kn = non- negative integer,
P(kn) = roadway entity probability, n having kn accidents per some time period,

M. E. Shaik & Q. S. Hossain
ICPACE 2019
3
n = Poisson parameter for roadway entity n,
Which is equal to roadway entity n’s expected number of accident per year, e [kn],
Poisson regression models were estimated by specifying the Poisson parameter n (the expected number of
accidents per period) as a function of explanatory variables, the most common functional form being
n = exp (xn),
Where xn is a vector of explanatory variables and  is a vector of estimable parameters.
2.4 Akaike’s Information Criterion (AIC)
The performance of different statistical model for given data is measured by Akaike’s Information Criterion
(Akaike, 1973). Akaike’s Information Criterion (AIC) compares the models quality relative to each other for
their collective data. Therefore, AIC is widely used for the selection of better model. Smallest value of AIC
indicates the best model (Omari-Sasu et al, 2016).
2.5 Bayesian Information Criterions (BIC)
Bayesian Information Criterion (BIC) is generally used for model selection among finite data sets of different
model. BIC is the exponential function and small parts of a likelihood function are closely related to Akaike’s
Information Criterion (AIC). Smallest value of Bayesian Information Criterions (BIC) indicates the best model
(Omari-Sasu et al, 2016).
3 Results and Discussions
The total accidents 231, 40 and 60 were recorded at the sites of Not junctions, T junctions and crossing junction
respectively for the study period 2000 to 2015. Only junction type is used and most of the parameter and variable
are not included for developing this model. Therefore, this model can be used only for approximate determinates
of accident severity in Khulna Metropolitan City.
Table 1 shows the narrative statistics of model data. Table 1 also shows that each variable contains 16 legal
observations and from their distributions it indicates quite reasonable. The outcome variable for unconditional
mean and variance are not immensely different. These values and predictor variable for different condition will
be equal by the model assumption.
Table 1. Narrative Statistics
N
Min.
Max.
Mean
Standard Dev.
No. of accident
16
1.80
0
32
4.56
Total .accident
16
1.85
12
67
32.19
Valid N (list wise)
16
1.93
Table 2 shows that the qualities fit of the model and the model output starts by this table. The statistics lists of
Table 2 indicate the model is quite fit. The first row of the Table 2 indicates the qualities of fit Chi- Squared test.
It was also found that the Akaike’s Information Criterion (AIC) of this model 55.669 and Bayesian Information
Criterions (BIC) equal to 58.760. Model also evaluates the deviance 20.20 as Chi-square distributed with the 12
degrees of freedom. Lowest value of both AIC and BIC indicates the developed model is the best model.
Table 2. Qualities of Fit
Value
DF
Value/DF
Deviance
20.200
12
1.683
Scaled deviance
20.200
12
Chi- Square (Pearson)
14.301
12
1.192
Chi- Square (Scaled-Pearson)
14.301
12
Log-likelihood
-23.835
AIC
55.669
Corrected AIC (AICC)
59.306
BIC
58.760
Consistent AIC (CAIC)
62.760
Dependent Variable: Number of Accident, Model: (Intercept), Parameter, Total Accident.

M. E. Shaik, Q. S. Hossain
ICPACE 2019
4
Table 3 shows the Estimate of Accident Parameters. These comprise the Poisson regression coefficients for each
variable including standard error, 95% confidence interval due to the coefficients. The regression coefficient for
total accident was found 0.082. This indicates that the expected increase in the log count for one unit increase in
total accident is 0.082. It was observed from the model effects that the output of this study is statistically
significant.
Table 3. Estimate of Accident Parameters
Parameter
B
Standard
error
95% Wald interval
confidence level
Hypothesis test
Lower
Upper
Wald Chi-
square
DF
Significance
Intercept
28.395
.4423
-29.262
-27.528
4121.570
1
.000
Parameter=1
26.548
.4027
25.758
27.337
4346.635
1
.000
Parameter=2
26.350
.
Parameter=2
0
.
Total
accident
.082
.0087
.065
.099
Scale
1
Dependent variable: Number of accident, Model: (intercept), parameter, total accident
Table 4 shows the parameter estimates of different types of junction. The average predicted value for Not
junctions was found 2.19. It indicates that the developed model evaluated 2.19 times more variation in road
accident at Not junctions and 1.80 times more variation at Crossing junctions than at T junctions respectively.
So, Not Junction is more severe for occurring accident among these junctions in Khulna Metropolitan City.
Table 4. Different types of parameter estimates
Types of parameter
Mean
Standard
error
95% Wald interval confidence
level
Lower
Upper
Not Junction
2.19
.582
1.30
3.69
Crossing Junction
1.80
.577
.96
3.37
T Junction
.00
.000
.00
.00
This Poisson regression model is the similar as that used in ordinary regression model except that the random
component is the Poisson distribution. The Poisson Regression model prediction is sometimes mentioned as a
Poisson Log linear model. Most of the regression model provides better for over dispersed data while Poisson
regression model provides better for equal- dispersion data.
4 Conclusions
The study of this research work was carried out the ability of Poisson regression model for prediction of accident
in Khulna Metropolitan City, Bangladesh. This paper developed the traffic accident prediction models to gather a
better knowledge by using this useful systems for predict the road traffic accidents including their hazard factors.
From the results it was found that the developed model evaluated 2.19 times more variation in road accident at
Not junctions and 1.80 times more variation at Crossing junctions than at T junctions respectively. So, Not
Junction is more severe for occurring accident among these junctions in Khulna Metropolitan City. It was found
from the Tests of Model Effects output that all the junctions overall, is statistically significant. It can be
concluded that the model fits reasonably well because the goodness-of-fit chi-squared test is not statistically
significant with 12 degrees of freedom. This model can able to predict the road accident at unsignalised junction
of Khulna Metropolitan City, Bangladesh.

M. E. Shaik & Q. S. Hossain
ICPACE 2019
5
References
Akaike, H. (1973). Information theory as an extension of the maximum likelihood principle. In the second
international symposium on information theory, edited B.V Petrov and B.F Csaki, Academical Kiado.
A.Y. Omari- Sasu, A. M. Isaac and R. K Boadi (2016). Statistical Models for Count Data with Applications to
Road Accidents in Ghana. International Journal of Statistics and Applications. vol. 6(3), 123-137.
Azad, A. (2017). Road Crash Prediction Models: Different Statistical Modeling Approaches. Journal of
Transportation Technologies. vol. 7, 190-205.
Ebrahim, S. and Hossain, Q. S. (2018). An Artificial Neural Network Model for Road Accident Prediction: A
Case Study of Khulna Metropolitan City. ICCESD 2018, 5193, 1-8.
Glenberg, A. (1996). Learning from Data: An Introduction to Statistical Reasoning. 2nd Edition, Lawrence
Erlbaum Associates, Mahwah.
Hoque. M.M. (1991). Accident investigation for the safety improvement of Dhaka- Aricha highway: A section of
Asian highway. Final report, Department of Civil Engineering, Bangladesh University of Engineering &
Technology, Dhaka, Bangladesh.
Khulna City Corporation (2015), Basic Statistics, Retrieved from:
http://www.khulnacity.org/Content/index.php?page=About_KCC&Z2Y&pid=30
Lord, D. and Mannering. F (2010). The statistical Analysis of Crash Frequency Data: A Review and Assessment
of Methodological Alternatives. Accident Analysis and Prevention. vol. 44, 292-303.
Sonia, R. (2012). Development of an Accident Prediction Model for Intersections of Dhaka City, Bangladesh.
International Journal of Computer Applications. vol. 47(16), 10-16.