Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
Modeling Road Accidents using Fixed Effects
Model: Conditional versus Unconditional Model
Wan Fairos Wan Yaacob, Mohamad Alias Lazim and Yap Bee Wah
remains the traditional Poisson and Negative Binomial
Abstract Modeling road accidents using panel data
distribution. When dealing with panel data type of road
approach recently has gained wide attention and application.
accident count, the most familiar panel data treatments are
As the nature of road crashes are non-negative count, the
the fixed effects (FE) and the random effects (RE) which
traditional linear computational approaches is inappropriate
were proposed for panel count data model by Hausman,
giving the nonlinear model of fixed effects (FE) the better
Hall and Griliches (HHG) [2]. We employed the panel
choice. This paper examines the road accidents relationship
with precipitation factors by estimating the FE Negative model approach of fixed effects negative binomial model
Binomial (NB) model. In the FE model two estimation
method since it has several advantages over individual time
methods were consider in this paper: conditional and
series and cross sectional model [3],[4], particularly, for its
unconditional estimation method. Thus, this paper compare
ability to account for heterogeneity in the data [5]. Since,
the conditional and unconditional FE model for road
many studies had proven that precipitation generally results
accidents and discuss the findings obtain. Results showed that
in more accidents compared with dry condition [6]-[8],
the unconditional FE Negative Binomial model gives
approximately the same results with conditional models. The therefore, in this study we will examines the relationship
effect of monthly rainfall with shorter spell period presents
between road accidents and various precipitation factors.
greater risk of accident rate. On the other hand, a negative
Given the discrete, non-negative nature of the road
relationship is found between the monthly rainfalls with
accidents count, the ordinary least square is not appropriate
longer spell period and accident rate.
to model this type of data [9]. Hence, the HHG negative
binomial model based on conditional estimation method
Index Terms Conditional Fixed Effects, Unconditional
Fixed Effects, Negative Binomial, Road accidents was employed first. Though analysis on the HHG Poisson
FE is simple and has been recognized to be exceptional
from incidental parameter problem [10],[11], the HHG
I. INTRODUCTION
formulation of conditional NB FE model is ambiguous [12],
[13]. Thus, to account for this ambiguity in HHG FE NB,
VER the past few years road accidents represent
O we also consider the unconditional FENB model [14]. The
among the leading cause of death and injury. Statistics
various models developed were applied in road accident
recorded had captured the interest of the researcher and
panel data set which allows for a detailed discussion and
policy maker to better understand the complexity of factors
comparison.
that are related to road accidents by developing statistical
In section 2 we review some related works on the
model. Models developed served as references for law
application of the model. Section 3 presents the models and
enforcement agencies and policy maker to implement
its properties. Application to examine the relationship of
corrective action aimed to reduce the number of road
road accident and precipitation factors using conditional
accidents. Thus, there has been considerable research
and unconditional FE NB is presented in Section 4. Results
conducted on the development of statistical model for
and discussions are presented in Section 5. Finally, the last
predicting road accident crash. A detailed review on
section discussed the policy lessons.
advancement of methodological approach in crash
frequency data can be found in Lord and Mannering [1].
II. RELATED WORK
Despite numerous advancement in estimation tools of
statistical model for count data, the most common
The literature on panel count model has grown
probabilities structure used for modeling road accident
considerably after the seminal work of Hausman, Hall and
Grilliches (HHG) et al. [2]. Application of panel count
model can be seen in varieties of application [15], [16].
Manuscript received March 6, 2012; revised April 12, 2012. This work
was supported in part by the Ministry of Higher Education, Malaysia under
Panel models have also become popular in road safety
Grant FRGS/2/2010/SG/UITM/02/34.
literature. Previous work on panel count model in road
W. F. W. Yaacob is with Faculty of Computer and Mathematical Sciences,
UiTM Shah Alam, 40450 Shah Alam, Selangor, Malaysia. (corresponding
accident application has been widely applying both fixed
author: phone: +6019-985-3350; fax: +603-5543-5503; e-mail:
effects and random effects model as suggested by Hausman
wnfairos@kelantan.uitm.edu.my).
et al. [4], [5],[ 7].
M. A. Lazim is with Faculty of Computer and Mathematical Sciences,
UiTM Shah Alam, 40450 Shah Alam, Selangor, Malaysia. (email:
Eisenberg [7] examined the relationship between
dralias@tmsk.uitm.edu.my)
precipitation and traffic crashes in 48 contiguous states in
Y. B. Wah is with Faculty of Computer and Mathematical Sciences, UiTM
Shah Alam, 40450 Shah Alam, Selangor, Malaysia. (email:
US using fixed effects negative binomial model for the
beewah@tmsk.uitm.edu.my)
period of 1975 to 2000. It was found that precipitation is
WCE 2012
ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
positively associated with fatal crashes. In terms of dry spell
where lit is the dependent variable of road accident count
effects, this study found that the rainfall amount has
for a given observation subscripted by state and time; ai is
enhanced effects on accident count after a dry spell due to
b ,g
the state specific effects; are the model parameter;
the slippery surface from accumulation of oil on the roads.
Time is the time trend; Xit includes other independent
Based on 6-year crash data set for urban and suburban
e
variables of interest; is the error term. To illustrate the
arterial of 92 counties in Indiana, Karlaftis and Tarko [4]
fixed effect negative binomial model, Hausman et. al [2]
employed fixed effects model of Poisson and negative
add individual specific effects of ai and the negative
binomial to develop the crash model. Their findings
indicated that the increase in the number of accidents is binomial overdispersion parameter of f into the model
i
associated with higher vehicle miles travelled, population,
replacing qi = ai fi . Here, the number of accident, yit for
the proportion of city mileage, and the proportion of urban
a given time period, t is assumed to follow a negative
roads in total vehicle miles travelled.
binomial distribution with parameters ailit and f ,
i
Kweon and Kockelman [17] investigated the safety
effects of the speed limit increase on crash count measure in where lit = exp xitób giving yit has a mean ailit fi and
( )
Washington State using the panel regression methods of
variance ailit fi 1+ai fi [9]. This model allows the
( ) ( )
both the fixed effects and random effects model assumption.
variance to be greater than mean. The parameter ai is the
They develop models for the number of fatalities, injuries,
individual-specific fixed effects and the parameter f is the
crashes, fatal crashes, injury crashes, and property-damage-
i
only (PDO) crashes using fixed effects and random effects
negative binomial overdispersion parameter which can take
Poisson and negative binomial model specification. They
on any value and varies across individuals. Obviously
found that the fixed-effects negative binomial model
ai andf can only be identified as the ratio of ai fi and this
i
performed best in describing injury count while for
ratio has been dropped out for conditional maximum
fatalities, injuries, PDO crashes and total crashes, the
likelihood [10].
pooled negative binomial model was a better choice.
The conditional approach of fixed effects Negative
There is also another study that applied fixed effects
Binomial model estimates the parameter b using the
negative binomial model in the analysis. Kumara and Chin
conditional joint distribution conditioning on the groups
[18] analyzed the fatal road accident data from the period of
total counts by maximizing the conditional joint
1980 to 1994 across 41 countries in the Asia Pacific region
distribution as below;
and found that road network per capita, gross national T T
ć ć
G G yit + 1
lit
Ti
product, population and number of registered vehicles were
ć
Ł t =1 ł Ł t =1 ł
P yi1 ,..., yiT yit =
positively associated with fatal accident occurrence.
T T
t =1
Ł łi G ć yit +
(2)
In another recent study, Law et al. [5] examined the lit
Ł t =1 t =1 ł
effect of motorcycle helmet law, medical care, technology
Ti
G yit + lit
( )
improvement, and the quality of political institution on
G lit G yit + 1
( ) ( )
t =1
motorcycle death on the basis of Kuznets relationships.
The fixed effects model for Poisson distribution does not
They used the HHG fixed effects negative binomial model
allow for an overall constant [10]. However, an overall
on a panel of 25 countries from the period of 1970 to 1999.
constant term is identified in the conditional distribution of
Their findings revealed that implementation of road safety
HHG NB formulation [17] indicating that HHG formulation
regulation, improvement in the quality of political
of FE NB model does not formulate the true fixed effects
institution and medical care and technology developments
model in the mean of random variable and conditioned out
showed significant effect in reducing motorcycle death.
of the distribution to produce the estimated model [13],
III. METHODOLOGY [19]. Hence, this study also considers the unconditional
estimator for both NB FE model.
This section discusses the formulation of panel count
model specification of the fixed effects Negative Binomial
B. Unconditional estimation of Fixed Effects Negative
model for both conditional and unconditional approach.
Binomial Model
The unconditional estimator of b is estimated by
A. Conditional estimation of Fixed Effects Negative
Binomial Model
specifying the conventional Negative Binomial model with
dummy variables for all group specific constant (less one)
The estimation method used in this study is the panel
to capture the fixed effects [12], [13], [14]. Hence Xit in
negative binomial regression developed by Hausman et al.
[2], a generalized version of Poisson regression that allows
model (1) also includes a set of dummy variables
the variance of dependent variable to differ from its mean.
representing fixed effects for each state and month effects.
The model can be expressed in the following way;
The unconditional FE Poisson model is estimated by a
direct maximization of the full log likelihood function
ó
ln lit = ai + ln Vehit +gTimeit + b Xit +eit (1)
( )
( )
given by
for i = 1, 2,...N and t =1, 2,...Ti
WCE 2012
ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
yit TABLE I
ł
exp ł
THE LIST OF STATES, WEATHER STATION AND YEAR OF DATA
exp
Ti -exp ai + xitób ai +xitób
N
ę ( ( ) ( ) ś
)
ę ś
Log L = ś (3) No
logę
State Station Period
yit !
i=1 ę t=1 ś .
ę ś
1 Perlis (PL) Chuping 1997 2007
2 Kedah (KD) Alor Setara 1997 2007
3 Pulau (PP) Bayan Lepas 1997 2007
with respect to all K + N parameters [14], [19]. While the Pinang
4 Perak (PR) Ipoh 1997 2007
unconditional FE NB model was estimated using the same
5 Selangor (SL) Petaling Jaya 1997 2007
approach by replacing the Poisson density with the NB
6 Kuala (KL) Parlimenb 1997 2007
Lumpur
counterpart of
7 Negeri (NS) Hospital 1997 2007
G q + yit yit
( ) Sembilan Serembanc
P yi1,..., yiT xit = .uq uit
( )
it (1- ) 8 Melaka (ML) Melaka 1997 2007
G q G yit +1
( ) ( )
9 Johor (JH) Senai 1997 2007
. (4)
10 Pahang (PH) Kuantan 1997 2007
where
11 Terengganu (TR) Kuala 1997 2007
Terengganu
uit = q q + lit (5)
( )
Airport
12 Kelantan (KN) Kota Bharu 1997 2007
in the FE Poisson log likelihood function given by
Weather data (state-day and therefore state-month) are missing for period:
yit a
ł 19-26 Dec 2005; b1-3 Aug 2004; c 1 Jun-15 Oct 2000, 16 May 2001-5Jun
exp ł
exp
Ti -exp ai + xitób ai +xitób
N 2001, 28 Nov 2003-2 Dec 2003, 4-26 Jan 2004, 6 Sep 2004-1 Oct 2004, 22
ę ( ( ) ( ) ś
)
ę ś
Log L = ś (6) Oct 2004-30 Apr 2005, 10-13 May 2005,18,31 Jul 2005, 1 Aug 2005-3
logę
yit !
Dec 2005, 1-31 Jul 2006.
i=1 ę t=1 ś
ę ś
used in previous work in road safety modeling literature
[6]-[8].
IV. DATA
Another climate factor considered was the number of
In this paper we worked on road accident panel data
rainy days (in days) for a particular month. The number of
comprising of a balanced panel monthly data in Peninsular
rainy days per month had been considered in previous
Malaysia from January 1997 to December 2007. The
studies of its relationship with road accident crash [7], [8].
number of observation per states was 132 with a total
Variation in the number of rainy days could be associated
number of 1584 observations from 12 states. The list of
with frequent expose of rain to road user [21]. Hence the
states included in the study is presented in Table 1.
number of rainy days was also used in this study. The data
The monthly total road accidents or road crash data were
were also collected from the Malaysian Meteorological
collected from the Royal Malaysian Police Headquarters in
Department (MMD) submitted by the same 12 selected
Kuala Lumpur for the year 1997 to 2007 [20]. The data
weather stations for rainfall amount data.
used referred to the total figure of their occurrences on
Another precipitation factor was the spell effects. The dry
public or private roads due to the negligence or omission by
spell effect took place when a consecutive series of days
any party concerned (on the aspect of road users conduct,
without rainfall was broken by the first rain after that
maintenance of vehicle and road condition), environmental
period [8]. This study used the spell period that referred to
factor (excluding natural disaster) resulting in a collision
the period of first rain occured since the last rain in a
(including out or control cases and collision of victims in
month that may take few days or few weeks as determined
a vehicle against object inside or outside the vehicle e.g. bus
by the rainfall recorded at 12 selected weather stations as in
passenger) which involved at least one moving vehicle
Table 1. The spell durations of gap between rain and no-
whereby damage or injury was caused to any person,
rain were broken down into the following category: (i) 1-7
property, vehicle, structure, or animal.
days; (ii) 8-14 days; (iii) 15-21 days; (iv) 22-28 days and
Data on the number of registered vehicles (VEH) were
(v) more than 28 days category. Then, the frequency of dry
also used which were collected from the Department of
spell for each spell period was obtained for the particular
Road Transport in the Malaysian Ministry of
month. If the highest frequency with the highest total
Transportation. The number referred to the total number of
number of no-rain day for the particular month fell within
vehicles (private and public) that was registered with the
the specified spell interval, then the dummy assigned was
Department of Road Transport. It included all vehicles
equal to 1 and the other spell interval dummy would be 0.
using either petrol or diesel which were motorcycles,
Note that the dummy for each spell period was mutually
motorcars, buses, taxis and hired cars, goods vehicle and
exclusive. This dummy was then interacted with the
other vehicles. However, the figure did not include army
precipitation (rainfall) variable and the interaction term
vehicle.
was included as an independent variable. These variables
Data for precipitation variables were collected from the
were created to examine what was the effect of this month
Malaysian Meteorological Department (MMD). The
precipitation with different spell period on this month
precipitation factor considered was the amount of monthly
crash. Thus, the accident counts were regressed with a list
rainfall (in millimeter) for a particular month. The data
of interaction variables between precipitation (rainfall) and
were captured from 12 selected weather stations in the
dry spell dummy.
respective 12 states. This factor had been most commonly
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ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
TABLE II
DESCRIPTIVE STATISTICS
Variable Unit Obs Mean S.D Min Max
Acc Road accidents crash 1584 1804.96 1709.65 54 8946
Veh Total number of registered vehicle 1584 4831.42 4765.75 136 27034
A_rain Monthly Rainfall (mm) 1584 206.12 150.31 0.2 1471.10
Rainy_D Monthly number of rainy days 1584 15.42 5.51 1 30
Prec_ds1-7 Interaction between rainfall and dry spell period
1584 190.47 161.48 0 1471.10
of 1 7 days
Prec_ds8-14 Interaction between rainfall and dry spell period
1584 13.30 47.54 0 461
of 8 14 days
Prec_ds15-21 Interaction between rainfall and dry spell period
1584 2.05 16.27 0 400.4
of 15 21 days
Prec_ds22-28 Interaction between rainfall and dry spell period
1584 0.09 1.55 0 35.9
of 22 28 days
Prec_ds>28 Interaction between rainfall and dry spell period
1584 0.28 6.61 0 180.9
of > 28 days
TABLE III
CORRELATION MATRIX
ARain RainyD Time Spell_1-7 Spell_8-14 Spell_15-21 Spell_22-28 Spell>28
ARain 1
RainyD 0.6527 1
Time 0.0548 0.0459 1
Prec_ds1-7 0.9509a 0.6761 0.0446 1
Prec_ds8-14 -0.0428 -0.1667 0.0251 -0.3301 1
Prec_ds15-21 -0.0624 -0.1748 0.0155 -0.1483 -0.0352 1
Prec_ds22-28 -0.0655 -0.1237 0.0445 -0.0652 -0.0155 -0.0069 1
Prec_ds>28 -0.0140 -0.0157 -0.0727 -0.0499 -0.0118 -0.0053 -0.0023 1
a
Correlation value greater than 0.7. Model in Table 5 was estimated without rainfall amount to cater for multicollinearity. It was found that excluding this
variable significantly affect other variables coefficient.
Missing observations for rainfall amount and dry spell and rainfall. The model in Table 4 was estimated without
were calculated by linear interpolation as suggested by rainfall variable to cater for multicollinearity. The second
previous study [5]. Extrapolations were only done for short highest of correlation was 0.654 for rainfall amount and
period of missing value by averaging the observations over number of rainy days. Table 4 presents the results for
preceding and posterior year. negative binomial FE model specification. Both conditional
In addition, the independent variables also included a and unconditional model were then estimated and
vector of dummy variables for all state (less one) compared. The specification was explored by including all
representing fixed effects for each state and month dummy. explanatory variables in a linear form of the exponential
The log of the total number of registered vehicle was function. The interpretation of the effect from exponential
incorporated in the model as an offset variable. The offset transformation used in panel count model (to ensure non-
term referred to the amount of exposure for a given negativity) is not as simple as in linear model. In
observation [7]. The risk of accident is not equal for each
ł
exponential case, E yit xit = exp xitób and each
( )
state. For instance, state with larger vehicle population size
will experience more accident than the state with less variable s marginal effects are as follows;
vehicle size. The different level of risk exposure can be
ł
śE xit
yit = exp xitób b = E yit xit ł b [12] which
normalized by creating a rate [22]. The rate can be included
( ) j
j
śx
ji
in the model by introducing the logged form of measure of
implies that a unit change in the jth variable leads to a
risk exposure as an offset variable. Hence, the logarithm
number of registered vehicle was chosen as the offset
ł
multiplicative change in E yit xit of b . The coefficients
j
variable in this study. The coefficient of independent
represent the effect of independent variables on the log of
variables will be interpreted as effects on rates rather than
the mean of dependent variable which can be interpreted as
count.
percentage changes in the expected count or rate for 1 unit
increase in the independent variable.
V. RESULTS AND DISCUSSIONS
The increase in the number of rainy days is predicted to
Table 2 presents the summary statistics for all variables
result in higher accident rate. The adverse effects are
included in the study. Table 3 presents the pairwise
estimated to be 1, which is the number of increase of rainy
correlation coefficients for the main variables used in this
days in a month associated with 0.3 percent increase in the
analysis. The highest correlation was 0.9509 for rainfall
monthly accident rate. This result is in accordance with the
amount and interaction effect for 1 7 days dry spell period
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ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
TABLE IV
FIXED EFFECTS REGRESSION MODELS FOR ROAD ACCIDENTS ON PRECIPITATION
Dependent variable: Road accidents
Unconditional Fixed Effects Conditional Fixed Effects
Negative Binomial Model Negative Binomial Model (HHG)
Model 1 Model 2 Model 3 Model 4
Coef. Z-stat Coef. Z-stat Coef. Z-stat Coef. Z-stat
RainyD 0.0035** 4.18 0.0032** 3.99 0.0032** 4.17 0.0031** 4.04
Time 0.0020** 25.04 0.0020** 25.12 0.0021** 29.33 0.0021** 29.42
Precipitation (mm)x (Dry spell
0.0001** 3.37 0.0001** 3.27 0.0001** 3.06 0.0001** 2.99
period 1 7 days dummy)
Precipitation (mm)x (Dry spell
0.0002** 3.24 0.0002** 3.09 0.0002** 3.76 0.0002** 3.66
period 8 14 days dummy)
Precipitation (mm)x (Dry spell
0.0324 1.69 - 0.0002 1.07 -
period 15 21 days dummy)
Precipitation (mm)x (Dry spell
0.0014 0.69 - 0.0017 0.91 -
period 22 28 days dummy)
Precipitation (mm)x (Dry spell
-0.0013** -2.66 -0.0013** -2.67 -0.0015** -2.56 -0.0015** -2.57
period > 28 days dummy)
State fixed effects ** **
Constant 1.7886 101.74 1.8011 103.16 0.6406 16.17 0.6419 16.22
N 1584 1584 1584 1584
Group (number of states) 12 12 12 12
Log likelihood -10,031.89 -10,033.56 -9,894.86 -9,895.79
Models 1 and 2 include state and month fixed effects. Models 3 and 4 include month fixed effects.
*
Significant at 0.05 level; ** Significant at 0.01 level.
findings on the traffic accident study done by Fridstorm [6]. the wet condition with shorter dry spell effect experienced
The time trend factor is also estimated in the model. This in a month. The surface of road might be slippery during
variable is used as a proxy to describe the technological the rainy month with shorter spell period that might affect
change that may also reflect the increase in the population the safety effect thus increase the risk of accident. This is in
volume and the development of road network over the time agreement with the findings obtained in the research done
that captures the effects of these exogenous time variables by Fridstorm [6]. Other possible explanation could be due
[5], [23]. The time variable coefficient in both conditional to accumulation of engine oil and gasoline on the road [7].
and unconditional FE Negative Binomial model shows a When the rain falls for the first time, the oil and dust that
positive and significant coefficient indicating an upward mixed with water may produce a thin liquid film on the
trend in the road accident rate in Malaysia. road surface which creates slick condition known as viscous
For more effect on weather condition, this study used hydroplaning [7],[24]. This may cause the vehicle to lose
two other weather variables to examine their effect on contact with the road surface and they tend to skid.
accident count; the rainfall and dry spell effect which were However, if the rain has fallen heavily after a certain spell
described by the interaction between rainfall amount (in period, the oil may have been washed of the road and the
millimeter) and dry spell period. The results follow the effect of viscous hydroplaning is lessening [7]. This may
expected pattern. The estimated effects from the model decrease the risk of accident occurrence. Another possible
imply that, over the course of a month, the monthly explanation is driven by a particular state of the country
accident rate is estimated to increase by 0.01% and 0.02% that has unique pattern of seasonal rainfall occurring
if the average monthly rainfall with shorter dry spell period regularly in particular months at different states in
of 1 to 7 days, and 8 to 14 days respectively increases by 1 Malaysia. As Malaysia climate is a tropical rainforest
millimeter. It is also interesting to see the effect is negative country coupled with local topography feature, it is not
for interaction between monthly rainfall amounts with surprising to see the negative effects coefficient for this
longer spell period. The effect is estimated to be one variable if the same model is estimated for every subset of
millimeter increase in monthly rainfall with longer spell the sample for 12 states in Peninsular Malaysia.
period of more than 28 days which is associated with
VI. POLICY LESSONS
0.015% decrease in the monthly accident rate. In other
words, the effect of rainfall in shorter spell period presents
As for now, Malaysia does not have a nationwide
greater risk in accident count. While the risk is lessening
programme to comprehensively cater for weather problems
with the rainfall in the month of longer spell period. This
in the context of road transportation. Hence, several policy
concludes that precipitation in a form of rainfall; dry spell
lessons and efforts that can be drawn from the results of
and number of rainy days are significant road safety
this study should be observed in all areas in the country.
hazards in Malaysia. Several interpretations are possible. A
The risk of road accident occurrence significantly increased
straightforward explanation for the positive effect would be
among drivers during the rainy month with shorter spell
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ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
Proceedings of the World Congress on Engineering 2012 Vol I
WCE 2012, July 4 - 6, 2012, London, U.K.
the Variation in Road Accident Counts, Accident Analysis and
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The authors would like to express greatest
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from
Professor Radin Umar Radin Sohadi for their guidance and
http://www.swov.n1/rapport/Factsheets/UK/FS_Influence_of_weather.p
valuable comments pertaining to this study. Special thanks df.
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Transport and the Malaysian Meteorological Department
for providing the data.
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WCE 2012
ISBN: 978-988-19251-3-8
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
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