Konferensi Nasional Teknik Sipil 9 (KoNTekS 9).
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
A COMPARISON BETWEEN ARTIFICIAL NEURAL NETWORKS AND
BINARY LOGIT MODELS TO ANALYSE THE INFLUENCE OF MALE MOTORISTS
ON MOTORCYCLE FATAL ACCIDENTS
Dewa Made Priyantha Wedagama
Jurusan Teknik Sipil, Universitas Udayana, Kampus Bukit Jimbaran Badung-Bali
Email: priyantha.wedagama@gmail.com
ABSTRACT
This study aims to develop and compare models that examine the influence of male motorists on
motorcycle fatal accidents using Tabanan Regency in Bali as a case study area. Both Artificial
Neural Network (ANN) and binary logit models were constructed using accident data set obtained
from the State Police of Bali Province. A feed forward with back propagation learning algorithm
was used in the ANN model to train the network. The accident data used in this study were fit to
both ANN and binary logit models. The model sensitivity shows that the ANN model estimated the
motorcycle fatal accidents about six out of ten events while the binary logit predicted five out of ten
events. In addition, the model efficiency indicated that the ANN and the binary logit models show
60% and 30% respectively of perfect performances. The ANN model therefore, developed the
relationship between male motorist accident factors and motorcycle fatal accident better than the
binary logit model. Using the ANN model, this study found that motorcycle fatal accidents in
Tabanan Regency in Bali are likely to occurr in accidents contributed by male motorist with
collision types including out of control, right angle, sideswipe, rear end and head on collisions .
Key words: fatal accident, gender, motorcycle, artificial neural networks, binary logit
1.
INTRODUCTION
The motorcycles have been extensively used as the main mode of passenger transportation in Indonesia.
Motorcycles share the roadways together with the other main modes consisting light and heavy vehicles. As the
results, there are always conflicts on the road amongst the three modes. Moreover, motorcyclist‟s behaviour such as
speeding and manoeuvring among vehicles to get ahead on the congested road worsened traffic condition. This
behaviour certainly is not favourable in terms of road safety. This circumstance leads to a high number of
motorcycle accidents in Indonesia including Bali Province. In fact, in Bali Province motorcycle accidents were
accounted for 70% of total road accidents (State Police of Bali Province, 2009).
Meanwhile, the accident data in Bali showed that male motorists at fault annually contributed about 80% to
motorcycle accidents (State Police of Bali Province, 2009). Amongst eight regencies in Bali, Tabanan regency has
been considered to have high number of motorcycle accidents (State Police of Bali Province, 2009). In 2008, there
were 34 motorcycle accidents and 11 motorcycle fatal accidents respectively per 100,000 population of Tabanan
regency. In addition, in 2008 there were 10 male motorists at fault per 100,000 population contributing on
motorcycle fatal accidents.
During period 2003-2008, in total there were 518 motorcycle accidents in Tabanan regency and male motorists
contributed about 89% (462 events) of these motorcycle accidents. Motorcycle fatal accidents were accounted for
more than half (260 out of 518) of all motorcycle accidents while male motorists at fault were up to 87% (227 out of
260) in motorcycle fatal accidents during the same period. This indicated that motorcycle fatal accidents were a
serious problem and male motorists significantly contributed on motorcycle fatal accidents in this regency.
Many previous studies have long investigated gender in relation to accident risk (Al-Ghamdi, 2002; Dissanayake,
2004; O‟Donnel and Connor, 1996; Wedagama, 2009b). These studies found a significant relationship between
gender and road accidents. In road safety analysis, logit models have been broadly used in several studies to
investigate motor vehicle accidents (Al-Ghamdi, 2002; Dissanayake, 2004; O‟Donnel and Connor, 1996). These
models were particularly used to analyse the probability of road accidents/injuries including fatal, serious and slight
accidents/injuries. Meanwhile, several studies results (Abdelwahab and Abdel-Aty, 2001; Abdelwahab and AbdelAty, 2001; Delen et.al, 2006) also showed that Artificial Neural Network (ANN) models have successfully
Paper ID : TR03 Transportasi
75
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
described the relationship between road accidents and their contributing factors. The ANN models have increased
the understanding of the relationship between injury severity and factors related to drivers, vehicles and
roadway/environment (Abdelwahab and Abdel-Aty, 2001).
A previous study has also been conducted for Tabanan regency to investigate contributing factors on motorcycle
fatal accidents (Wedagama, 2009a). The study however, did not specifically examine the influence of gender on
such fatal accidents. This study however, aims to develop and compare models of logistic regression and ANN
models to examine the influence of male motorists on motorcycle fatal accidents in Bali. Due to data constraints,
motorcycle fatal accidents in Tabanan Regency during period 2003-2008 were used as the case study area. In so
doing, the ANN and binary logit models are developed given that a fatal motorcycle accident has occurred. These
two models are compared to identify the better model to estimate the significant factors of male motorists that
contributed to motorcycle fatal accidents in Bali.
2.
LITERATURE REVIEW
Some previous studies have used ANN to model and examine road accidents. A previous study by Abdelwahab and
Abdel-Aty (2001) compared between the two well-known ANN models: the Multi-Layer Perceptron (MLP) and
Fuzzy Adaptive Resonance Theory (ART) and an ordered logit model to predict driver injury severity in traffic
accidents at a signalised intersection. The study showed that the classification accuracy of the MLP model
performed better for both training and testing phases than the fuzzy ART and the ordered logit models. Another
previous study by Abdelwahab and Abdel-Aty (2002) also compared between two neural ANN models, the MultiLayer Perceptron (MLP) and Radial Basis Function (RBF), and a logit model to analyse traffic safety of toll plazas.
The results showed that two level nested logit model was the best in describing probabilities of accident location
while the RBF was the best in analysing driver injury severity.
The ANN had also been compared to multiple discriminate analysis and binary logit models to predict vessel
accidents on the lower Mississippi River (Hashemi et.al, 1995). The ANN model‟s prediction power was 1.6 times
better than the other two. The ANN models were also developed to predict intersection crashes based upon driver,
vehicle and roadway surface characteristics (Akin and Akbas, 2010). That study showed that the ANN model was
capable in providing a very accurate prediction (90.9%) of the crash types. In addition, the results were considered
very promising and encouraging for further research to estimate future year dependent variables with the model
built. The ANN model has also been developed and compared to the log linear model to identify number of persons
injured fatality in motor vehicle accidents (Cansiz et.al, 2009). The study concluded that the ANN model performed
better than the log linear regression.
One of the challenging tasks in training an ANN model is to determine the appropriate number of neurons in the
hidden layer. However, there is no accurate answer to this question. In general, the number of neurons in the hidden
layer should not be underestimated or overestimated. The ANN has a few difficult conditions called its
disadvantages. One of these is over-fitting problem. The parameters of the problem can be overestimated by the
model, if the training part is taken into consideration to appraise the output variables without testing the ANN
model. Underestimation prevents the network from building a complete representation of inputs. By contrast,
overestimation can also lead to a compact representation of the relationship between the input patterns (Abdelwahab,
and Abdel-Aty, 2001). This problem will be resolved by using data that is proportionately divided as training,
testing and validation (Cansiz et.al, 2009). In addition, limiting the number of iterations can reduce the possibility of
over-fitting problem. While there are no firm rules, the use of some heuristics will help avoid over-fitting problem.
One such rule is to stop training when the ANN Mean Square Error (MSE) no longer declines significantly. In
addition, using fewer hidden layer nodes reduces the possibility of over-fitting (Bjornson, and Barney, 1999).
A feed forward with back propagation learning algorithm was used to train the ANNs and developed in three phases:
modelling, training and testing phases. The data collection, identification of input parameters and the internal rules
were considered in the modelling phase. The preparation of the data and the adaptation of the learning law for the
training were carried out during the training phase. The prediction accuracy of the model was evaluated at the
testing phase, that is, the comparison of the actual outputs and the estimated outputs. The ANN typically starts out
with randomised weights for all their neurons. This means that weights are to be estimated for the solution of a
particular problem. When a satisfactory level of performance is reached, the training ends, and the network uses
these weights to make a decision. One hidden layer was used in the ANN model since many experimental results
seem to confirm that one hidden layer may be enough for most traffic forecasting problem (Cansiz et.al, 2009). In
addition, theoretical works have shown that a single hidden layer is sufficient for ANNs to approximate any
Paper ID : TR03 Transportasi
76
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
complex non linear function (Cansiz et.al, 2009). In this study, the number of neurons in the hidden layer was
determined by trial and error.
In this study, a tangent sigmoid transfer function was used in the hidden layer because many of the input variables
were binary values and the tangent sigmoid is the preferred function under such conditions (Wilmot and Mei, 2004).
The log sigmoid transfer function was used in the output layer so that the output would be in the range zero to one
(Wilmot and Mei, 2004). The output layer contained a single neuron which produced the probability of accident. In
order to obtain the best form, various ANN models having various architectures including number of neurons (12,
18, 24 and 30), random connection weights with a maximum number of epochs of 100 were evaluated (Abdelwahab
and Abdel-Aty, 2001). The ANN model was trained with Gradient Descent Moment (GDM) learning and
Levenberg-Marquardth training algorithms. Matlab software was used to implement this training method. The MSE
was used to evaluate performances of the ANN models. The MSE is defined as the difference between the actual
observations and the response predicted by the model and is used to determine if the model fits the data or not and
whether the model can be simplified by removing terms. MSE formula is:
MSE
1 j
( yˆ i yi ) 2
h i 1
(1)
Where:
y i = actual data
ŷ i =output data
h=number of data
In addition, the performance of the ANN model was determined in terms of correlation coefficient (R). The
optimum number of hidden neurons was found out for obtaining the lowest value of MSE and the highest value of
R.
Meanwhile, binary logit is useful for predicting a binary dependent variable as a function of independent variables.
The goal of binary logit is to identify the best fitting model that describes the relationship between a binary
dependent variable and a set of independent or explanatory variables. The dependent variable is the population
proportion or probability (P) that the resulting outcome is equal to 1. Parameters obtained for the independent
variables can be used to estimate odds ratios for each of the independent variables in the model. The specific form of
the binary logit model is:
(x) = P =
e o 1 x
1 e o 1 x
(2)
The transformation of conditional mean (x) binary logit function is known as the logit transformation. The logit is
the LN (to base e) of the odds, or likelihood ratio that the dependent variable is 1, such that
Logit (P) = LN
Where:
Bo
Bi
Xi
P
Pi
1 Pi
:
:
:
:
:
Pi
= Bo + Bi.Xi
1
P
i
(3)
the model constant
the parameter estimates for the independent variables
set of independent variables (i = 1,2,.........,n)
probability ranges from 0 to 1
the natural logarithm ranges from negative infinity to positive infinity
The binary logit model accounts for a curvilinear relationship between the binary choice Y and the independent
variables Xi, which can be continuous or discrete. The binary logit curve is approximately linear in the middle range
and logarithmic at extreme values. A simple transformation of equation (4) yields
Pi
= exp Bo Bi . X i = exp Bo .exp Bi . X i
1 Pi
(4)
The fundamental equation for the binary logit shows that when the value of an independent variable increases by
one unit, and all other variables are held constant, the new probability ratio [P i/(1-Pi)] is given as follows:
Paper ID : TR03 Transportasi
77
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
Pi
= exp Bo Bi ( X i 1) = exp Bo .exp Bi . X i .exp Bi
1 Pi
(5)
When independent variables X increases by one unit, with all other factors remaining constant, the odds [P i/(1-Pi)]
B
increases by a factor exp i . This factor is called the odds ratio (OR) and ranges from 0 to positive infinity. It
indicates the relative amount by which the odds of the outcome increases (OR>1) or decreases (OR
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
A COMPARISON BETWEEN ARTIFICIAL NEURAL NETWORKS AND
BINARY LOGIT MODELS TO ANALYSE THE INFLUENCE OF MALE MOTORISTS
ON MOTORCYCLE FATAL ACCIDENTS
Dewa Made Priyantha Wedagama
Jurusan Teknik Sipil, Universitas Udayana, Kampus Bukit Jimbaran Badung-Bali
Email: priyantha.wedagama@gmail.com
ABSTRACT
This study aims to develop and compare models that examine the influence of male motorists on
motorcycle fatal accidents using Tabanan Regency in Bali as a case study area. Both Artificial
Neural Network (ANN) and binary logit models were constructed using accident data set obtained
from the State Police of Bali Province. A feed forward with back propagation learning algorithm
was used in the ANN model to train the network. The accident data used in this study were fit to
both ANN and binary logit models. The model sensitivity shows that the ANN model estimated the
motorcycle fatal accidents about six out of ten events while the binary logit predicted five out of ten
events. In addition, the model efficiency indicated that the ANN and the binary logit models show
60% and 30% respectively of perfect performances. The ANN model therefore, developed the
relationship between male motorist accident factors and motorcycle fatal accident better than the
binary logit model. Using the ANN model, this study found that motorcycle fatal accidents in
Tabanan Regency in Bali are likely to occurr in accidents contributed by male motorist with
collision types including out of control, right angle, sideswipe, rear end and head on collisions .
Key words: fatal accident, gender, motorcycle, artificial neural networks, binary logit
1.
INTRODUCTION
The motorcycles have been extensively used as the main mode of passenger transportation in Indonesia.
Motorcycles share the roadways together with the other main modes consisting light and heavy vehicles. As the
results, there are always conflicts on the road amongst the three modes. Moreover, motorcyclist‟s behaviour such as
speeding and manoeuvring among vehicles to get ahead on the congested road worsened traffic condition. This
behaviour certainly is not favourable in terms of road safety. This circumstance leads to a high number of
motorcycle accidents in Indonesia including Bali Province. In fact, in Bali Province motorcycle accidents were
accounted for 70% of total road accidents (State Police of Bali Province, 2009).
Meanwhile, the accident data in Bali showed that male motorists at fault annually contributed about 80% to
motorcycle accidents (State Police of Bali Province, 2009). Amongst eight regencies in Bali, Tabanan regency has
been considered to have high number of motorcycle accidents (State Police of Bali Province, 2009). In 2008, there
were 34 motorcycle accidents and 11 motorcycle fatal accidents respectively per 100,000 population of Tabanan
regency. In addition, in 2008 there were 10 male motorists at fault per 100,000 population contributing on
motorcycle fatal accidents.
During period 2003-2008, in total there were 518 motorcycle accidents in Tabanan regency and male motorists
contributed about 89% (462 events) of these motorcycle accidents. Motorcycle fatal accidents were accounted for
more than half (260 out of 518) of all motorcycle accidents while male motorists at fault were up to 87% (227 out of
260) in motorcycle fatal accidents during the same period. This indicated that motorcycle fatal accidents were a
serious problem and male motorists significantly contributed on motorcycle fatal accidents in this regency.
Many previous studies have long investigated gender in relation to accident risk (Al-Ghamdi, 2002; Dissanayake,
2004; O‟Donnel and Connor, 1996; Wedagama, 2009b). These studies found a significant relationship between
gender and road accidents. In road safety analysis, logit models have been broadly used in several studies to
investigate motor vehicle accidents (Al-Ghamdi, 2002; Dissanayake, 2004; O‟Donnel and Connor, 1996). These
models were particularly used to analyse the probability of road accidents/injuries including fatal, serious and slight
accidents/injuries. Meanwhile, several studies results (Abdelwahab and Abdel-Aty, 2001; Abdelwahab and AbdelAty, 2001; Delen et.al, 2006) also showed that Artificial Neural Network (ANN) models have successfully
Paper ID : TR03 Transportasi
75
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
described the relationship between road accidents and their contributing factors. The ANN models have increased
the understanding of the relationship between injury severity and factors related to drivers, vehicles and
roadway/environment (Abdelwahab and Abdel-Aty, 2001).
A previous study has also been conducted for Tabanan regency to investigate contributing factors on motorcycle
fatal accidents (Wedagama, 2009a). The study however, did not specifically examine the influence of gender on
such fatal accidents. This study however, aims to develop and compare models of logistic regression and ANN
models to examine the influence of male motorists on motorcycle fatal accidents in Bali. Due to data constraints,
motorcycle fatal accidents in Tabanan Regency during period 2003-2008 were used as the case study area. In so
doing, the ANN and binary logit models are developed given that a fatal motorcycle accident has occurred. These
two models are compared to identify the better model to estimate the significant factors of male motorists that
contributed to motorcycle fatal accidents in Bali.
2.
LITERATURE REVIEW
Some previous studies have used ANN to model and examine road accidents. A previous study by Abdelwahab and
Abdel-Aty (2001) compared between the two well-known ANN models: the Multi-Layer Perceptron (MLP) and
Fuzzy Adaptive Resonance Theory (ART) and an ordered logit model to predict driver injury severity in traffic
accidents at a signalised intersection. The study showed that the classification accuracy of the MLP model
performed better for both training and testing phases than the fuzzy ART and the ordered logit models. Another
previous study by Abdelwahab and Abdel-Aty (2002) also compared between two neural ANN models, the MultiLayer Perceptron (MLP) and Radial Basis Function (RBF), and a logit model to analyse traffic safety of toll plazas.
The results showed that two level nested logit model was the best in describing probabilities of accident location
while the RBF was the best in analysing driver injury severity.
The ANN had also been compared to multiple discriminate analysis and binary logit models to predict vessel
accidents on the lower Mississippi River (Hashemi et.al, 1995). The ANN model‟s prediction power was 1.6 times
better than the other two. The ANN models were also developed to predict intersection crashes based upon driver,
vehicle and roadway surface characteristics (Akin and Akbas, 2010). That study showed that the ANN model was
capable in providing a very accurate prediction (90.9%) of the crash types. In addition, the results were considered
very promising and encouraging for further research to estimate future year dependent variables with the model
built. The ANN model has also been developed and compared to the log linear model to identify number of persons
injured fatality in motor vehicle accidents (Cansiz et.al, 2009). The study concluded that the ANN model performed
better than the log linear regression.
One of the challenging tasks in training an ANN model is to determine the appropriate number of neurons in the
hidden layer. However, there is no accurate answer to this question. In general, the number of neurons in the hidden
layer should not be underestimated or overestimated. The ANN has a few difficult conditions called its
disadvantages. One of these is over-fitting problem. The parameters of the problem can be overestimated by the
model, if the training part is taken into consideration to appraise the output variables without testing the ANN
model. Underestimation prevents the network from building a complete representation of inputs. By contrast,
overestimation can also lead to a compact representation of the relationship between the input patterns (Abdelwahab,
and Abdel-Aty, 2001). This problem will be resolved by using data that is proportionately divided as training,
testing and validation (Cansiz et.al, 2009). In addition, limiting the number of iterations can reduce the possibility of
over-fitting problem. While there are no firm rules, the use of some heuristics will help avoid over-fitting problem.
One such rule is to stop training when the ANN Mean Square Error (MSE) no longer declines significantly. In
addition, using fewer hidden layer nodes reduces the possibility of over-fitting (Bjornson, and Barney, 1999).
A feed forward with back propagation learning algorithm was used to train the ANNs and developed in three phases:
modelling, training and testing phases. The data collection, identification of input parameters and the internal rules
were considered in the modelling phase. The preparation of the data and the adaptation of the learning law for the
training were carried out during the training phase. The prediction accuracy of the model was evaluated at the
testing phase, that is, the comparison of the actual outputs and the estimated outputs. The ANN typically starts out
with randomised weights for all their neurons. This means that weights are to be estimated for the solution of a
particular problem. When a satisfactory level of performance is reached, the training ends, and the network uses
these weights to make a decision. One hidden layer was used in the ANN model since many experimental results
seem to confirm that one hidden layer may be enough for most traffic forecasting problem (Cansiz et.al, 2009). In
addition, theoretical works have shown that a single hidden layer is sufficient for ANNs to approximate any
Paper ID : TR03 Transportasi
76
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
complex non linear function (Cansiz et.al, 2009). In this study, the number of neurons in the hidden layer was
determined by trial and error.
In this study, a tangent sigmoid transfer function was used in the hidden layer because many of the input variables
were binary values and the tangent sigmoid is the preferred function under such conditions (Wilmot and Mei, 2004).
The log sigmoid transfer function was used in the output layer so that the output would be in the range zero to one
(Wilmot and Mei, 2004). The output layer contained a single neuron which produced the probability of accident. In
order to obtain the best form, various ANN models having various architectures including number of neurons (12,
18, 24 and 30), random connection weights with a maximum number of epochs of 100 were evaluated (Abdelwahab
and Abdel-Aty, 2001). The ANN model was trained with Gradient Descent Moment (GDM) learning and
Levenberg-Marquardth training algorithms. Matlab software was used to implement this training method. The MSE
was used to evaluate performances of the ANN models. The MSE is defined as the difference between the actual
observations and the response predicted by the model and is used to determine if the model fits the data or not and
whether the model can be simplified by removing terms. MSE formula is:
MSE
1 j
( yˆ i yi ) 2
h i 1
(1)
Where:
y i = actual data
ŷ i =output data
h=number of data
In addition, the performance of the ANN model was determined in terms of correlation coefficient (R). The
optimum number of hidden neurons was found out for obtaining the lowest value of MSE and the highest value of
R.
Meanwhile, binary logit is useful for predicting a binary dependent variable as a function of independent variables.
The goal of binary logit is to identify the best fitting model that describes the relationship between a binary
dependent variable and a set of independent or explanatory variables. The dependent variable is the population
proportion or probability (P) that the resulting outcome is equal to 1. Parameters obtained for the independent
variables can be used to estimate odds ratios for each of the independent variables in the model. The specific form of
the binary logit model is:
(x) = P =
e o 1 x
1 e o 1 x
(2)
The transformation of conditional mean (x) binary logit function is known as the logit transformation. The logit is
the LN (to base e) of the odds, or likelihood ratio that the dependent variable is 1, such that
Logit (P) = LN
Where:
Bo
Bi
Xi
P
Pi
1 Pi
:
:
:
:
:
Pi
= Bo + Bi.Xi
1
P
i
(3)
the model constant
the parameter estimates for the independent variables
set of independent variables (i = 1,2,.........,n)
probability ranges from 0 to 1
the natural logarithm ranges from negative infinity to positive infinity
The binary logit model accounts for a curvilinear relationship between the binary choice Y and the independent
variables Xi, which can be continuous or discrete. The binary logit curve is approximately linear in the middle range
and logarithmic at extreme values. A simple transformation of equation (4) yields
Pi
= exp Bo Bi . X i = exp Bo .exp Bi . X i
1 Pi
(4)
The fundamental equation for the binary logit shows that when the value of an independent variable increases by
one unit, and all other variables are held constant, the new probability ratio [P i/(1-Pi)] is given as follows:
Paper ID : TR03 Transportasi
77
Prosiding Konferensi Nasional Teknik Sipil 9 (KoNTekS 9)
Komda VI BMPTTSSI - Makassar, 7-8 Oktober 2015
Pi
= exp Bo Bi ( X i 1) = exp Bo .exp Bi . X i .exp Bi
1 Pi
(5)
When independent variables X increases by one unit, with all other factors remaining constant, the odds [P i/(1-Pi)]
B
increases by a factor exp i . This factor is called the odds ratio (OR) and ranges from 0 to positive infinity. It
indicates the relative amount by which the odds of the outcome increases (OR>1) or decreases (OR