Estimating the Influence of Accident Related Factors on Motorcycle Fatal Accidents using Logistic Regression (Case Study: Denpasar-Bali)

In Denpasar the capital of Bali Province, motorcycle accident contributes to about 80% of total road accidents. Out of those motorcycle accidents, 32% are fatal accidents. This study investigates the influence of accident related factors on motorcycle fatal accidents in the city of Denpasar during period 2006-2008 using a logistic regression model. The study found that the fatality of collision with pedestrians and right angle accidents were respectively about 0.44 and 0.40 times lower than collision with other vehicles and accidents due to other factors. In contrast, the odds that a motorcycle accident will be fatal due to collision with heavy and light vehicles were 1.67 times more likely than with other motorcycles. Collision with pedestrians, right angle accidents, and heavy and light vehicles were respectively accounted for 31%, 29%, and 63% of motorcycle fatal accidents.


Introduction
Motorcycle is widely used as the main mode of transportation in Indonesia including Bali Province.Motorcycle in Bali is reported for almost 85% of the total registered vehicles with an average annual growth rate of approximately 11% [1].Meanwhile, in the capital city, Denpasar, the number of registered motorcycles was 390,000 of the total number of 457,000 registered vehicles in 2007.Furthermore, during the daytime on weekdays, the number of vehicles tends to double to about 800,000 units considering trips make by commuters and students to and from Denpasar [1].
It is a common view in Bali that three main transportation modes; private cars, heavy vehicles (bus and truck), and motorcycles share the roadways including highways.Commuters use the highways, which connects the capital city and the surrounding areas.Consequently, all these roads passed daily high traffic flows in which approximately 70% are motorcycle.
The majority of motorcycles on the road are smallsize motorcycles with engine capacity ranges between 100-150 cc.These small-size motorcycles have very high mobility on the road.
People use motorcycles for many purposes including work, shopping, leisure, and education either for short or long distance trips.For instance, students use motorcycles during weekdays for a return trip of 55 km between the capital city of Denpasar and a university in Jimbaran, Southern Bali.This is mainly due to poor quality of the current public transport services.On the other hand, a motorcycle is more practical to cope with traffic congestion and more efficient in comparison with private cars or public transport.
As there are no special lanes dedicated to motorcycle, there are always conflicts on the road amongst the three modes.The behavior of motorcycle users such as speeding and maneuvering among vehicles to get ahead, worsened traffic condition and is not favorable in terms of road safety.This may lead to high proportion of motorcycle accidents and casualties.In fact, during the period of 2003-2007 there were 4489 road accidents and 8498 casualties in Bali in which almost 60% involving fatal and seriously injured casualties.Of these road accidents, on average 70% of which involve motorcycles [2].A motorcyclist in Bali, therefore, could be regarded as a vulnerable road user.
In the city of Denpasar, during the period of 2006-2008 there were 676 accidents involving motorcycle, which accounted for about 67% of total road accidents [2].Of those accidents, 32% were motorcycle fatal accidents.Motorcycle fatal accident is defined as at least one motorcyclist died on the event of road accidents [2].
With regard to this high proportion of motorcycle fatal accidents, the city of Denpasar is chosen as a case study area.This paper aimed at examining several accident related factors contributing to motorcycle fatal accidents in the city of Denpasar, Bali Province, using a logistic regression.The accident related factors were obtained from the local police accident reports.

Previous Studies
Many studies have been carried out to estimate motorcycle accidents in both developed and developing countries [3][4][5][6][7].There are significant differences between motorcyclists in developing and developed countries.For example, pillion passengers are very uncommon in western countries.In addition, motorcycles in developing countries are more popular for commuting or utilitarian trips as opposed to recreational trips [3].
A study conducted in the United Kingdom (UK) [4] described growth of scooter and motorcycle corresponded to the increase in fatal and serious injuries.The study concluded that junction influenced significantly motorcycle accidents.This is mostly because older drivers have difficulties in identifying approaching motorcycles.Other significant factors influencing motorcycle accident included accident location (on bends), collision when overtaking vehicle(s) and skills of young and inexperienced motorcyclists and older motorcyclists.
Meanwhile, a study also conducted in the UK focusing on motorcyclist' behavior and accidents [5].The study found that speed was significantly related to motorcycle accident.In addition, errors and not violations dominantly influenced motorcycle accident.These because motorcyclists were likely to make errors during their trip due to the relative instability of a motorcycle.This study's suggestions included reducing the errors by changing and improving the riding style.This could be achieved by doing appropriate training and making motorcyclists aware of the risk of doing such errors.Other related studies, however, were more concerned on helmet and motorcycle accidents and casualties [6,7].
A study conducted in Saudi Arabia [8] applied a logistic regression to investigate the influence of accident factors on fatal and non fatal accidents for motor vehicle in Saudi Arabia.The study found that accident location and cause of accident significantly associated with fatal accidents.Accident factors used in the study including accident location, accident type, collision type, accident time, accident cause, driver age at fault, vehicle type, nationality, and license status.
Logistic regression has been considered as an appropriate method of analysis to compare severity of affecting factors between young and older drivers involved in single-vehicle accidents [9].The study found that factors influencing accidents of both driver groups were the same, except alcohol and drugs as the significant factors for older drivers accidents.Factors influencing young and older drivers' accidents included speeding and non-usage of a restraint device.In addition, ejection and existence of curve/grade significantly influenced higher young driver accident severity at all levels.Meanwhile, a frontal impact point was the main significant factor for older drivers accidents at all levels.

Logistic Regression Model
Logistic regression is useful for predicting a binary dependent variable as a function of predictor variables [10].The goal of logistic regression 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 one.Parameters obtained for the independent variables can be used to estimate odds ratios for each of the independent variables in the model [10].
The specific form of the logistic regression model is: The transformation of conditional mean π(x) logistic 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 one, such that Where: Bo = : the model constant Bi = the parameter estimates for the independent variables Xi = set of independent variables (i = 1, 2,.........,n) P = probability ranges from 0 to 1 LN = the natural logarithm ranges from negative infinity to positive infinity The logistic regression model accounts for a curvilinear relationship between the binary choice P and the predictor variables Xi, which can be continuous or discrete.The logistic regression curve is approximately linear in the middle range and logarithmic at extreme values.A simple transformation of Equation ( 1) yields: (3) The fundamental equation for the logistic regression shows that when the value of an independent variable increases by one unit, and all other variables are held constant, the new probability ratio [Pi/(1-Pi)] is given as follows: When independent variables X increases by one unit, with all other factors remaining constant, the odds [Pi/(1-Pi)] increases by a factor e Bi .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<1) when the value of the corresponding independent variable increases by one unit.
In logistic regression, there is no true R 2 value as there is in Ordinary Least Squares (OLS) regression.Alternatively, Pseudo R square can approximate an R-squared based on lack of fit indicated by the deviance (-2LL) as shown in Equations ( 5) and (6).In this study, there are two versions of Pseudo-R 2 , one is Cox & Snell Pseudo-R 2 and the other is Nagelkerke Pseudo-R 2 [11].
Where the null model is the logistic model with just the constant and the k model contains all predictors in the model.The Cox & Snell Pseudo-R 2 value cannot reach 1.0, however Nagelkerke Pseudo-R 2 value can be used to modify it.
A common method, which is also used to measure the goodness of fit is Hosmer-Lemeshow Test [10].The null hypothesis for this test is that the model fits the data, and the alternative is that the model does not fit.The test statistic is constructed by first breaking the data set into roughly ten groups.The groups are formed by ordering the existing data by the level of their predicted probabilities.The data are first ordered from least likely to have the event to most likely for the event.Then equal sized groups are formed, the observed and expected number of events is computed for each group.The statistic test is, Where: C ˆ = The Hosmer-Lemeshow test (H-L test) Ok = Observed number of events in the k th group Ek = Expected number of events in the k th group vk = Variance correction factor for the k th group If the observed number of events differs from what is expected by the model, the H-L test will be large and there will be evidence against the null hypothesis.

Case Study Area
Province of Bali has an area of 5,634.40km 2 and a population of about 3.4 million.The island is widely known as a tourist destination.Most popular tourist destinations are located in Southern areas including Kuta, Sanur, and Nusa Dua.Therefore, these areas are the most densely populated than any other parts of Bali.The capital city, Denpasar, is also located in the Southern Bali as shown in Figure 1.Denpasar has an area of 127 km 2 with the population of 608,595 [1].

Data Description
The number of motorcycle in Denpasar accounted for about 81% of the total registered vehicles [1].Meanwhile, motorcycle accidents were reported about 67% of motor vehicle accidents.Figure 2

Model Development
Data availability has been the primary consideration in determining independent variables for this study.All variables mentioned in Table 1 were obtained from the police.This study attempted to consider all relevant factors influencing motorcycle fatal accidents, despite the shortcoming of existing accident data in Bali.Some of accident related factors employed as the independent variables in this study (i.e.variables type no. 2 -6 in Table 1) followed the method used by a previous study conducted in Saudi Arabia [8].Furthermore, following suggestions from previous studies [12,13] age and gender have long been a high priority in accident risk assessment.Therefore, age and gender of driver or motorcyclist at fault were also considered as independent variables.As the results, variable types no. 2 -8 in Table 1 are employed as the independent variables in this study.All independent variables are categorical, except age which is a continuous variable.Meanwhile, the dependent variable is fatal accidents, which is binominal in nature.
In order to represent categorical variables, dummy variables are created following the coding system in SPSS [14] software used in this study.The categorical variables have several levels, so that they require the use of dummy variables defined as 0, 1, 2, 3, and so forth.This coding system is applied for the rest of categorical variables as shown in Table 1.It should be noticed that the SPSS is able to carry out this coding automatically once the end user has set the levels of the categorical variables.According to data related statistics shown in Table 2, some variable classifications can be neglected because of their small proportion.The hypothesis testing technique for proportions was used in this study to test whether a classification could be reduced [8,10].The following typical test was used: H0: pi = 0 and, Ha: pi ≠ 0, where, H0 = Null hypothesis (a classification can be neglected because of small proportion) Ha = Alternate hypothesis (a classification can not be neglected) pi is the proportion of an independent variable classification.
If the pi is significantly different from zero and falls in the rejection region at the 5% significance level, the null hypothesis is rejected.On the other hand, of the pi is sufficiently close to zero, the null hypothesis is accepted [10].
Based on the test, for motorcycle fatal accident analysis, there are three accident factors excluded from the model development stage, those are (marked with star in Table 2); 'accident type-with fixed object', 'vehicle type at fault-heavy vehicle', and 'accident location-junction'.The proportions of these classifications are statistically close to zero and have small proportions.Consequently, they can be excluded from model development stage [10].This exclusion however, is carried out by merging and putting these classifications as reference for the rest of classification within each variable.For instance, the accident type factor, 'with-fixed object' is merged with another significant factor 'overturned'.This is based on the assumption that these two factors could be considered as a single accident.In addition, 'heavy vehicle' and 'light vehicle' are merged together and generated as a new classification 'heavy and light vehicles'.The location factor 'junction' is not used as predictors considering that statistically most of fatal accidents occurred on road link.The entry method of logistic regression was followed using SPSS version 15 [14].The Omnibus Test [14,15] of motorcycle fatal accidents model coefficients is analysed in order to assess whether the data fit the model as shown in Table 3.In the table, the specified model is significant (Sig.< 0.05) so it is concluded that the independent variables improve on the predictive power of the null model.In contrast, the odds that a motorcycle accident will be fatal due to collision with heavy and light vehicles were 1.67 times more likely than with other motorcycles.This indicated that collision with heavy and light vehicles influenced 63% motorcycle fatal accidents.
Right angle accidents as one of the significant factors is consistent with a past study conducted in Saudi Arabia [8].Right angle accidents in Saudi Arabia were common cause of accidents especially at junction.The main reason was that motorists and motorcyclist behavior which failed to give way to other motorists [8].Similarly, this sort of motorist behavior is common in the city of Denpasar.More campaign such as introducing the risk of 'fail to yield' violation especially for motorcyclist is required to reduce such behaviour.In addition, such a violation may influence collision with pedestrians, in particular, when crossing the road.Meanwhile, accidents due to other factors are significantly higher than right angle accidents in contributing to motorcycle fatal accidents.Accident because of other causes, however, would imply broad range of factors which have not been thoroughly recorded within the accident data.Therefore, further works including data elaboration and improvement on accident recording system by the police are required before suggesting action plan to prevent accident because of other causes.
In relation to collision with other vehicles and collision with heavy and light vehicles can probably be explained by the fact that in typical mixed traffic, motorcycles shared the roadways together with heavy and light vehicles, in which motorcycles are the most vulnerable ones.Introducing special lane for motorcycle along the road link and enforcing safety riding program for motorcyclists including awareness to use the left lane, can be used to reduce fatal accidents.The analyses show that the odds that a motorcycle accident will be fatal due to collision with pedestrians and right angle accidents are about 0.44 and 0.40 times respectively lower than for collision with other vehicles and accidents due to other factors.In contrast, the odds that a motorcycle accident will be fatal due to collision with heavy and light vehicles are 1.67 times more likely than collision with other motorcycles.Collision with pedestrians, right angle accidents and heavy and light vehicles are accounted for 31%, 29% and 63% respectively to influence motorcycle fatal accidents.

Conclusions
The result of this study could be used to develop strategies to prevent and reduce fatal accidents in particular for motorcyclists in Bali.These strategies include introducing special lane for motorcycle along the road link and enforcing safety riding program for motorcyclists including awareness to use the left lane.In addition, further works including data elaboration and improvement on accident recording system by the police are required before recommending action plan to prevent an accident because of other causes.

Figure 1 .
Figure 1.Case Study Area -The City of Denpasar

Figure 2 .
Figure 2. Motorcycle Accidents in The City of Denpasar

Fatal 1 =
Day time, 0 = Night time Time 7. Gender (of driver/ motorcyclist at fault) 1 = Male, 0 = Female Gender 8. Age (of driver/ motorcyclists at fault) Year Age This study employs a logistic regression technique to investigate the influence of accident factors on motorcycle fatal accidents on arterial roads in the city of Denpasar, Bali Province.Based on the State Police of Bali Province accident data during the period of 2006-2008, seven predictor variables are employed in the model development.

Table 1 .
Variables Selected for the Study

Table 2 .
Hypothesis Testing: Data Statistics

Table 3 .
Omnibus Test of Model Coefficients

Table 4 .
Goodness of Fit (Pseudo R 2 and H-L Test)