Modelling motorcycle accident on the road section by using general linear model: Case studies in Batu City

Abstract: In the present study, we consider modelling the transportation and traffic problems in Batu City of East Java Province. Based on the accident data, the number of traffic accidents in Batu City is considered too high. Thus, the objective of this research is to develop a suitable model for motorcycle accidents around Batu City in East Java Province. Using some statistical analysis it is found that the best-fit motorcycle accident model is computed by : Acc = 7.019 × 10−6F1.702 exp (−0.2884S W + 0.091S) where : Acc = number of accident, F = Flow, pcu/h, SW = shoulder width, m, S = speed, km/h. This model shows that the affecting factors are flow, shoulder width and speed, therefore local government should improve some related factors (flow, shoulder width and speed) that can reduce the number of motorcycle accidents at crossing road in Batu City.


PUBLIC INTEREST STATEMENT
Road safety is a global issue and every day many people are killed or injured on roads, the cost of the damages during the accidents are economically very costly. Thus, it is an important topic to study the modelling the cases. In the present study, we consider modelling the transportation such as traffic problems and motorcycles accidents in Batu City of East Java Province. Based on the data, the number of traffic accidents in Batu City is considered very high. Thus, the objective of this research is to develop a suitable model for the motorcycle accidents around Batu City in East Java Province.
transportation for low-income people can be routine daily work and cost the 30-40% of total revenues, which reasonable cost should only amount to 10% of revenues (Sulistio, 2007).
On the other side, the transportation safety is a global problem and not solely a problem of transport, but has become a social problem in the society. WHO's concern for the safety of road transport is realized by setting the World Health Day 2004 with the theme: Road Safety is no Accident in order to reduce the toll of deaths and injuries. According to WHO, road transport accident rate in the world has reached 1.2 million deaths and over 30 million injured/disabled per year. As many as 85% of the victims who died in traffic crashes occur in developing countries, the number of vehicles is only 32% of the total number of vehicles in the whole world.
From the description in Table 1 we can see the number of traffic accidents at this time is quite high, especially, a motorcycle accident and a serious threat to traffic safety.
Among the accidents, motorcycle accidents have the largest percentage, about 63% of all traffic accidents. This is due to lack of seriousness in handling the road safety. Therefore, the objective of this study is to develop a model of a traffic accident involving a motorcycle in the town of Batu.

Model accident
Model as a tool or media that can be used to reflect and simplify a reality (the real world) is scalable. The models might display the properties of the complexity to be understood by everyone who translated into written form or image (Bhat, 2015). While the transportation model is an mathematical expression and is used to illustrate the relationship among the parameters (Comi & Russo, 2004;Ortuzar & Wilumsen, 1994;Tamin, 1999).
Modelling the accidents on roads (X-roads) by using Generalized Linear Model done in (Swan et al., 1994), and the format of the model is as follows:  where A = average motorcycle accident, Q = traffic flow, g 1 , g 2 , … = variables of geometry, α, k, b 1 , b 2 , … = parameters for estimation To develop a model of traffic accident, in particular to motorcycle accident, should be carried out to minimize the number of accidents by using multiple distribution in statistics (Aitkin, Anderson, Francis, & Hindle, 1989). Based on the several related literature, we conduct a study on traffic accidents, especially motorcycle accidents on several roads in the town of Batu. In the process of research we apply Geometric distribution. The data input in Batu City can be seen in Table 2.
Input data were provided by 15 of data (15 roads), then the data are processed by performing several iterations. Similarly, we develop a model based on eight roads' location data models that have shown the best and most significant parameters (most suitable). For crash analysis SPSS version 16 (Ghozali, 2006) and Software Easyfit 5.2 Standard version of the data were used and can be seen in Table 2.

Test distribution
Before we set up a model of a motorcycle accident on the town of Batu, we use the input data which is necessary to check the suitability of the distribution of each variable (Conover, 1999). Thus, we need to determine the shape of the distribution of the data in the study and to determine which distribution is most appropriate. Testing is only done on the variable distribution of the number of accidents (Acc) as the dependent variable or response variable (Zuherman, 2014).
To determine the suitability of the distribution, Kolmogorov-Smirnov test was done on Standard Software Easyfit 5.2 and calculations are carried out directly using the formula: The calculation of the distribution tests were conducted on roads with eight data involving one variable response and five explanatory variables. Among them are: the number of accidents (Acc) as the response variable, the variable number of lanes (NL), lane width (LW), road shoulder width (SW), a variable average speed (S) and variable traffic volume (F) (Tables 3 and 4).

Calculation Kolmogorov-Smirnov test
Based on standard output above 5.2 easyfit indicates that the distribution of data on the number of motorcycle accidents (Acc) is to follow the Geometric distribution (first order) with the value of KS statistic which is 0.25451, Negative Binomial distribution (second order) with the value of KS statistic 0.35276 and distribution Logarithmic ranks third with KS statistical value of 0.44737.
Furthermore, the Kolmogorov-Smirnov hypothesis is details in order to determine a distribution is not denied or rejected from a distribution of empirical data by using Goodness of Fit-Details (Table 5).
where H 0 = Data Acc follows distribution Geometric distribution and H 1 = Data Acc does not follow the distribution Geometric distribution Statistical Test Kolmogorov-Smirnov or D max = 0.25451 Critical Value Kolmogorov-Smirnov 5% or D (5%) = 0.45427.
Conclusion: With an error rate of 5%, it can be said that the accident data (Acc) following distribution Geometric distribution, with p = 0.0708.
Distribution of test results and graphs P-P plot above shows that the distribution that best fits the data field distribution is Geometric distribution, so it can be concluded that the data motorcycle accident on roads in the town of Batu are following the Geometric distribution.

Distribution of geometric on Kolmogorov-Smirnov test statistics
For more specifically, on the following steps performed statistical calculations Kolmogorov-Smirnov test against Geometric distribution based on the value of the maximum absolute deviation (D max ) defined as follows:  From Table 6 we observe that the values D max = 0.25452. This value is almost equal to the value obtained using software Dmaks easyfit 5.2 standard.
We can conclude that the calculation of the suitability of the distribution of Kolmogorov-Smirnov test is the same as the distribution of the test performed by using the statistical program Easyfit version 5.2 standard.

Initial parameter estimation
In the initial parameter estiomation, we use three stages in the case of a motorcycle accident in the town of Batu and we use the software SPSS 16.0 for Windows. The calculations can be seen as follows: Based on Table 7, it can be explained that the coefficient of determination of the model is indicated by the adjusted R 2 that is equal to 0.943 which means the variability motorcycle accident (Acc) as the response variable can be explained by the shoulder width, speed and flow as a predictor or independent variable was 94, 3% and the remaining 5.7% is explained by other variables not included in the model. Table 8 Variance Analysis above are used to determine whether the independent variables or predictor variables together or simultaneously affect the response variable or the dependent variable. This can be seen in the value of the F test of 39.526 and 0.002 significant at 0.002 or 0.050, which means that the independent variables (predictors) flow, shoulder width and speed simultaneously influence the variable speed motorcycle accident (Acc). Table 9 can determine the effect of each independent variable (predictor) and dependent variable (response). Of the three independent variables included in the model, all significant at 0.05. These variables are: flow, speed, and shoulder width significantly at 0.05 for all grades assymtotic x

Simultaneous effect (F test) in
Frek Frek Kum  significantly much smaller than 0.05, then from here we can conclude that a motorcycle accident variable (Acc) is influenced by factors flow, speed, and road shoulder (shoulder width).

Model accident
Model accidents on roads (X-roads) by using the approach of Generalized Linear Model (GLM), using Equation (1) and paying attention to Table 9 in the above equation maths can be formed, where the value of the coefficients can be put into the equation following (Aitkin et al., 1989): If it is defined by:

Non linear regression analysis
To predict non-linear regression model equation can be used non-linear regression analysis (nonlinear regression analysis) on SPSS version 16.
Having regard to the model of a motorcycle accident above, it can result in the following calculation: From Table 10, estimation Parameters (Parameter Estimate) above can be seen the estimated values of the parameters to form a non-linear regression model equation which is a model of motorcycle accidents on roads in the town of Batu, as the following equation: Acc = 7.019 × 10 −6 F 1.702 exp(−0.2884SW + 0.091S).

Observation data comparison
Model A, good model, is expected to give a prediction or estimate the value of close observation data, for it is necessary to check the model of motorcycle accidents on these roads. Table 11 and Figure 1 show that the estimation of the model is approaching the observation data (95% confidence level), so that the resulting model can be considered in accordance with existing conditions.

Pairwise test
Further testing Paired Sample t_Test to the data of observation and data estimation results, to see how relations between the two data produced from SPSS can be seen as follows: In Table 12 Paired Sample Statistics show that the observational data have increased very little to the data of the average estimate of 13.12 into 13.21. Table 13 Paired Samples Correlation analyses whether there is a relationship between the data and the observation data estimation. Here, we can see that the correlation with the estimated observation data is very strong (0.992). When viewed value Sig (0.000) < α it can be concluded very significant correlation.