Background of the study

Vehicle is one of the most widely used transport alternative and the major source of road traffic accidents in the world. Due to road traffic accidents, a greater part of road users could not return to home: farewell this world for once and all, spent long days, weeks, months, and even years in health centers and/or hospitals, and never be able to work or play as they used to do before. Particularly, nowadays, road traffic accident has been both public health and development issue and attracted the attention of governments, civil society organizations, and business and community leaders alike throughout the world. According to the World Health Organization (WHO, 2016) report, every year more than 1.25 million people now die on the world’s road and about 50 million people are injured or disabled as a result of road traffic crashes. Principally, injured people have occupied 30 to 70 percent of orthopedic beds in developing countries hospitals.  If business as a usual continuous, according to WHO, “road traffic injuries are estimated to be the ninth leading cause of death across all age groups globally, and are predicted to be the seventh-leading contributor to the global burden of disease and injury by 2030.” A recent GRSP study shows that about 10 per cent of global road deaths in 1999 took place in Sub-Saharan Africa where only 4 per cent of global vehicles are registered. Conversely, in the entire developed world, with 60 per cent of all globally registered vehicles, only 14 per cent of road deaths occurred. However, given the widely recognized problem of under-reporting of road deaths in Africa (like the rest of the developing world); the true figures are likely to be much higher, as the police- reported road fatalities represent only the tip of the injury pyramid. According to this GRSP study, the adjusted true estimate of total road deaths for all Sub-Saharan African countries for the year 2000, based on the police department’s records, ranges between 68,500 and 82,200. However, the estimated fatality figure of 190,191 for Sub-Saharan Africa presented in the 2004 World Report, based on health care data, is much higher, and reflects the magnitude of under-reporting in police statistics. While low and middle income countries account for 54% of world’s registered vehicles, every year about 90% of road traffic deaths occur in these countries showing that the countries bear an asymmetrical number of deaths corresponding to their level of motorization. Particularly, road traffic crashes are the worst in low and middle income countries which is responsible for about 5% loss of GDP, more than double of development assistance that they receive.  As far as the African Region is concerned, the continent has the highest road fatality rates of all the world’s regions  that is 26.6 per 100, 000 population relative to global rate of 17.5 per 100, 000 population. While the Region owns only 2% of the world’s vehicles, it contributes 16% to the worldwide deaths. The region will continue to have the highest road traffic death rates due to high rate of urbanization and motorization but lagging road infrastructural development as well as poor road and vehicles’ safety. The increased importance of transportation does not only demand new standards for efficiency, but also for safety precautions (Trafikverket, 2010). As of today, many fatalities and injuries are caused by road accidents. Ethiopia is one of those developing countries with low level of income accompanied by high rate of population growth. As part of the developing world, Ethiopia is predominantly an agrarian country with low level of urbanization. The economic performance of different sectors of the national economy is very low. This low performance is due to a number of constraints such as low level of investment in different sectors of the national economy. Among these the existing transport could be mentioned as one. Transport is an important sector for facilitating different economic activities in the national economy. Accident prediction models are important tools for estimating road safety with regards to roadway, weather and accidents conditions. There are different empirical equations developed for accident prediction models. However, new regression techniques have recently found application opportunities in this area. It is obvious that the model development and subsequently the model results are strongly affected by the choice of the regression technique used. This study evaluates the influence of roadway, weather and accidents conditions, and type of traffic control on accident severity (number of person killed) using regression models. Negative Binomial and Poisson regression models were deployed to measure the association between accident severity and roadway, weather and accidents conditions.

Statement of the Problem

Ethiopia is one of the developing countries with low level of income coupled with high rate of population growth. As part of the developing world, Ethiopia is predominantly an agrarian country with low level of urbanization. The economic performance of different sectors of the nation is very low. This low performance is due to a number of constraints in relation to investment in different sectors. The existing transport system could be mentioned as one. Transport is an important sector for facilitating different economic activities in the national economy. Nevertheless, due to low level of urbanization and the poor economic performance, transport is said to be at its infant stage in Ethiopia. In Ethiopia, the rate of road traffic accidents is very high; because road transport is the major transportation mechanism along with poor road infrastructure, poor traffic laws enforcement and other factors. The Ethiopian traffic control system archives data on various aspects of the traffic system, such as traffic volume, concentration, and vehicle accidents. With more vehicles and traffic takes the lion’s share of the risk, with an average of more than 20 accidents being recorded a day and even more going unreported (WHO, 2010). Road traffic accidents have also a gigantic impact on national economy by consuming the already inadequate resources, damaging invaluable property, and killing and disabling the productive age group of the community. In general, the severity of the problem is becoming horrific shockingly and reaching a catastrophic level. Showing that sufficient work has not been done to control and/or reduce alarming rate of the accident. This also implies that timely, accurate, and relevant data need to be collected and analyzed periodically so as to examine the trends, scope, and severity of the problem and come up with reasonable solution(s). The aim of this paper is thus to scrutinize the trends, causes, and economic implication of road traffic accidents in Kembata Tembaro zone.

Research questions

In general, the motivation behind this study is intended to address the following two major research questions.  What is the trend of road traffic accidents (deaths, serious injuries, slight injuries, and property damage) at zonal levels? What are the underlying causes of road traffic accidents in Kembata Tembaro zone?

Objectives of the study

The objective of this study is to analysis causes of traffic accident by using Generalized Linear Modelsin Kembata Tembaro zone.

Source of Data and Design

The study is cross-sectional and retrospective which was conducted from January 2017 to June 30, 2020. And the data was obtained both Primary and Secondary sources, to collect the primary data the researcher distribute questionnaires that are use to select respondents and structural form of interviews. Local enumerators were recruits from each study areas among candidates who has complete high school education and who has capable of speaking the local language. Orientation training on proper administration of the questionnaire was given to enumerators. The filled-in-questionnaire was examined on the daily basis to check for completeness and consistency. Secondary data was collected by verifying Kembata Tembaro zone transport office documents and other publish books and materials.

Modeling an expected value as a linear combination of a set of independent variables is in many cases possible, making general linear models a useful tool. However, linear relations might be inappropriate when the dependent variable is restricted to binary or counting numbers. Also, assuming normality of residuals might not be ideal when describing real world phenomena. Furthermore, homoscedasticity is sometimes an impossible assumption to make, for example when the variance tends to depend on the mean. Hence, the assumptions of linearity, normality and homoscedasticity limit the application range of the general linear models. The generalized linear model, GLM, extends the general linear models to address these issues. This research work mainly utilized secondary data obtained from the Building and Road Research Institute (BRRI) of the Council of Scientific and Industrial Research (CSIR). The data for the research was originally collected with the help of the Police accident report by the Traffic accident of the Kembata Tembaro zone Police Service. This research work considered a data for four years period from 2017 to 2020. The mean or expected number of persons killed in individual road accidents for the four years period will be used as the dependent or response variable and other categorical variables such as collision type, weather conditions, light condition, type of vehicle and driver error as, the explanatory or independent variables.

When facing a problem where the outcome of a random variable can take count values only, it makes sense to assume that the distribution of only considers count data. One distribution that fulfills this criterion and comes from the family of exponential distributions is the Poisson distribution. The most basic model for event counts is the Poisson regression model. If the variance of the counts approximately equals the mean counts, then the Poisson regression model is expressed as:

Where, yi is the number of counts (persons killed in accidents) for a particular period of time i , θi is the expected or mean number of counts (persons killed in road accidents) per period, which can be modelled as;

Where, xi is the vector of the explanatory or independent variables and β is the vector of unknown regression parameters. Equation 3 above as a result gives the indication that a unit increase in xi increases θi by a multiplicative factor of exp(x’βi). The main constraint of the Poisson regression model is that, the mean and the variance are approximately equal, that is;

As a result when there is heterogeneity or over-dispersion (when the variance increases faster than what the Poisson regression allows), the Poisson regression model does not work well hence there is the need to fit a parametric model that is more dispersed than the Poisson model and a natural choice is the Negative binomial and the Conway-MaxwellPoisson models. The Log-likelihood function of the Poisson model is expressed as;

By substituting equation 2 into equation 5, we further obtain the Log-likelihood function as;

Estimating the regression coefficient in the Poisson regression model is not obtained from a direct equation but rather the Newton Raphson method is used for estimating the parameters that are unknown in the model (Anseline, 2002)

Negative Binomial Regression Model

The Negative Binomial model can be obtained from the mixture of Poisson and Gamma distributions and is expressed as;

Where, yi is the number of road accidents for a road segment i and θi is the mean or expected number of persons killed in a road accidents per period, which can be expressed as;

The conditional mean and variance of the Negative Binomial distribution are respectively. Hence the NB model is over-dispersed and allows extra variation relative to the traditional Poisson model. It has more desirable properties than the Poisson model (Chin and Quddus, 2003). The variance of the Negative Binomial is significantly greater than the mean. The NB model, α represents the dispersion parameter which allows or indicates the degree of over-dispersion. For instance, if α =0, the NB model reduces to the traditional Poisson model.

Model Specification

Models considered in this research work has the mean or expected number of persons killed in road accidents within a particular period of time as a function of the categorical variable; collision type, driver error, type of vehicle, weather condition and light condition. Each mode parameterizes;

Where i= 1,....., n individuals, CT denotes the Collision Type, DE represents the Driver Errors, TV is the Type of Vehicle, LC as the Light Condition and WC representing the Weather Condition.

Descriptive Analysis of Road Traffic Accident in Kembata Tembaro Zone

This research shows briefly the review of the study of road traffic accident analysis done on the previous four years data from Kembata Tembaro Zone transport office documents and three month pedestrian survey of detail study on characteristics and trends of road traffic accident. The analysis of the road traffic accident data report from the Kembata Tembaro Zone  Police Commission between 2017 and 2020 showed  the road traffic  accidents data with respect to the number of persons killed,  revealed that there were  284  road accidents in  Kembata Tembaro zone  which killed 169  people, In terms of gender, males constituted 130 (76%) compared to females (39 or 24%) and also different levels of injury, 232 were Serious Injury, 172 or 74.2% were males compared to  60 or 25.8% females, 257 were  minor Injury while property damage as a result of the crashes which did not include costs of injuries for road users was estimated to be over  11 million birr.  This as a result gives indication that on the average, 71 road accidents occur every year and 43 lives were lost through road accidents. The table 4.1 below shows that the time in years for which road accidents that resulted in death of people occurred and additionally presents the total trends of road traffic accidents in road accidents yearly from 2017-2020.

Results of the Poisson Regression Model

The table 4.3 below presents the results on the estimate of the Poisson count regression model for the association of collision type, weather condition, type of vehicle, light condition prevailing during accident and driver error resulting in death. The table contains the parameter estimates, standard errors, death rates, the respective p-values of the various categories of variables used in the model and 95% Confidence interval for death rate. The parameter estimate from the table 4.3 below were interpreted in terms of the rate of the number of persons killed or died in road traffic  accidents.   These rates reflects the multiplicative effect           of  the                 various collision types, driver errors, type of vehicles, weather conditions, and light conditions on the number of persons killed in road traffic  accidents in Kembata Tembaro Zone.  In this model, hit  off road,  loss control , car, other and  night street light on  were used as reference levels for the categorical variables Collision type, Driver error, Type of vehicle, Weather condition and Light condition respectively due to the R and SPSS statistical software’s. With respect to the categorical variable Collision type from table 4.3 below, rear-end ,ran off ,side swipe and hit object on with p-values 0 .382, 0.483,0 .719 and 0.646 respectively were not significantly associated with the number of persons killed in road accidents . However, The estimated number of persons dead in road traffic accidents for the categorical variable Collision type from table 2 above overturn, right angle and hit on road are 1.483 (95% CI: 1.092- 1.694, p=.028), .619 (95% CI: .361 - .962, p=.031 and .460 (95% CI: .243 - .871, p=0.017), respectively were significantly associated with the number of persons killed in road traffic accidents. The parameter estimates of these significant collision types that overturn collision, right  angle collision and hit  on road collision  are  were .089,  -.480 and -.777 with death rates of  1.483,  .619 and .460 respectively. The death rate value for overturn collision suggests that, the rate of death in road accidents is 1.483 times higher among  deaths caused by overturn collision compared to hit off road  collision, the death rate value for right angle collision suggests that, the rate of death in road accidents is .619 times higher among  deaths caused by right  angle   collision compared to hit off road   collision,     whilst that of head-on collision on the other hand indicates that, the rate of death in road accidents is .460 times higher among deaths caused by hit-on road collision compared to deaths caused by hit off road  collision. The estimated relative risk of death for covariate driver error from table 4.3 below, only category inattentiveness on part of drivers with their p-value 0.113 was not significantly associated with the number of persons killed in road traffic accidents. However, inexperience of drivers, too fast, too close and no signal with their Rates, 95% CI and p-values   1.480 (95% CI: 1.096 - 1.998, p=.010), 1.719 (95% CI: 1.263 - 2.340, p=.001) , 2.011 (95% CI: 1.469 - 2.752, p=.000) and 1.462 (95% CI: 1.051 - 2.034, p =0.024), respectively were significantly associated with the number of persons killed in road traffic accidents.  The estimated rate of death for inexperience of drivers from the table 4.3 below was 1.480 indicating that, the rate of death in road traffic  accidents is 1.480 times higher with deaths caused by drivers inexperience  compared to drivers Loss control , estimated death rate for Improper too fast driving  was  1.719 which means that the rate of death in road accidents in Kembata Tembaro zone is 1.719 times higher with Improper too fast driving  compared to loss control , estimated death rate for Improper too close driving  was also 2.011 which means that the rate of death in road accidents in Kembata Tembaro zone is 2.011times higher with Improper too close driving  compared to loss control and that of no  signal is 1.462 indicating that the rate of death or number of persons killed in road accidents is 1.462 times higher with no  signal compared to loss control. In addition,  two types of vehicles were significantly associated with the number of persons killed in road traffic  accidents motor cycle and minibus with their Rates, 95% CI and p-values   1.230 (95% CI: 1.051- 1.590, p=.015) and 1.222 (95% CI: 1.032- 1.601, p=.047) , respectively. From the table 4.3, motor cycle as a type of vehicle contributing significantly to number of persons killed in road accidents had a rate value of 1.230 indicating that the rate of number of persons killed in road accidents was 1.230 times higher with motor cycle   compared to cars whilst the rate value for Minibus was obtained as 1.222 meaning that the rate of death in road traffic accidents was 1.222 times higher with Minibus compared cars in Kembata Tembaro Zone. Furthermore, clear weather conditions was the only category of the variable weather condition which was not significantly associated with the number of persons killed in road accidents since it had a p-value is  0.184 greater than the 5 percent  level of significance. Thus, Fog and Rain with their Rates, 95% CI and p-values   1.592 (95% CI: 1.183- 2.143, p=.002) and 1.453 (95% CI: 1.030 -2.048, p=.033), respectively proofed to be significantly associated with the number of persons killed in road accidents in Kembata Tembaro Zone.  Fog and Rain as types of weather conditions from the table 2 above had their rate values as 1.592 and 1.453 respectively indicating that, the rate of death in road accidents in the country is 1.592 times higher with fog compared to when the weather is other and rate of death in road accidents is 1.453 times higher with Rain compared to other weather condition. Lastly from the table 4.3 below, the last variable Light condition was classified into four categories of which two were not significantly associated with the number of persons killed in road traffic accidents in Kembata Tembaro Zone. These categories include “Night no street light” and “Night street light off” with p-values 0.335 and 0.210 respectively being greater than 5 percent level of significance. However, Day light condition with their parameter rate, 95% CI and p-values   1.229 (95% CI: 1.032 - 1.274, p=.031) respectively was significantly associated with the number of persons killed in road accidents.  The rate of death in road accidents on the other hand of these categories contributing significantly to number of persons killed was 1.229 respectively. This as a result gives the indication that, the death rate in road accidents in Kembata Tembaro Zone is 1.229 times higher with accidents that occur in the day compared to the night street light on.  Hence the mean of the Poisson count regression model with the significant variables for estimating the mean or the average number of persons killed in road accidents is:

Where,  OT is Overturn, RA is Right angle, HR is Hit on road, IE is Inexperience, TF is too fast, TC is Too close, NS is No signal, MC is Motor cycle, MB is Minibus, FG is Fog, RN is Rain and Day light condition.

Table 1: The Parameter Estimates, Standard Errors and the Rates of the Poisson Regression Model.

The table 4.5 below shows that the results of Negative Binomial regression model with collision type, driver error, and type of vehicle, light condition and weather condition as the independent categorical variables and the number of persons killed as the response variable. The parameter estimates associated with the categorical independent variables were the same as those of the Poisson regression model. As a result the estimated rate of the number of persons killed in road accidents associated with collision type, driver error, type of vehicle, light condition and weather condition remained unaltered. However, the standard errors, 95% CI and the respective probability values or p-values changed from one variable to the other. From the table 4 above, the intercept which depicts the effects of the other variables which were not considered in the model was not significant with a parameter estimate. With respect to the categorical variable Collision type from table 2 above, rear-end ,ran off ,sideswipe head on and hit object on road with p-values 0 .521,0.943,0.898,0.553  and 0.116 respectively were not significantly associated with the number of persons killed in road accidents . However, The estimated number of persons dead in road traffic accidents for the categorical variable Collision type from table 2 above overturn and right angle  are  1.885 (95% CI: 1.544- 2.165,  p=.017) and  .658 (95% CI: .298 -  .957,  p=.023, respectively were significantly associated with the number of persons killed in road traffic accidents. The parameter estimates of these significant collision types that overturn collision, and right angle collision   are   0.823 and -0.418 with death rates of 1.885 and .658 respectively. The death rate value for overturn collision suggests that, the rate of death in road accidents is 1.885 times higher among deaths caused by overturn collision compared to hit off road collision and the death rate value for right angle collision suggests that, the rate of death in road accidents is .658 times higher among deaths caused by right angle   collision compared to hit off road collision. The estimated rate of death for covariate driver error from table 4.5 below too close, no signal and inattentiveness on part of driver with their respective p-values 0.193, 0.174 and 0.319 were not significantly associated with the number of persons killed in road accidents. However, inexperience of drivers and too fast with their estimated rate, 95% CI and p-values 1.454 (95% CI: 1.04 - 2.227 p=.0.006) and 1.789 (95% CI: 1.149 - 2.785, p=0.01), respectively were significantly associated with the number of persons killed in road traffic accidents. The estimated rate of death for inexperience of drivers from the table above was 1.454 indicating that, the rate of death in road traffic accidents is 1.454 times higher with deaths caused by drivers inexperience compared to drivers Loss control and estimated death rate for Improper too fast drive was also 1.789 which means that the rate of death in road accidents in Kembata Tembaro zone is 1.789 times higher with Improper too fast driving compared to loss control. In addition, only motor cycle vehicle type was significantly associated with the number of persons killed in road traffic accidents  with their Rates, 95% CI and p-values  1.453 (95% CI: 1.095 - 1.674  and  0.023 respectively.  From the table 4.5, motor cycle as a type of vehicle contributing significantly to number of persons killed in road accidents had a rate value of 1.453 indicating that the rate of number of persons killed in road accidents was 1.453 times higher with motor cycle   compared to other cars in Kembata Tembaro Zone. Furthermore, clear weather conditions was the only category of the variable weather condition which was not significantly associated with the number of persons killed in road traffic accidents since it had a p-value is  0.307 greater than  the 5 percent  level of significance. Thus, Fog and Rain with their estimated rate, 95% CI and p-values   1.520 (95% CI: 1.095 - 2.321 p=.0.043) and 1.541 (95% CI: 1.045- 2.513, p=0.033), respectively were significantly associated with the number of persons killed in road traffic accidents in Kembata Tembaro Zone.  Fog and Rain as types of weather conditions had their rate values as 1.520 and 1.541 respectively indicating that, the rate of death in road accidents in the country is 1.520 times higher with Fog compared to when the weather is other and rate of death in road accidents is 1.541 times higher with rain compared to other weather condition. Lastly from the table 2 above, the last variable light condition was classified into four categories of which two were not significantly associated with the number of persons killed in road accidents in Kembata Tembaro Zone. These categories include “Night no street light” and “Night street light off” with p-values 0.548 and 0.411 respectively being greater the 5 percent level of significance. However, Day light condition with their Estimated rate, 95% CI and p-values   .948 (95% CI: -.676 - .990, p=.034) was significantly associated with the number of persons killed in road traffic accidents. The rate of death in road accidents on the other hand of these categories contributing significantly to number of persons killed was 0.948. This as a result gives the indication that, the death rate in road traffic accidents in Kembata Tembaro Zone is 0.948 times higher with accidents that occur in the day compared to the night street light on. The mean regression of the negative binomial model for estimating the expected number of persons killed in road accidents within a specific year with significant variables is therefore formulated as;

where,  OT is Overturn, RA is Right angle, IE is Inexperience, TF is too fast, MC is Motor cycle, MB is Minibus, FG is Fog, RN is Rain and Day light condition.

Model Evaluation and Comparison

The final step in the model assessment is to measure the overall goodness of fit. With respect to the table 4.9 presented below, there is a clear evidence that Negative binomial model performs best and is the best model which best fit the accident data well with respect to the expected number of persons killed in road accidents as compared to the Poisson  model. This is because in order to select the best model that performs best or best fits with respect to a certain data among other models with the help AIC, BIC or deviance, the criterion set is that, the smaller the value of the AIC or BIC or Deviance the better that model becomes. Hence by comparing the respective values of the AIC, BIC as well as the residual deviance of the Poisson and Negative Binomial, it is seen that the Negative binomial has the smallest AIC value of 749.10, BIC value of 758.46 and a residual deviance value of 65.6 as compared those of Poisson model. Although both the Negative Binomial and the CMP model takes care of over dispersion, the dispersion parameter value from the table 4.9 indicates that the Negative binomial regression takes care of over dispersion more than that of the CMP model. The above statistics therefore gives an indication that, the model that best fits accident data with number of persons killed in the Kembata Tembaro Zone is the Negative Binomial model followed by the CMP model. Hence in order for one to estimate the expected number of persons killed in road accidents in KTZ per year, the mean of the negative binomial regression model with the significant variables head-on collision as a collision type, Improper overtaking and right angle, Inexperience and too fast as driver errors, Motor cycle and minibus as type of vehicle, Fog/midst and rain as weather condition and day Light condition must be used and is given as:

Table 2: Results of the generalized linear model evaluation and comparison.

Where,  θi represents the expected number of persons killed in road traffic accidents in a particular period of time,  OT is Overturn, RA is Right angle, IE is Inexperience, TF is too fast, MC is Motor cycle, MB is Minibus, FG is Fog, RN is Rain and Day light condition.

Conclusion

This research work was aimed at examining the efficiency of different statistical models for count data with application to road traffic accidents in Kembata Tembaro Zone. As a result three statistical models including Poisson, Negative Binomial and Conway Maxwell-Poisson count regression models were fitted. All the fitted models include significant explanatory variables. Based on the deviances, AIC and BIC of the respective fitted models it appeared that only Negative Binomial model performed best as compared to Poisson and the Conway-Maxwell-Poisson model. The predictors in this model were investigated using their respective p-values and was found out that improper overtaking and right angle as a collision type, Inexperience and too fast as driver errors, Motor cycle and minibus as type of vehicle, Fog and rain as weather condition and day Light condition were the key predictors or independent variables contributing significantly to the expected number of persons to be killed in road traffic accidents in Kembata Tembaro Zone. The empirical study of this research work additionally revealed that in the presence of over-dispersion, both the Negative Binomial and Conway-Maxwell-Poisson count regression models are potential alternative to the Poisson count regression model due to its major assumption of equi-dispersion. Thus the Poisson count regression model serves well under equi-dispersion condition whiles both Negative binomial and CMP count regression models serve better whiles the data is over-dispersed. The traffic accident data analysis indicates that most of the accidents are caused due to driver error; these errors are behavioral and could be corrected through education and awareness. But the awareness of drivers and pedestrian about road traffic rule and regulation is limited and road users do not give enough attention to road traffic accident. The drivers don’t give a priority for a pedestrian in any road section even when pedestrians are rightfully using road crossings such as Zebra Crosses. And also there is no intelligent traffic controlling device and modern traffic controlling machines.

Recommendation

Based on this study finding, the following recommendations can be forwarded for government program planners, decision makers, pedestrian, drivers, traffic police and other stakeholder who work in the areas of giving care, support and treatment for reducing road traffic accidents. Road traffic accident and safety education should be given for all society including for pedestrian ,drivers and traffic police too, and give a gradual examination for drivers how made a frequently crossing laws of traffic rule and regulation. If the drivers do not give a priority for pedestrian, the traffic police will put adequate amount of penalty how don’t give a priority for a pedestrian. And also governments should have national road safety policies and strategies. Police control of speed and drunk driving must be intensified on the highways to stem the high incidence of traffic fatalities and injuries. Governments should allocate adequate financial and human resources to reduce road traffic accident and government should create regular public education programmer on road traffic accident. Awareness creating activities should be given to all people about the cause and effects of road traffic accident on human lives and property damage. Therefore, continuing, comprehensive and holistic awareness creation programs should be conducted regularly.

1. Abdel-Aty M, Abdalla MF. Modelling drivers’ diversion from normal routes under ATIS using generalized estimating equations and binomial probit link function. 2004.
2. Akaike H. Information theory as an extension of the maximum likelihood principle. In the second international symposium on information theory. edited BV Petrov, BF Csaki, Academical Kiado. 1973.
3. Commandeur J, Bijleveld F, Bergel R, Antoniou C, Yannis, G. On statistical inference in time series analysis of the evolution of road safety. Accident Analysis & Prevention. 2013; 60: 424-434.
4. Models for traffic and safety development and interventions. Technical Report EUR 20913-COST329. 2004.
5. Elvik R, Christensen P, Amundsen A. Speed and road accidents an evaluation of the Power Model. TOI report. 2004; 740.
6. Hausman J, Hall B, Griliches Z. Econometric models for count data with application to the patents- R and D relationship. Econometrica. 1984; 52: 909-938.
7. Kweon Y, Kockelman M. Spatially disaggregate panel models of crash and injury counts: The effect of speed limits and design. 2004.
8. Lord D. Modelling motor vehicle crashes using Poisson-gamma models: Examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter. Acct. Anal. Prev. 38: 751-766.
9. Stipdonk H, Bijleveld F, Vannorden Y, Commandeur J. Analysing the development of road safety using demographic data. Accident Analysis & Prevention. 2013; 60: 435-444.
10. Strandroth J. Validation of a method to evaluate future impact of road safety interventions, a comparison between fatal passenger car crashes in Sweden 2000 and 2010. Accid Anal Prev. 2015; 76, 133-140.
11. Strandroth J, Sternlund S, Tingvall C, Johansson R, Kullgren A. A new method to evaluate future impact of vehicle safetytechnology in Sweden. Stapp car crash journal. 2012; 56: 497-509.
12. Wiklund M, Simonsson L, Forsman A. Traffic safety and economic fluctuation: long-term and short-term analyses and a literature survey. 2012.
13. World Health Organization. Trends in maternal mortality: 1990 to 2008. Estimates developed by WHO, UNICEF, UNFPA and the World Bank Geneva: WHO. 2010.
14. Ye Z, Zhang Y, Lord D, Goodness-of-fit testing for accident models with low means. Accident Analysis and Prevention 2013; 61: 78-86.