Modeling Simple and Combination Effects of Road Geometry and Cross Section Variables on Traffic Accidents

Transcription

1 Modeling Simple and Combination Effects of Road Geometry and Cross Section Variables on Traffic Accidents Terrance M. RENGARASU MS., Doctoral Degree candidate Graduate School of Engineering, Hokkaido University N3,W8, Kita-Ku, Sapporo, , Japan Tel: , Fax: Toru HAGIWARA Ph.D., Associate Professor Graduate School of Engineering, Hokkaido University N3,W8, Kita-Ku, Sapporo, , Japan Tel/Fax: Masayuki HIRASAWA Ph.D., Senior Researcher Civil Engineering Research Institute for Cold Region, Japan Hiragishi , Toyohira-Ku, Sapporo, , Japan Tel: Fax: Abstract: This study aimed to find the effects of road geometry and cross section variables on the number of accidents. In addition this study developed a methodology to combine variables using decision trees. Combination variables for road geometry and cross-section variables were developed using the Chi-squared Automatic Interaction Detection (CHAID) algorithm. Three Negative Binomial models were developed: two with homogeneous road segments, and the other with -km road segments. The accuracy of negative binomial models developed with different road segments was compared. The negative binomial model using homogeneous road segments based on horizontal alignment was found to be the most accurate of the three models. Combination variables showed a significant effect on the number of accidents. It was found that the number of accident in a segment is influenced by the average accident rate in the adjacent road segments. Key Words: combination variable, negative binomial model, decision tree, homogeneous road segments. INTRODUCTION Modeling traffic accidents is important step in accident prevention. Accident prediction models enable the identification of variables effecting traffic accidents. Quality of the information that can be obtained from an accident prediction model depends on the variables used and the suitability of the type of model. In previous studies traffic accident have been modeled using linear (Hauer et al. 987), Poisson (Miaou et al. 992) and negative binomial (Savolainen, et al. 2005) regression models. Each of this type of models have there own strengths and weaknesses. Selection of the type of model depends on the independent variable i.e. traffic accident distribution. Apart from the selecting the most suitable model type it is important to include appropriate dependent variables into the model. Most previous studies into the traffic accident modeling have used simple variables. For example the all the studies

2 mentioned above (Hauer et al. 987, Miaou et al. 992, Savolainen, et al. 2005) used only simple variables in their models. Using simple variables implies a hypothesis that the variables affect traffic accidents individually. These studies did not use combination variables. However, Shanker et al. (995) showed that combination variables have a significant effect on traffic accidents. In that study, Shanker et al. used combination variables by coalescing two simple variables. To coalesce two variables the mean or the 75 th percentile value of the simple variables was used as the threshold. The threshold divides the plane created by the two simple variables into two sub-planes (or combinations). These sub-planes are represented by a dummy indicator (i.e. if the two variables meet the required threshold the dummy indicator takes value, otherwise 0). The method used by Shanker et al. is simple; however, deciding on a threshold is not. By simply selecting for example, the mean or the 75 th percentile value of the simple variables as the threshold value, the under laying distribution of the variables is ignored. When there are more than two simple variables to combine, the difficulty in deciding the threshold increases. Further using dummy indicators (0 and ) limits the possible combinations to two. Studies are needed to find a methodology to define suitable thresholds and creating combination variables. Data handling too can contribute towards increasing the quality of the results. Selection of the road segment type is the first step in a data handling process. Previous studies have used fixed-length or homogeneous road segments. For example Shanker et al. (995) and Rengarasu et al. (2007) developed models with fixed-length road segments to predict traffic accidents in terms of roadway variables. Young et al. (2005) and Mayora et al. (2003) used homogeneous road segments in Traffic accident prediction models. Using fixed-length segments in models simplifies the data collection procedures immensely. However, using fixed-length road segments may divide one roadway factor (e.g., a curve or a bridge) between two or more road segments. Thus, the developed model may not accurately capture the effect of that particular roadway factor. Using homogeneous road segments tends to increase the difficulty of data collection. In addition, if homogeneous road segments are to be used a detailed and accurate database for the roadway variables must be available. The first aim of the study is to develop combination variables. The second aim is to compare the accident-predicting abilities of three negative binomial models, one using fixed-length road segments and the other two using homogeneous road segments. The third aim is to determine the effects of simple and combined roadway variables on the traffic accidents. Following text of this paper is devided into five sections. Data handling follows introduction section. In the Data handlin section papaer deals with the selection of road segments, the introduction of accident data and roadway variables and the selection of least leangth of the road segments. Next section deals with the introduction and the creation of the combination variables. Then the paper goes to describe the Negative binomial model. This papaer ends with results and corresponding conclusions. 2. DATA HANDLING 2. Segment Type Selection Three databases, two with homogeneous road segments and other with fixed-length road segments, were compiled. For the first databases with homogeneous road segments, the roads were divided into smaller road segments based on the horizontal alignment of the road (referred as DH here after). Other database with the homogeneous road segments was based

3 on horizontal and vertical alignment of the road (referred as DHV here after). In DH the road segments were either straight or curved. In addition to the conditions of the DH, the segments in DHV have a uniform horizontal grade. For the database with fixed-length road segments, the roads were divided into -km segments (referred as D here after). Division of roads into homogeneous road segments (DH and DHV) is shown in Figure. 2.2 Accident Data Accident data of national roads 5, 38, 39, 40, 44 and 274 in Hokkaido, Japan, for the 5years from 997 were collected. All types of accidents except pedestrian accidents and train accidents were selected for the study. Accident data were collected from the Traffic Accident Analysis System (TAAS) developed by the Civil Engineering Research Institute for Cold Region, Hokkaido, Japan (Hirasawa, 2003). Accident data were collected separately for the 3 databases. Accident data were divided into two categories according to the season of occurrence: winter, and non-winter. Accidents from 997 to 200 were aggregated into winter and non-winter accidents. To indicate whether the accidents occurred during winter or nonwinter, the dummy variable Winter was introduced. That dummy variable takes a value of for accidents that occurred in winter months (January to March and November to December), and a value of 0 for accidents that occurred in non-winter months. 2.3 Simple Roadway Variables Data for 4 simple roadway variables were collected from the Michi database. Michi is a road database compiled by the Japanese Ministry of Land, Infrastructure and Transport. The collected simple roadway variables can be classified into 5 classes: road geometry, road cross section, road structure, traffic flow and built-up area. For road geometry class, data for hilliness, maximum grade, horizontal radius and bendiness were collected. The variable Hilliness is defined as the absolute sum of the vertical ascents and descents of a vehicle in a segment. The variable Maximum Grade is defined as the maximum value of vertical grade (%) within a given segment. Equations and 2 show the calculations of Hilliness and Maximum Grade, respectively. Hilliness = n i= h i Maximum Grade = MAX ( n+ s i ) i= () (2) Figure Division of the homogeneous road segments

4 where, h i is an absolute value of ascent or descent of the road in meters, s i is the absolute value of the vertical grades and n is the number of different vertical grades within a given road segment. The variable Horizontal Radius is defined as the radius of the horizontal curve of a road measured at the centerline. In the case of the database with homogeneous road segments, if a road segment is straight then Horizontal Radius is set as,000,000 m and if the road segment is curved then Horizontal Radius takes the value of the horizontal radius of the curve. For the database with homogeneous road segments, if a segment is straight then the value of Bendiness set to 0 and if the segment is curved then Bendiness takes the value of the deflection angle of the curve in the segment. In the case of the database with -km segments, since there can be multiple horizontal curves in a segment, the variable Horizontal Radius is defined as the average horizontal radius (see Equation 3) and the Bendiness is defined as the sum of all deflection angles within that road segment (see Equation 4). Horizontal Bendiness = Radius m i= Li Ri m i= = m i= L i Li Ri 80 = π m i= θi 80 π (3) (4) where R i is horizontal curve radius, L i is horizontal curve length, θ i is horizontal curve deflection angle and m is the number of horizontal curves within the given segment. For the road structure class, location data were collected for tunnels, bridges and snow sheds. Three separate dummy variables were used to identify the road segments with these structures. The dummy variable Tunnel takes the value of when there is at least one tunnel in a segment and 0 otherwise. Similarly, the dummy variable Bridge takes a value of when there is at least one bridge in the segment and 0 otherwise. A dummy variable was used to indicate whether there is at least one snow shed (Structure with roof to prevent snow slides covering the road) in the road segment. The dummy variable Snow shed takes a value of when there is at least one snow shed in the segment, and 0 otherwise. For cross-section class, data were collected for maximum shoulder width, average lane width, number of lanes and truck lane. The variable Maximum Shoulder Width is defined as the maximum width of the shoulder in a segment. For the segments with an equal number of lanes throughout, the variable Number of Lanes is defined as the number of lanes in the segment. The variable Number of Lanes is not defined for the segments with varying number of lanes. To indicate the segments with a truck lane (climbing lane for truck on grades), a dummy variable was used. The dummy variable Truck Lane takes a value of in the segments with a truck lane, and 0 otherwise. The variable Average Lane Width is defined as the weighted average of lane width over the length (see Equation 5). Average Lane Width = p i= p LW l i l i i= i where LW i is lane width in meters, l i is the length of each section in meters and p is the number of sections corresponding to the different lane widths in a given segment. (5)

5 For traffic flow class, AADT data were collected. Since there is a reduction of traffic flow in the harsh winter, the need arose to collect AADT data separately for winter months and nonwinter months. The AADT data were obtained from census measurements carried out by the Ministry of Construction, Japan. For the purpose of AADT measurement each road is divided into smaller census divisions. The Census divisions are decided so that the flow rate within a division remains fairly equal. For the 6 national roads selected for this study AADT was measured at 69 census divisions with an average length of km. Details of the census AADT measurements are shown in Table. However, the measurements were limited to the non-winter months (April to October). The winter (January to March and November to December) AADT was estimated using the winter to summer AADT ratio obtained from the AADT count of the year 999 measured by the Hokkaido Development Bureau. For built-up area class, location data for densely inhabited district (DID) and railway stations were collected. The variable DID is defined as the percentage of segment length designated as densely inhabited district. The variable Railway Station (Front of the railway station is connected directly with the segment) is defined as the number of railway stations per kilometer. 2.4 Selection of the Least Length of Segments Unlike the database with -km segments, the databases with homogeneous road segments (DH and DHV) have segments with varying lengths. For the purpose of identifying the effects of road geometry and cross-section variables on the number of accidents, smaller segments are not useful. In addition, the accuracy of the available accident data and the roadway variables influence the selection of the shortest length of segment to be used. A minimum of 200 m was selected as the shortest length of a segment in DH and DHV. Segments shorter than 200 m were filtered out of DH and DHV. 2.5 Data Description The DH had,98 segments with a mean length of 62 m. In total, 0,653 accidents were recorded in DH. The DHV database had 2,305 segments with a mean length of 373 m. DHV recorded 6,678 accidents in total. The D database had,395 segments. For the database with -km road segments, 2,86 accidents were recorded. The accident frequency distribution in DH, DHV and D are shown in Figure 2 to 4 respectively. Descriptive statistics of the simple Road Table Details of the census AADT measurements Number of Census divisions Avg. Length of Census division (km) Total Length of the Road (km) Max. AADT (Number of Vehicles) Min. AADT (Number of Vehicles) Total

6 roadway variables in DH, DHV and D are shown in Table 2. Difference in the number of accidents between -km road segments and homogeneous road segment databases (DH and DHV) is due to the fact that -km road segment database covers the whole length of the road while the homogeneous road segment databases (DH and DHV) have left out segments which were less than 200 m in length. 3. COMBINATION VARIABLES In practice it is a common knowledge that simple road way variables interact with each other and resulting in high number of accidents. For example taken individually a highly sloping road segment and a road segment without a median might have some number of accidents. However if these two conditions occur at the same road segment then the number of accidents might increase far beyond the combined accidents of the two individual road segments. This effect is called the combination effect. It has to be understood that this is a perception and has to be tested using standard statistical methods. One method of testing for the combination effect is the combination variable. Combination variables are placed in a model to capture interaction, if there is any, between the simple variables. In this study decision tree was utilized to create the combination variables. Previous studies like Richter et al. (2000) and Sohn et al. (200) have used decision trees in traffic accident analysis. There are several types of decision tree algorithms available. The Chi-Squared Automatic Interaction Detection (CHAID) algorithm was selected for this study, due to the fact that the CHAID algorithm can generate non-binary decision trees, meaning that some splits have more than two branches. CHAID therefore tends to create a wider tree than binary decision tree growing algorithms. The CHAID algorithm uses chi-squared statistics to identify optimal split points. First the most significant variable is selected using a chi-squared independence test. Next, using chi-squared statistics, the optimal points for dividing the selected variable are calculated. A database including the entire input variable is divided into sub-databases along the optimal points. This ends one loop in the algorithm for the decision tree. The same process is carried out in each sub database. Tree growth is stopped when there is no significant difference chi-squared statistics. The combinations of variables and the average accident rate per kilometer in each of the combinations are obtained from the tree. The combination variable is created by representing each combination of variable by the corresponding average of the accident rate per kilometer. SPSS Clementine Desktop was used to develop the CHAID decision trees. In this Study Two combination variables were computed using CHAID decision tree: Combination of Cross-Section Variables and Combination of Road Geometry Variables. In addition a third combination variable called Combination of Adjacent Segments is computed with out the use of a decision tree (method is explained proceeding section). The variables Combination of Cross-Section Variables and Combination of Road Geometry Variables were computed using the CHAID decision tree. The accident rate per kilometer was used as the target variable for the both variables. For the Combination of Cross-Section Variables, Average Lane Width, Number of Lanes and Maximum Shoulder Width were used as input variables. For the variable Combination of Road Geometry Variables, Hilliness, Maximum Grade, Bendiness and Horizontal Radius were used as input variables. For both of these decision trees chi-square statistic of 5% was used with a minimum sample size of 50 at the leaf nodes. The variable Combination of Adjacent Segments was

7 Number of segments , Number of segments ~ Number of accidents in 5 years of winter or non-winter months Figure 2 Accident frequency distribution with homogeneous road segments (DH) , ~ Number of accidents in 5 years of winter or non-winter months Figure 3 Accident frequency distribution with homogeneous road segments (DHV) Number of segments ~ Number of accidents in 5 years of winter or non-winter months Figure 4 Accident frequency distribution with -km road segments (D)

8 Table 2 Descriptive statistics of the simple roadway variables in DH, DHV and D databases Variable Unit DH DHV D Max Min Number Max Min Number Max Min Number Horizontal Radius m Bendiness Degree Max. Grade % Hilliness m Tunnel Dummy Bridge Dummy Snow Shed Dummy Average Lane Width m Number of Lanes /Direction Max. Shoulder m Width Truck Lane Dummy AADT Vehicles/ Direction/ Day Railway Stations Stations/ km DID % Winter Dummy Segment Length m

9 calculated as the average of the accident rates of two adjacent segments. Equation 6 shows the calculation of the variable Combination of Adjacent Segments for the i th segment. Interaction of ( Accident rate per kilometer) i i + ( Accident rate per kilometer) i+ Adjacent Segmentsi = 2 (6) 4. NEGATIVE BINOMIAL MODEL A Negative Binomial model was used to model the number of accidents. According to the negative binomial model, the probability of n number of accidents occurring in the i th segment in the j th season (j= for winter, j=0 for non-winter) is given by Equation 7. Γ( θ + n ij ) n P ( n ij ij ) = u θ ij ( u ij ) (7) Γ( θ ) n ij θ where, u ij =, θ =, λ is the mean of accidents and α is the over-dispersion factor. θ + λij α The over- dispersion factor (α) can be estimated using the mean and the variance of accidents, as shown in Equation 8. The mean is linked to the independent variables using the log link function shown in Equation 9. Var ( accidents ) = (+ α ) E( accidents ) Ln ( λ ) X β ij = ij (8) (9) where X ij is the vector containing simple and combination variables and β is the vector containing coefficients. The coefficients are estimated using maximum likelihood procedures. The econometric software package TSP was used to estimate the coefficients. The log likelihood ratio is used as the goodness of fit index. The T-test is used to test the null hypothesis that the estimated coefficients are equal to zero. A critical P value of 0% is used to dismiss the null hypothesis. 5. RESULTS 5. Results of the CHAID Decision Trees In total six decision trees were attempted and all the decision trees showed a significant tree growth at a significance level of 0%. Considering the readability and the length of this paper only two decision trees are presented in this paper. The decision trees developed for DH (as explained later negative binomial model with DH shows the highest accuracy thus used to draw conclusions) are presented in this paper. In the case of homogeneous road segments with horizontal alignment (DH) both decision tree for the Cross Section and Road Geometry variables showed a significant tree growth. Decision tree deveoped for the case of DH are shown in Figure 5 (A) and (B). Both trees grew to 3 levels below the root node. Three variable; number of lanes, average lane width and maximum shoulder width were significant variables for the decision tree developed for the combination of cross-section variables. In the case of the decision tree developed for the combination of road geometry variables four

10 Figure 5 Decision tree deveoped for thecase of DH

11 variables were found to be significant; average horizontal radius, hilliness, Bendiness and Slope. 5.2 Results of Negative Binomial Model with Homogeneous Road Segments (DH) The results of the three negative binomial regression models are shown in Table 3. Ten variables were found to have a significant effect on the number of accidents at a critical P value of 0%. The over dispersion factor was found to be significant in the negative binomial model developed. The model achieved a log likelihood ratio of With the increase in the maximum grade, the number of accidents increased. With increase of hilliness, the number of accidents decreased. Bridges and snow shed had a significant effect of increasing the number of accidents. AADT showed a significant increasing effect. DID showed a increasing effect on number of accidents. Segment Length showed an increasing effect on accidents. Three combination variables (Adjacent Segments, Cross Section and Road Geometry) showed significant increasing effects on the number of accidents. 5.3 Results of Negative Binomial Model with Homogeneous Road Segments (DHV) At a critical P value of 0% eight variables were found to have a significant effect on number of accidents. The model achieved a log likelihood ratio of 0.3. Snow shed had a significant effect of increasing the number of accidents. Increase of Average lane width shows a significant increasing effect on number of accidents. Number of lanes showed a decreasing effect on number of accidents. AADT showed a significant increasing effect. DID showed a increasing effect on number of accident. Segment Length showed an increasing effect on number of accidents. Two combination variables (Adjacent Segments and Cross Section) showed significant increasing effects on number of accidents. 5.4 Results of Negative Binomial Model with -km Road Segments (D) The model showed a significant over-dispersion factor. The model achieved a log likelihood ratio of A total of 8 variables showed a significant effect on the number of accidents. Bridge and Snow shed Showed a significant increasing effect on number of accidents. Average lane width had a significant increasing effect and Number of lanes had a decreasing effect on number accidents. AADT showed a significant increasing effect. DID showed a significant increasing effect on number of accidents. Two combination variables (Adjacent Segments and Cross Section) showed significant increasing effects on number of accidents. 6. DISCUSSIONS AND CONCLUSIONS In this study, the same data were used to compile three databases: two with homogeneous road segments, and other with fixed-length road segments of km. The results obtained from using these three databases in a Negative Binomial model were shown in the preceeding section of this paper. Variables showed a consistant effects across the models. For the purposse of darwing conclusion and finding the effects of variables on traffic accidents one model had to be selected. The model with road segments based on road geometry and cross section controls for road geometry and cross section variables thus higher accuracy of the model will be expected. Therefore negative binomial model based on horizotal and vertical alignment would be expected tohave high accuracy model. However form the results clear that the negative binomial model based on horizotal and vertical alignment has the least log likelihood ratio (ρ 2 ) value. This might be due to the smaller segment sizes in the database. By comparing the log likelihood ratio (ρ 2 ) of the three negative binomial models, it became clear

12 Table 3 Results of the negative binomial regression models Variable Constant NB-DH NB-DHV NB-D Estimate P-value Estimate P-value Estimate P-value Max. Grade NS - NS - Hilliness NS - NS - Bridge NS Snow Shed Average Lane Width NS Number of Lanes NS AADT DID Segment Length Not used - Combination of Cross-Section variables Combination of Road Geometry Variables NS - NS - Combination of Adjacent Segments Overdispersion Log likelihood function Restricted log likelihood ρ Number of significant variables Note : Seven variables (Horizontal Radius, Bendiness, Tunnel, Max. Shoulder Width, Truck Lane, Railway Stations and winter) did not show significant effect on any of the three models. Note 2: NS in the table stands for Not significant

13 that the model with the homogeneous segments based on horizontal alignment of the road and nagative binomial model based on kilometer segments were of comparable log likelihood ratio (ρ 2 ). However when number of significant variables in the model are compared, the model with the homogeneous segments base on horizontal alignment has more significant variables than the negative binomial model with road segments based on horizontal alignment. Based on log likelihood ratio and number of significant variables the negative binomial model with road segments based on horizontal alignment was used here to draw conclusions. Generally, the average number of accidents is expected to increase with increased hilliness of the road. However, this study found that a -m increase in hilliness decreases the average number of accidents by 0.7%. This result seems unexpected. The decrease of accidents may be due to the constant attention required by the drivers in the hilly segments of the road. Thus this will reduce accident occurred due to the fatigue and sleepiness of the drivers. According to the results a m increase in the maximum grade within a segment increase the accidents by 4%. When the maximum grade increases the road design is severe. It reduces the sight distance of the drivers. Further in winter conditions higher slopes may increase the chance of accidents due to the slipperiness of the road. The Negative Binomial model with homogeneous road segments (DH) showed that bridges and snow shed have a significant increasing effect on the number of accidents. If a segment has at least one bridge, then the average number of accidents is 4% greater. If a segment has at least one snow shed, then the average number of accidents is 97% greater. Because of high construction costs and difficult terrain, road segments immediately adjacent to Snow sheds and bridges tend to have poor alignment. The model suggest that a % increase in DID area increases the average number of accidents by 0.7%. The combination variables used in the model showed a significant effect on the number of accidents. This result shows the prevalence of combination effect in the traffic accidents. Quantifying the effect of combination of cross section variables and combination of road geometry variables is difficult with in the scope of this study. However, the results indicate that the significance of the combination effect on traffic accidents. In the case of combination of adjacent segments, if the average accident rate in the adjacent segments increase by one unit then the accident rate increase by 50%. This is an important finding. This shows that the accident tendency in the adjacent segments effect the current segment. According to this results when a segment is found to be accident prone, one may have to look into the adjacent segments too. In this study simple average of accident rates was used to represent the effect of adjacent variables however, other possible representations must be tested. Further variation of the effect of adjacent segments with variables such as length of the road segments and weather may be of great research interest. The models developed in the study are of reasonable accident predictability with plausible signs for the variables. Even so, creating an accident prediction model with zero inflated negative binomial models might further increase the accident predicting ability of the model. Characteristics of tunnels, bridges and snow sheds (like width, type etc.) were not included in the study. However the effect of roadway hazards may vary with the characteristics of the hazard. Inclusion of characteristics of roadway structures in a study will increase the understanding the effect of road way structures on number of accidents. This study uses the results from the regression analysis to draw conclusions. However it will be desired if conclusion can be drawn from regression analysis and decision trees. Future studies also

14 might have to develop an effective methodology to interpret the results obtained from the decision trees and regression analysis in parallel. REFERENCES Hauer, E., Persaud, B. N. (987) How to Estimate the Safety of Rail-Highway Grade Crossings and the Safety Effects of Warning Devices, In Transportation Research Record: Journal of the Transportation Research Board, No.4, TRB, National Research Council, Washington, D.C, pp Hirasawa, M., Asano M. (2003) Development of Traffic Accident Analysis System Using GIS. Proceedings of the Eastern Asia Society for Transportation Studies, Vol.4, pp Mayora, J.P., and Llamas Rubio R. (2003) Relevant Variables for Crash Rate Prediction in Spain's Two-Lane Rural Road, Presented at 82nd Annual Meeting of the Transportation Research Board, Washington, D.C., Miaou, S., Hu, P. S., Wright, T., Rathi, A. K., Davis S. C. (992) Relationship between Truck Accidents and Highway Geometric Design: A Poisson Regression Approach, In Transportation Research Record: Journal of the Transportation Research Board, No.376, TRB, National Research Council, Washington, D.C., pp Rengarasu T.M., Hagiwara T., Hirasawa M. Effects of Road Geometry and Season on Head- On and Single-Vehicle Collisions on Rural Two Lane Roads in Hokkaido Japan, Journal of the Eastern Asia Society for Transportation Studies, Vol. 7 pp Richter, M., Otte D., Pohlemann T., Krettek C. and Blauth M. (2000) Whiplash-Type Neck Distortion in Restrained Car Drivers: Frequency, Causes and Long-Term Results, European Spine Journal, Vol.9, No.2, pp Savolainen, P.T., Tarko, A.P. (2005) Safety Impacts at Intersections on Curved Segments, In Transportation Research Record: Journal of the Transportation Research Board, No.908, Transportation Research Board of the National Academies, Washington, D.C., pp Shanker, V., Mnnering F., Barfield W. (995) Effects of Roadway Geometrics and Environmental Factors on Rural Freeway Accident Frequencies, Journal of Accident Analysis and Prevention, Vol.27, No. 3, pp Sohn, S.Y. and Shin H.(200) Pattern Recognition for Road Traffic Accident Severity in Korea, Ergonomics, Vol. 44, No., pp Young J.K. and Kara M. K.(2005) Safety Effects of Speed Limit Changes: Use of Panel Models, Including Speed, Use, and Design Variables, In Transportation Research Record: Journal of the Transportation Research Board, No.908, TRB, National Research Council, Washington, D.C., pp