**by G Dell’Acqua · Cited by 40 — Dell’Acqua G. and F. Russo. 2. ABSTRACT. This paper analyzes roadway safety conditions using the network approach for a number of Italian roadways within **

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SAFETY PERFORMANCE FUNCTIO NS FOR LOW-VOLUME ROADS By: Gianluca Dell™Acqua Assistant Professor, Ph.D., P.Eng. Department of Transportation Engineering ﬁLuigi Tocchettiﬂ ﬁFederico IIﬂ University of Naples Via Claudio 21, I-80125 Naples, Italy Phone: +39 0817683934 Fax: +39 0817683946 E-mail: gianluca.dellacqua@unina.it Francesca Russo Ph.D., P.Eng. Department of Transportation Engineering ﬁLuigi Tocchettiﬂ ﬁFederico IIﬂ University of Naples Via Claudio 21, I-80125 Naples, Italy Phone: +39 0817683372 Fax: +39 0817683946 E-mail: francesca.russo2@unina.it Submission date: November 15, 2010 Word count: 5,722+250×7 = 7,472 TRB 2011 Annual MeetingPaper revised from original submittal.

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Dell™Acqua G. and F. Russo 2 ABSTRACT This paper analyzes roadway safety conditions using the network approach for a number of Italian roadways within the Provin ce of Salerno. These road ways are characterized by low-volume conditions with a traffic flow of under 1,000 vehicles per day and they are situated partly on flat/rolling terrain coveri ng 231.98 kilometers and partly on mountainous terrain for 751.60 kilometers. Since 2003, the Department of Transportation Engineering at the University of Naples has been conducting a large-scale research program based on crash data collected in Southern Italy. The research-study presented here has been used to calibrate crash prediction models (CPMs) per kilometer per year. The coefficients of the CPMs are estimated using a non-linear multi-variable regression analysis ut ilizing the least Œ square method. In conclusion, two injurious crash predic tion models were performed for two-lane rural roads located on flat/rolli ng area with a vertical grade of less than 6 percent and on mountainous terrain with a vertic al grade of more than 6 per cent. A residuals analysis was subsequently developed to assess the adjusted coefficient of determination and p-value for each assessable coefficient of the prediction model. CPMs are a useful tool for estimating th e expected number of crashes occurring within the roads™ geometric components (inters ections and road sectio ns) as a function of infrastructural, environmental, and roadway features. Several procedures exist in the scientific literature to predict the number of crashes per kilometer per year. CPMs can also be used as a tool for safety impr ovement project prioritization. Keywords: crashes, prediction models, road safety analysis TRB 2011 Annual MeetingPaper revised from original submittal.

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Dell™Acqua G. and F. Russo 3 PROBLEM STATEMENT Roadway safety is a multidisciplinary sc ience involving several elements: (a) the components of the roadway system – people, ve hicles, and the roadways themselves, (b) the agencies and groups that plan, design, build, and use roads and promote roadway safety, and (c) the public health and safety communities th at are concerned with injury prevention, response, treatment, and rehabilitation.( 1). While vehicle characteristics can contribute to traffic accident s (e.g., the lack of regular maintenance or vehicle overloading) human error is the most frequently cited factor contributing to both fatal and non-fatal injuries in motor vehicle accidents. Furthermore, driver behavior is improved more by enforc ement and engineering than by training and education. Low-volume roads, as analyzed in this pa per, comprise a significant portion of the rural roadway network in Italy and in many ot her countries in the world. Because of the higher frequencies of documented crashes and more severe injuries on these roads, many researchers have examined the f actors leading to these crashes. Stamatiadis et al. ( 2) have observed that low-volum e roads (e.g., roads carrying under 1,000 vehicles per day) make up 70 percent of the roadway network in the United States. Although such highways carry low volumes, historic al data indicate that they have higher crash rates than other roadways. The authors found that the crash rates, and especially fatality rates, were higher for southeastern states th an the national rates. Crashes in Kentucky and North Carolina for 1993 – 1995 were used for the sample. The tendency to crash among drivers grouped by age and gender and vehicles grouped by age and type were examined. The results showed that drivers under the age of 25 and drivers over the age of 65 were more likely to crash than middle-aged drivers. On av erage, female drivers were safer than male drivers, and young drivers (under the age of 25) experienced more single-vehicle crashes, and drivers over 65 were more likely to be involved in two-vehicle crashes. The drivers of older vehicles were more likely to be involved in two-vehicle crashes on low-volume roads than drivers of newer vehicles. In single-vehicle cr ashes, drivers of older vehicles were more likely to have a serious injury than drivers of newer vehicles, and large trucks had the highest two-vehicle crash rate on low-volume roads, followed by sedans, pick-up trucks, vans, and station wagons. Achwan and Rudjito ( 3) later described the magnitude of the road crash characteristics on low-volume roads by using data from rural areas. Crash data from 1993 to 1995, recorded by the traffic police in the Purwak arta Police District were used. These data included three districts in Indonesia (Karawa ng, Purwakarta, and Subang). The authors found a serious road safety problem on low-volume ro ads in the Purwakarta region. These crashes caused significant losses in production, as well as damage and suffering. Clearly, all institutions involved in road safety should ma ke every effort to reduce crashes. The study showed that the key vulnerable groups were motorcyclists and pedestrians, with truck casualties also being a problem on low-volume roads. Rollover was a common collision type and it appeared that this was caused by poor shoul der conditions in the majority of crashes; it was relatively rare on the nati onal highway network. A systematic ﬁTriple L Trialﬂ approach – meaning data processing, crash, traffic-to crash investigation, prevention, and reduction proved successful and useful. In fact the au thors found that although the number of accidents is small, it appeared that different road links do have different crash patterns. They introduced processes for identifying common contributory factors by using a stick diagram for hazardous locations. For more than 40 years, multivariate regressi on techniques have been applied both in North America and in Europe to investigate th e quantitative relationships between accident counts and road and traffic characteristics and to establish accident prediction models. TRB 2011 Annual MeetingPaper revised from original submittal.

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Dell™Acqua G. and F. Russo 4 Several pieces of research have focused on id entifying variables to account for the impact of the interactions betw een highway design parameters on safety ( 4). OBJECTIVE The research described in this paper aims to calibrate two injurious crash prediction models (CPMs) per kilometer per year for tw o-lane rural roads in low-volume conditions: one for roadways located on flat/rolling land with a vertical grade of less than 6 percent and the other for roadways in the mountainous area with a vertical grade of more than 6 percent. This study illustrates a ﬁnetwork ﬂ approach to safety in or der to identify the ﬁblackﬂ roadway segment where the frequency of injurious crashes is higher than on the rest of the roadway. This experimental analysis is only one component of a larger study under way for several years now on a number of rural roads in low-volume conditions within the Salerno road network with a view to improving performance and safety ( 5). LITERATURE REVIEW For more than 30 years, relationships between traffic crashes and geometric roadway design have been modeled by traffic safety engi neers and researchers to estimate and predict accident frequency or rates under different roadway design conditions. It has been demonstrated that vehicle accidents are complex events involving the interaction of drivers, traffic, the road itself and the environment. It is believed that a significant proportion of variations in accident frequency are the result of differences in the major factors from site to site and time intervals ( 6), and that a significant portio n of accidents occur due to bad infrastructure, and lack of Alignment Consistency ( 7). Performing accident prediction models is a means of summarizing these complex interactive effects on the basis of information c ontained in the accident data, as well as using engineering judgment and analytical assu mptions about the accident process. Many types of regression models have been used over the years to develop accident prediction models: researchers are finding that conventional normal or lognormal regression models simply do not have the statistical proper ties necessary to adequately describe vehicle accident events on the road. Traffic accident s are better modeled by assuming a Poisson accident frequency distribution. The exponential f unction is a natural candidate to describe the interactive effects and at the same time ensure that th e function values are always non- negative (8). Miaou et al. ( 8) studied the effect of over-dispersion of accident frequency distribution on model forms. They showed that when the variance of the accident rate distributions is greater than the mean, zero-in flated Poisson or nega tive binomial regression models should be used. They developed an extended negative binomial model allowing variables with multiple values along a segment of road. Fridstrøm et al. ( 9) at the Norwegian Transportati on Institute developed Poisson regression models to break down th e variations in accident count s into parts attributable to randomness and the systematic factors that cause accidents. They correl ated the number of crashes with four variables: traffic flow, speed limits, weather and light conditions. They also proposed a set of specialized goodness-of-fit measures explic itly taking into account the inevitable amount of random variation that woul d be present in any set of accident counts. Persaud and Lord ( 10) illustrated the application of the Generalized Estimating Equations (GEE) procedure to traffic- safety studies when data spanning several years are TRB 2011 Annual MeetingPaper revised from original submittal.

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Dell™Acqua G. and F. Russo 5 available and when it is desira ble to incorporate trend. The application is for a sample of four-legged signalized inters ections in Toronto, Canada, using data for the years 1990 through 1995. GEE procedure was introduced to develop a mathematical equation incorporating a trend in accident data. The quali ty of fit was examined using the Cumulative Residuals (CuRe) method. Saccomanno et al. ( 11) described an integrated and user-friendly GIS platform for road accident analysis and prediction to develop and evaluate alternative safety countermeasures. The database employed was obtained from the Ontario Ministry of Transportation. The Poisson regression and Empiri cal Bayesian (EB) model were used for the analyses. For illustration purposes, the authors also designated the num ber of BS sections along the selected highway. A BS section is de fined as any section where the number of accidents observed exceeds the predicted numbe r by at least one standard deviation from either the Poisson or the EB model estimates. Hauer (12) calibrated an accident rate model for multilane urban roads by using a binominal negative regression. The variables used were the annua l average daily traffic, the percentage of trucks, th e vertical grade, the horizontal curve length, roadway width, the type and width of clear zones, speed limits, points of access, and the presence of, and nature of, parking areas. Pardillo et al. ( 4) described a research project conducted at Madrid Polytechnic University, with the objective of refining the negative binomial accident prediction models that had been developed previously for two-lane rural roads in Spain. Because over- dispersion had been detected in the sample, a negative binomial regr ession model with an additional exponential linkage equation was ad opted. Injury accident counts (IACC) were used as the dependent variable. To test the significance of the regression coefficients, a new variable in addition to the criterion based on the p-value was used: the authors also proposed a set of specialized goodness-of-f it measures, such as the deviance of the model and the log- likelihood. The final equation of the resulting model contains the total traffic flow, access density, the minimum sight distance within the 1 kilometer segment, the minimum design speed of the alignment elements included in the 1km segment, the maximum longitudinal grade, and reduction in design speed in relati on to the section analyzed starting from a distance of 1km on the segment preceding the sec tion being investigated. Cumulative scaled residuals plots were then used to identify where the model over- or underestimated accident frequencies. EI-Basyouny and Sayed (13) compared two types of regression techniques: the traditional negative binomial (TNB) and the mo dified negative binomial (MNB). While the TNB approach assumes that the shape parameter of the negative binomia l distribution is fixed for all locations, the MNB approach assumes that the shape parameter can vary from one location to another. The differe nce between the two approaches is investigated in terms of their goodness of fit. The study employs accident data for 58 arterials (392 segments) in the cities of Vancouver and Richmond, in British Columbia, Canada. Tarko (14) presented two alternative formulations for the calibration problem in line with the maximum likelihood approach. Two methods are addressed to pr edict safety for the individual links and nodes of a transportati on network. In both methods a planner has the freedom to portion a road network in a way th at addresses expected local and sub-regional safety differences. Furthermore a planner may identify routes, corridors and areas to focus calibration on these locations if planning fo cuses on them. The study demonstrated the feasibility of those proposed approaches that may be helpful in developing a new class of tools for safety-conscious planning. TRB 2011 Annual MeetingPaper revised from original submittal.

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Dell™Acqua G. and F. Russo 6 DATA COLLECTION The crash data used in this research st udy involve 983.58 kilometers of two-lane rural roads in Southern Italy, of which 231.98 kilometers are located on flat an d rolling areas with a vertical grade of less than 6 percent and 751.6 kilometers on mountainous terrain with a vertical grade greater than 6 percent. Roadway segments on flat, rolling and mount ainous terrains reflect some results of previous studies ( 15) where several processes and met hodologies were developed to reach acceptable standards to classify geometric design and maintenance standards for low-volume roads. Road classification sy stems were examined by numerous countries, namely Australia, South Africa, the United Kingdom, and the United States . For example, Austroads (16) has defined a national system of functional classifications for urban and rural roads across Australia. The Austroads rural areas category further subdivides the road classification into five levels. For each road class there are guidelines for geometric standards that relate to design speed, cross-sectional elements, and horiz ontal and vertical curve requirements for flat, hilly, and mountainous terrain. The USA Forestry Manual (17) has also proposed a low- volume road classification for two-lane a nd single-lane roads based on the roadways™ geometric and infrastructural featur es for rolling and hilly terrain. A daily traffic volume is generally included in the research studies for each road class as a guide to the range of likely traffic for each class ( 15). Traffic volume is expressed as the average daily traffic (ADT) and represents tra ffic over the peak season. A description of the road type for each road class has also been in cluded. In describing th e road type, the service quality factor has been included to highlight the overall character of the road class which may be linked to adjacent land use or the recreational facilities it se rves. The various levels of service were based on the subjec tive judgments of numerous pract itioners closely associated with road network management. Quality of serv ice is a qualitative term based on the concept of providing various levels of convenience, comfort, and safety to a driver. The rural roads analyzed in Italy which ar e presented in this study are in low-volume conditions with an ADT of less than 1,000 vehi cles per day for which a 3-year (2003-2005) crash database was used. Table 1 shows the descriptive features observed on the roads analyzed. TABLE 1 Geometric Features of the Low-Volume Roads Analyzed 3.60Average µ 3.40Standard Deviation 7.20Average µ 1.40Standard Deviation 56.00Average µ 12.00Standard Deviation Lanes2 Vertical Grade [%]< 6% Curve Radius [m]150-500 FLAT AND ROLLING TERRAIN Roadway Segment Length [km] Roadway Width [m] Predicted Speed [km/h] 4.90Average µ 3.70Standard Deviation 6.80Average µ 1.20Standard Deviation 54.00Average µ 7.30Standard Deviation Lanes2 Vertical Grade [%]> 6% Curve Radius [m]<150 Roadway Segment Length [km] Roadway Width [m] Predicted Speed [km/h] MOUNTAINOUS TERRAIN TRB 2011 Annual MeetingPaper revised from original submittal.
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Dell™Acqua G. and F. Russo 8 high curvature for a mean value of all curve radius falling within the analyzed roadway segment of less than 150m: the indicator is between 2 and 3 Vertical grade the vertical grade indicator can acquire the following synthetic and simple levels by using a range of values from 1 to 3 after a deep analysis and careful study of all discrete values in the database: low gradient when the mean value of grades associated to the analyzed roadway segment is of less than 3 percent (the indicator is equal to 1) medium gradient when the mean value of grades associated to the analyzed roadway segmen t is between 3 percent and 6 percent (the indicator is between 1 and 2) high gradient when the mean value of grades associated to the analyzed roadway segment is over 6 percent (the indicator is between 2 and 3) Roadway Width travel lanes plus shoulders Predicted Speed is the mean speed at each analyzed roadway segment in which the Administration has divided the entire roadway segment length Crashes Count number of total and in jurious crashes each year Table 2 shows the descriptive statistics of the crashes observed on the rural roads from 2003 to 2005. It can be observed that the av erage injury count for the 3-year period is 0.94 crashes per kilometer and 0.32 crashes per kilometer for the road s on flat/rolling and mountainous terrain respectively. The employed database is not wholly comp lete: it may not learn the principal crash types at each roadways neither th e accurate location or the weather conditions when the crash happened nor the eventually presence of obstruc tions within the lateral clearance area that may add to crash severity when vehicles exite d the traveled way. Used reports refer to the general features of the analy zed crash counts; it needs to improve them for the future developments of the safety analyses and to be tter explain the average crashes/segment™s year to year variability. TABLE 2 Descriptive Statistics of Analyzed Crash Counts Total numberAverage per Roadway segment INJURIOUS CRASHES IN 3 YEARS (2003-2005) 590.94 Analyzed YearTotal numberAverage per Roadway segment 200390.14 2004320.51 2005180.29 FLAT/ROLLINGTERRAIN INJURIOUS CRASHES Total numberAverage per Roadway segment INJURIOUS CRASHES IN 3 YEARS (2003-2005) 490.32 Analyzed YearTotal numberAverage per Roadway segment 2003140.09 2004140.09 2005210.14 INJURIOUS CRASHES MOUNTAINOUS TERRAIN A user-friendly GIS platform for road cras h analysis and prediction models has been used. A geographic information system (GIS) in tegrates hardware, software, and data for capturing, managing, analyzing, and displaying all forms of geographically referenced TRB 2011 Annual MeetingPaper revised from original submittal.
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Dell™Acqua G. and F. Russo 9 information. GIS allows to view, understand, ques tion, interpret, and visualize data in many ways that reveal relationships, patterns, and trends in the form of maps, globes, reports, and charts. A GIS helps answer ques tions and solve problems by looking at data in a way that is quickly understood and easily shar ed. GIS technology can be integr ated into any enterprise information system framework. This platform makes use of GIS Arc View and the Visual Basic programming language. The GIS enables the user to see th e environmental conditions, as well as the geometric and accident information on the roadway segment ( 11). DATA ANALYSIS Two predictive injurious crash models were developed for the roadways analyzed in low-volume conditions: the first can be applied for roads located on flat/rolling terrain (vertical grade of less than 6 percent) an d the second was associated with the roads on mountainous terrain with a vertical grade greater than 6 percent). The prediction models were performed by us ing the only number of injurious crashes because since 1991, according to many European countries, the Italian Administrations, responsible for the collection and dissemination of crash data , recorded only the injurious accidents defined how "events that occur on pub lic roads in which one or more people are killed or wounded and in which at least one vehicle is involved in a movement. " Hauer suggested the possibility of stratifying the models to overcome the lack of flexibility of the most common exponential functional forms ( 12). Specialized software - (STATI STICA 7) - was used to fit the models. The injurious crashes per kilometer per year were used as dependent variables. An iterative process was applied in the development of the two crash prediction models. Hauer (12) distinguished two steps in the process: ( a) the choice of model form (model equation) and ( b) estimating the parameters. Both steps are repeated in each phase of the model development process. In fitting the models, weighting was applied to the explanatory variables of each record in propor tion to the roadway segment length. Operating in this way, emphasis was given to the key ro le played by the different characteristics of roadway segments into which the total road length was broken down by the Salerno Province Administration for the urbanized area. The Gauss-Newton method, based on the Taylor series, was used to estimate the coefficients of employed variables by using ordinary least- square regression. All the parameters included in the model are significant to a 95 percent confidence level. The significance of the regressi on equations™ coefficients were investigated by using two criteria: 1) the models were kept where the p-value of the coefficients was under 5 percent; 2) the cumulative residual analysis , which is discussed in the next section. Injurious Crash Prediction Models The best crash prediction model on low-volume roads located in areas with flat/rolling terrain , in injurious accidents per year per kilometer, was worked out from data for 59 crashes reported over three years; the equation form is the following: W0.81VGI1.42-V0.255.15CI1061061000YeeADT (1) where TRB 2011 Annual MeetingPaper revised from original submittal.
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Dell™Acqua G. and F. Russo 10 Y = number of injurious crashes per year per kilometer ADT = average daily traffic in vehicles per day V = mean speed at each analyzed roadway segment CI = the curvature indicator as explained above VGI = the vertical grade indi cator as explained above W = lanes plus shoulders width in meters A reasonably-goodness-of-fit indicator was made for this regression: the adjusted coefficient of determination ² is 91 percent. As can be seen from Equation 1, where all the variables are statistically significant as show n in Table 3, the ADT variable has little influence on the predicted number of crashes: as could be imagined, the road is in low- volume conditions, but its presence is due to the increase in ² value. The best crash prediction model on low-volume roads located in areas with mountainous terrain , in injurious accidents per year per kilometer, was worked out from data for 49 crashes reported over three years; the equation form is the following: W7.15-VGI6.81CI13.83-224.5165.01000ADT5.98190.48-eeYV (2) where Y = number of injurious crashes per year per kilometer ADT = average daily traffic in vehicles per day V = mean speed at each analyzed roadway segment CI = the curvature change rate indicator as explained above VGI = the vertical grade indi cator as explained above W = lanes plus shoulders width in meters The adjusted coefficient of determination ² is 99 percent. The structural form of this model is close to the representative cras h models presented by Vogt and Bared ( 16) calibrated from data coming from the states of Minneso ta and Washington on rural two-lane highways for segments and three-legged and four-legged stop-controlled intersections on minor legs. In these models the ADT is introduced as a primary effect in the EXPO m variable (a product of ADT and time), and as a secondary effect in the exponential form. The following visual aid shows p-values for each coefficient of the variables in the prediction Equations 1 and 2, respectively. TABLE 3 Coefficient of the Variables in CPMs 1 and 2 Crash Prediction Model on Low-Volume Roads located in areas with Flat/Rolling terrain Descriptive Variable Estimated Coefficient Standard Error t-value ; df = 1 p-level Lo. Conf. Limit Up. Conf. Limit ADT/1,000 0.00006 0.000000 0.00 0.00 0.0001 0.00006 CI 5.1106 0.000000 0.00 0.00 0.0001 0.00006 V 0.24556 0.2546692 0.00 0.00 -2.9906 3.48172 VGI -1.42373 2.760914 0.00 0.00 -36.5045 33.65701 W 0.80841 0.604812 0.00 0.00 -6.8765 8.49328 TRB 2011 Annual MeetingPaper revised from original submittal.
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Dell™Acqua G. and F. Russo 11 Crash Prediction Model on Low-Volume Roads located in areas with mountainous terrain Descriptive Variable Estimated Coefficient Standard Error t-value; df = 1 p-level Lo. Conf. Limit Up. Conf. Limit - -190.481 0.000000 0.00 0.00 -190.481 -190.481 ADT/1,000 5.988 1.577217 0.00 0.00 -14.053 26.028 V 0.651 0.386234 0.00 0.00 -4.256 5.559 - 224.513 0.000000 0.00 0.00 224.513 224.513 CI -13.834 7.219135 0.00 0.00 -105.562 77.893 VGI 6.807 6.639895 0.00 0.00 -77.560 91.175 W -7.150 2.692705 0.00 0.00 -41.364 27.064 Analysis of the Residuals Hauer recommends analyzing re sidual plots as an essentia l tool in this process ( 12). The residual is the value of the difference meas ured between the predicted value of injurious crashes using the model and the re al value of the number of in jurious crashes surveyed on the same roadway segment. The goal is to graphica lly observe how well the function fits the data set. The CuRe (Cumulative Residuals) method ha s the advantage of not being dependent on the number of observations, as are many othe r traditional statistical procedures (e.g., 2) (4, 10, 12). The CuRe method was adopted in addition to using the p-value criterion to test the significance of the regression equation, Pardillo et al. ( 4) used cumulative scaled residuals analysis to identify the regions where models under- or over-estimated accident rates, which provides a basis for the stratification of the models. The research demonstr ated the usefulness of this type of analysis in detecting redundancies in the statistical in formation contained in the calibration data sample and in comparing alternative prediction models calibrated with different sample sizes. Lord and Persaud ( 10) also applied cumulative residuals analysis to evaluate prediction models showing the vari ation in the crash rate in cons ecutive years, but they rule out the use of the conventional 2. For this reason, a diagram of cumulative residuals was plotted based on the ADT values analyzed. Figure 2 shows the residuals of two prediction models where it can be seen how the models offer a correct in terpretation of reality. There is a fair distribution of residuals around the mean. Positive values in the residuals plots correspond to the regions where the model underestimates crash densities, while negative values reflect the oppo site situation. For a good fit, the fluctuations must be homogeneous around the mean. Abrupt decreases or increases in the graph may reflect lack of flexibility in the functional form in the model and, in some cases , the existence of redundant data for a given value of the explanatory variable. For roads lo cated in the flat/rolling area, the observed residuals, in injurious crashes per year per kilometer, have a minimum value of 0.0001, a maximum value of 0.09, a mean value of 0.022 a nd a standard deviation of 0.023. For roads located in the mountainous area, the observed re siduals, in injurious ac cidents per year per kilometer, have a minimum value of -0.03, a maximum value of 0.080, a mean value of 0.012 and a standard deviation of 0.021. TRB 2011 Annual MeetingPaper revised from original submittal.
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