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Modeling the Frequency of Opposing Left-Turn Conflicts at Signalized Intersections Using Generalized Linear Regression Models a
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Xin Zhang , Pan Liu , Yuguang Chen , Lu Bai & Wei Wang
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School of Transportation, Southeast University, Nanjing, China Accepted author version posted online: 12 Nov 2013.Published online: 27 May 2014.
Click for updates To cite this article: Xin Zhang, Pan Liu, Yuguang Chen, Lu Bai & Wei Wang (2014) Modeling the Frequency of Opposing LeftTurn Conflicts at Signalized Intersections Using Generalized Linear Regression Models, Traffic Injury Prevention, 15:6, 645-651, DOI: 10.1080/15389588.2013.860526 To link to this article: http://dx.doi.org/10.1080/15389588.2013.860526
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Traffic Injury Prevention (2014) 15, 645–651 C Taylor & Francis Group, LLC Copyright ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2013.860526
Modeling the Frequency of Opposing Left-Turn Conflicts at Signalized Intersections Using Generalized Linear Regression Models XIN ZHANG, PAN LIU, YUGUANG CHEN, LU BAI, and WEI WANG School of Transportation, Southeast University, Nanjing, China
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Received 24 May 2013, Accepted 25 October 2013
Objective: The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Methods: Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. Results: The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. Conclusions: The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation. Keywords: safety, conflict, prediction, generalized linear model, signalized intersection
Introduction Traditionally, traffic safety assessment at signalized intersections has often been undertaken using crash data. In practical engineering applications, however, reliable crash data may not always be available. This is particularly true for developing countries such as China, where traffic engineers often rely on surrogate safety measures for safety assessment. Traffic conflict techniques are probably the most developed surrogate safety assessment method. A traffic conflict has been defined as an observable situation in which 2 or more road users approach each other in space and time to such an extent that there is a risk of collision if their movements remain unchanged (Tarko et al. 2009). Previous studies have suggested that there is a strong relationship between conflict frequency and crashes (Glauz et al. 1985; Karim and Sayed 2013; Meng and Qu 2012; Pietrzyk 1996;
Associate Editor Clay Gabler oversaw the review of this article. Address correspondence to Pan Liu, School of Transportation, Southeast University, Si Pai Lou #2, Nanjing, China 210096. E-mail: pan [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gcpi.
Sayed 1997; Sayed and Zein 1998). It is then assumed that the change in the frequency of conflicts reflects the change in safety. Even though controversies still remain regarding the validity of this assumption, the traffic conflicts technique has attained a measure of popularity in road safety assessment (Autey et al. 2012; Glauz and Migletz 1980; Harwood et al. 2003; Johansson and Leden 2007; Liu et al. 2008). Over the past several decades, there have been numerous studies looking at various aspects of the traffic conflicts technique. However, little attention has been given to the analytical methods for safety evaluation using traffic conflicts as safety measures. Several researchers recently started using the simulated conflicts generated by microscopic traffic simulation models to automate the process of traffic conflicts analyses (Archer 2005; Cunto and Saccomanno 2008; Dijkstra et al. 2010; Duong et al. 2010; Gettman and Head 2008). However, controversies still remain regarding the validity of using simulated conflicts for safety assessment because many believe that microscopic traffic simulation models cannot accurately reproduce the complex behaviors of drivers in the real world. Traffic conflict data share some similar traits with crash data. Both conflicts and crashes are random events whose occurrences are affected by various external factors, such as traffic, geometric design, and traffic control. Clearly, the frequencies of both conflicts and crashes are nonnegative
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646 integers that follow a specific distribution. If we agree that traffic conflicts can be used as surrogate measures for safety, it is very likely that the methods developed for crash data analysis may also be applied to traffic conflicts data. For example, numerous existing studies have developed various statistical models to link the safety of an entity to explanatory variables. Theoretically, a similar relationship can also be established between the frequency of traffic conflicts and contributing factors. Several existing studies have investigated the relationship between conflict frequency and traffic volumes (Salman and Al-maita 1995; Sayed and Zein 1999). These studies used the conventional linear regression technique to evaluate the relationship between conflict frequency and traffic flow rate. One of the major assumptions of the classical linear regression model is that the dependent variable is continuous and normally distributed with a constant variance. The assumption may not be appropriate for conflict data that are nonnegative, random, and discrete in nature. The use of a continuous distribution, such as the normal distribution, is at best an approximate to a truly discrete process. Previous studies have suggested that using linear regression models to fit the count data may provide biased results (Cameron and Trivedi 1998; Hauer 2004; Hauer et al. 1988; Maher and Summersgill 1996; Miaou and Lum 1993). The primary objective of this study was to identify whether and how the frequency of traffic conflicts can be modeled. The focus of this study was on signalized intersections where the conflicts between various turning movements often constituted a safety concern. More specifically, the study sought answers to the following questions: (1) What was the underlying distribution of the conflict frequency during a specific period of time? (2) What kind of model should be selected given the underlying distributions of conflicts data? (3) Does the conflict-predictive model provide reasonable estimates for the frequency of traffic conflicts?
Data Field data collection was conducted at 30 four-leg signalized intersections in the Kunming area in China. The study area at each selected signalized intersection started from approximately 30 m upstream of the stop lines in different approaches. Four video cameras were set up in the field to cover the study area from different angles. The cameras were set up on top of roadside buildings to achieve adequate viewing height (see Figure A1, see online supplement). Field data collection was conducted during weekday peak periods under fine weather conditions. A total of 167 h of traffic data was recorded. The recorded videos were reviewed in the laboratory. The following information was extracted from videos: (1) the number and types of traffic conflicts, (2) the time to collision (TTC) for each conflict, and (3) the traffic volume for different movements. Data were counted in 5-min time intervals. A trained graduate student was designated to review all of the videos to ensure that consistent criteria were applied for identifying conflicts at different sites. The identification of traffic conflicts started from detecting the evasive actions between motor ve-
Zhang et al. hicles, such as braking, swerving, and noticeable deceleration. Once a noticeable evasive action was detected, the observer estimated the TTC associated with the maneuver to identify whether it can be considered a conflict. Only the evasive maneuvers with TTC less than 2 s were used for safety assessment (Minderhoud and Bovy 2001; Sayed and Zein 1999; Vogel 2003). Based on our field observation a conflict with TTC greater than two sec can be considered of low risk. A grid system was added in the video using the media software VideoStudio (Corel Video Studio, Version Pro X6.0, Ottawa, ON: Corel Corporation 2012) to help the observer estimate the TTC for each evasive action (see Figure A2, see online supplement). The following information was collected: (1) the time when the first vehicle took an evasive action to avoid a collision; (2) the distance between the vehicles to the conflict point; and (3) the speed of each conflicting vehicle. Speed of each conflicting vehicle was calculated by measuring the elapsed time for each vehicle to travel a particular distance in the video (V 1 and V 2 in Figure A2). VideoStudio was used to process the video files in a frame-by-frame way at a rate of 25 frames per second so that the observer can identify the speed of conflicting vehicles by comparing their locations in different frames. Field observation showed that the volume of the conflicting flows was the most important factor that affected the number of conflicts, and different conflict types were affected by different conflicting traffic flows. Thus, instead of developing an overall intersection level model, conflict predictive models should be developed for different conflict types from different approaches to better understand the effects of different combinations of conflicting traffic flows. In this study, the opposing left-turn conflicts were selected as an example for the development of conflict predictive models. The opposing leftturn conflicts accounted for 57.14 percent of the total conflicts at the selected signalized intersections. The data were divided into 2 groups, including a calibration group, which included 125 h of data collected from 20 approaches at 15 intersections, and a validation group, which include 42 h of data collected from 10 approaches at the other 5 intersections.
Distribution of Conflicts In total, 6063 traffic conflicts were observed and identified at the selected signalized intersections, including 3465 opposing left-turn conflicts, 390 right-turn-on-red conflicts, 296 opposing right-turn conflicts, 1802 rear-end conflicts, and 110 conflicts that cannot be easily defined as any conflict types. The TTC of each conflict varies from 0.5 to 2 s with a mean of 1.32 s. Chi-square and the Kolmogorov-Smirnov tests were conducted to test the hypothesis that the frequency of the opposing left-turn conflicts followed a particular probability distribution. The chi-square goodness-of-fit test was conducted to identify whether the conflict frequency followed a Poisson or negative binomial distribution. The Kolmogorov-Smirnov test was used to examine whether conflict frequency can be approximated by a normal distribution. The time intervals of 5, 15, and 30 min were used to identify whether the distribution of conflict frequency is also affected by the length of the time
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Opposing Left-Turn Conflicts interval in which conflicts were counted. We did not examine the distribution of conflict frequency in 1-h time intervals because the sample size was not sufficiently large. The conflict frequency data were divided into 3 categories, including a low, median, and high conflicting volume regime. Note that the conflicting volume was defined as the product of the left-turn volume and the opposing through traffic volume. The histogram and the cumulative distribution curves are illustrated in Figure 1. Results of the goodness-of-fit tests showed that the conflict frequency generally followed a negative binominal (NB) distribution (see Table A1, online supplement). The only exception was that the conflict frequency followed a Poisson distribution when data were counted in 5-min time intervals in the high-volume regime. In most cases normal distribution was not found to be a good approximation for the distribution of conflicts, except for the data counted in 30-min intervals in the medium- and high-volume regimes. The finding suggested that the linear regression model that assumed that the dependent variable was normally distributed was not appropriate for modeling conflict frequency. The time interval also affected the dependent variable that would be included in the conflict predictive model. In this study, the conflict frequency counted in 15-min intervals was selected as the dependent variable in a conflict-predictive model considering both the results of the distributional analysis and the requirements for sample size. Note that for many traffic engineering applications, 15 min is the standard time period used, primarily based on the belief that this is the shortest period of time over which flow rates are statistically stable (Roger et al. 2010).
647 Table 1. Descriptive statistics of candidate independent variables Variables
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SD
Frequency (%)
Opposing through volume in 6 300 105 78.89 500 15 min Left-turn volume in 15 min 2 97 28 14.04 500 Median type 1 for raised median; 0 otherwise 139 (27.8) 1 for barrier; 0 otherwise 191 (38.2) 1 for double yellow line; 0 170 (34) otherwise Presence of white line extension 1 (Yes) 240 (48) 0 (No) 260 (52) Number of lanes on the opposing approach (n1 ) and cross street (n2 ) 1 if n1 a = 3, n2 b = 6; 0 otherwise 60 (12) 1 if n1 = 3, n2 = 4; 0 otherwise 57 (11.4) 1 if n1 = 2, n2 = 6; 0 otherwise 65 (13) 1 if n1 = 2, n2 = 4; 0 otherwise 88 (17.6) 1 if n1 = 2, n2 = 2; 0 otherwise 72 (14.4) 1 if n1 = 1, n2 = 4; 0 otherwise 85(17) n1 = 1, n2 = 2 73 (14.6) Average turning radius of left-turn 32 57 40.38 7.39 500 traffic Proportion of large cars in 0 0.28 0.036 0.062 500 left-turn traffic Proportion of large cars in 0 0.31 0.052 0.060 500 opposing through traffic Available green time allocated to 34 68 48 10 500 left-turn phase in seconds Percentage of green time allocated 0.35 0.57 0.45 0.062 500 to left-turn phase an bn
1 2
represents the number of lanes on the opposing approach. represents the number of lanes on the cross street.
Model Specification Linear Regression Model A linear regression model was developed to relate conflict frequency to various explanatory variables. The dependent variable of the model was the number of the opposing leftturn conflicts from one approach at a signalized intersection in 15 min. The data originally collected in 5-min time intervals were aggregated into 15-min levels, resulting in a sample size of 500 for 125 h of data in the calibration group. The number of the opposing left-turn conflicts in 15-min intervals varied from 0 to 15 with a mean of 4.98. Ten independent variables were initially considered for model specification. The research team did not consider the type of left-turn phase because all of the selected approaches had permitted left-turn phases. Descriptive statistics of the initially considered independent variables are given in Table 1. To linearize the relationship between the dependent and independent variables, different transformations, such as the logarithmic, exponential, power, and logistic transformations of the continuous independent variables, were tested. The stepwise regression technique was then used to determine the variables that should be included in the linear regression model. Results of the linear regression model are given in Table A2 (see online supplement). The best model had 6 independent variables. All of these variables were statistically significant with a 95 percent level of confidence. The model yielded a moderate adjusted R2 value of 0.490. All of the estimated co-
efficients can be considered intuitive. The final equation of the linear regression model was given by C F = 1.447 × ln(T) + 1.573 × ln(L) + 2.286 ×R1 + 1.455 × R2 + 0.982 × R3 + 0.075 ×RL − 1.325 × M − 0.030 × G − 8.234,
(1)
where CF represents the expected number of opposing leftturn conflicts per 15 min; T represents the opposing throughtraffic volume in 15 min; L represents the left-turn volume in 15 min; where R1 , R2 , and R3 are 3 indicator variables for the number of lanes on the opposing approach and the cross street (R1 = 1 if there are 3 lanes in the opposing approach and 6 lanes on the cross street in both directions and 0 otherwise; R2 = 1 if there are 3 lanes in the opposing approach and 4 lanes on the cross street in both directions and 0 otherwise; R3 = 1 if there are 2 lanes in the opposing approach and 6 lanes on the cross street in both directions and 0 otherwise). M is the binary variable for the presence of white line extension for the left-turn lane (see Figure A3, online supplement). RL represents the average turning radius provided for left-turn traffic. G represents the green time allocated to the left-turn movement. Residuals analysis was conducted to identify possible violations of the basic assumptions of the linear regression model. As shown in Figure A4 (see online supplement), the deviations of the residuals from zero became greater as the dependent variable became larger, indicating that the
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Fig. 1. Distributions of conflict frequency for different volume regimes in different time intervals.
disturbances were heteroscedastic (Washington et al. 2003). The results of the residual analysis suggested that a generalized linear regression model is more appropriate for modeling the conflict frequency data. Generalized Linear Regression Model Using the generalized linear regression technique, conflict modeling started with a Poisson model in which the dependent variable was the conflict frequency in 15 min from one approach at a signalized intersection. The 7 candidate variables given in Table 1 were considered. Different functional forms were tested using the cumulative residuals method (Maher and Summersgill 1996). Stepwise regression was used to determine the variables that should be included in the conflict-predictive model. The correlation matrix was estimated to ensure that there was no multicollinearity problem between the selected independent variables. The scaled deviance and Pearson’s χ 2 were used to detect the overdispersion or underdispersion in the Poisson regression model. Pearson’s χ 2 divided by the degrees of freedom for the Poisson model was 1.17. The scaled deviance divided by
the degrees of freedom was 1.27. The statistics suggested that the conflict data were overdispersed and an NB model should be used. The regression results of the best model are given in Table A3 (see online supplement). The final equation of the model was given as (2) C F = 0.068 × T 0.4482 × L0.4681 × exp(0.6270R1 +0.4767R2 + 0.3884R3 − 0.4939S1 − 0.2718S2 −0.1852M + 0.0083RL − 0.0060G), where S1 and S2 are 2 indicator variables for median type on main streets (S1 = 1 if there is a raised median on the main street and 0 otherwise; S2 = 1 for the presence of a barrier on the main street and 0 otherwise). The median types considered in this study are displayed in Figure A5 (see online supplement). The coefficients of the model suggest that the frequency of opposing left-turn conflicts increases as the left-turning radius increases and decreases with an increase in the green time that is allocated to the left-turn movement. The coefficients of the opposing through and left-turn volumes were positive,
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indicating that the conflict frequency increased with an increase in the conflicting traffic volume. The coefficients of the 2 indicator variables for median type were negative, implying that using a divided median was helpful to reduce the opposing left-turn conflicts. The coefficients of the categorical variables for the number of lanes generally indicated that conflict frequency increased with an increase in the number of lanes on the opposing approach and cross street. The cumulative residuals of the NB model were plotted against the opposing through volume and left-turn volume in Figure A6 (see online supplement). Generally, a good cumulative residuals plot is one that oscillates around 0 within the limits of ±2σ ∗ (n), which can be estimated as (Hauer 2004)
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∗
σ = σ (n) 1 −
σ 2 (n) , σ 2 (N)
(3)
where σ (n) represents the sum of the squared residuals from observation 1 to n and N represents the number of the observations used for model specification. The curves in Figure A6 show that the goodness-of-fit between the conflict frequency and the conflicting volumes were not so satisfactory. The curve for the opposing through volume showed that the conflict predictive model consistently underestimated the conflict frequency when the opposing through volume was small and overestimated the conflict frequency when the opposing through volume exceeded 55 vehicles in 15 min. The curve for the cumulative residuals also encroached the ±2σ ∗ (n) bands in 2 ranges of the opposing through volume. Field observation revealed that the relationship between the frequency of the opposing left-turn conflicts and conflicting volumes was actually quite complex and, accordingly, may not be modeled with an overall conflict predictive model. Almost all of the opposing left-turn conflicts were caused by the leftturning vehicles that did not yield to the right-of-way of the opposing through traffic during the permitted left-turn phases. Theoretically, a vehicle at the left-turn lanes with permitted left-turn phases had to wait until there was a suitable gap in the opposing through traffic flow to cross the intersection. The gap acceptance behavior of the drivers of left-turning vehicles was affected by both the opposing through traffic volume and the delay that the driver experienced at the leftturn lane. Generally, the drivers who experienced longer delays at the left-turn lane were more likely to accept small gaps to cross the intersection without yielding to the opposing through traffic. To better understand the effects of conflicting traffic volumes, the traffic conditions were divided into 4 scenarios based on the estimated average volume to capacity (v/c) ratio of the opposing through traffic (0.48) and the left-turn traffic (0.38). Note that the v/c ratio greatly affects delay at a signalized intersection. The definition of the 4 traffic scenarios was illustrated in Figure 2. Separate conflict predictive models were then developed for various traffic scenarios and the results are given in Table A4 (see online supplement). The NB models were found to be the best for most of the traffic scenarios except traffic scenario 3, for which the Poisson model was found to be the best.
Fig. 2. Definition of 4 traffic scenarios based on v/c ratio.
2
Both opposing through volume and left-turn volume were statistically significant in the models for traffic scenarios 1, 2, and 3. Even though the left-turn volume was not found to be significant for traffic scenario 4, the variable was still included for the purpose of comparison. The variables such as the number of lanes on the opposing approach and the cross street and the median types were not found to be significant. Inspection of the data showed that these variables were quite homogeneous in each traffic scenario. By analyzing the cumulative residuals of different conflict predictive models, it was found that the separate conflict predictive models provided better goodness-of-fit than did the overall NB model (see Figure A7, online supplement). The coefficients of the conflict predictive models showed that the conflicting traffic volumes had different effects on the occurrences of opposing left-turn conflicts under different traffic scenarios. The results of elasticity analysis showed that a 1 percent increase in the opposing through volume would increase the conflict frequency by 0.38, 0.53, 0.19, and 1.15 percent for traffic scenarios 1, 2, 3, and 4, respectively, given that other independent variables remain the same. Accordingly, a 1 percent increase in the left-turn volume would increase the conflict frequency by 0.59, 0.62, 0.44, and 0.26 percent for traffic scenarios 1, 2, 3, and 4, respectively. The lowest number of conflicts was predicted and observed in traffic scenario 2, which represented the condition in which the v/c ratios for both opposing through and left-turn traffic were relatively small. The opposing vehicles in this condition generally arrived in platoons. Left-turning vehicles can easily find suitable gaps between the platoons of the opposing through traffic to cross the intersection. The greatest number of conflicts was predicted and observed in traffic scenario 1, which represented the situation in which both opposing through and left-turn traffic had a relatively high v/c ratio. In this condition it was difficult for left-turning vehicles to find suitable gaps in the opposing through traffic. Drivers who experienced long delay at the left-turn lane may lose their patience and accept a small gap in the opposing through traffic
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to cross the intersection, forcing opposing through vehicles to apply brakes to avoid a collision. The effects of left-turn volume were not found to be significant in traffic scenario 4, which represented the condition in which the v/c ratio for left-turn traffic was relatively high and the v/c ratio for the opposing through traffic was relatively small. In this condition, the occurrence of conflicts was mainly dependent on the available gaps in the opposing through traffic because the left-turn traffic demand was always high. The number of available gaps would decrease as the opposing traffic volume increased. Drivers who experienced a long delay at the left-turn lane may select small gaps to cross the intersection, resulting in conflicts with the opposing traffic.
Comparison of the Prediction Performance The prediction performance of various conflict-predictive models was compared. The data used for model validation were collected from the 10 approaches at the 5 signalized intersections that were not used for model specification. A total of 168 observations in 15-min intervals were used for the validation of conflict predictive models. Two statistics were used for comparing the prediction performance, including the mean absolute deviation (MAD) and the mean squared prediction error (MSPE). These two statistics can be estimated as n 1 | yˆ i − yi | n
(4)
n 1 ( yˆ i − yi )2 , n
(5)
MAD =
i =1
MSPE =
i =1
where yˆ i and yi are the predicted and observed conflict frequency in 15-min, respectively, and n is the sample size used for model validation. The MAD and MSPE for different conflictpredictive models for different traffic scenarios are given in Table A5 (see online supplement). It was found that the generalized linear regression models generally provided smaller MAD and MSPE than the linear regression model. The conflict-predictive models developed for different traffic scenarios yielded the lowest MAD and MSPE. The conflicts predicted using different conflictpredictive models were then plotted against the observed conflicts (see Figure A8, online supplement). The linear regression model systematically overestimated the conflict frequency when the conflicting volumes were low and underestimated the conflict frequency when the conflicting volumes were high. In addition, the linear regression model provided some negative estimates for the conflict frequency, which was not realistic. The model validation results confirmed that the linear regression model was not appropriate for modeling the conflict frequency data. It was again found that the generalized linear regression models developed for different traffic scenarios outperformed the overall NB model because the data points for the separate models were more evenly distributed against the ideal line.
Discussion The major finding of the study is that the occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The traditional crashpredictive models relate the average crash frequency of an entity over a relatively long time period to some aggregated data such as AADT. The information lost in the process of aggregation sometimes makes it difficult to obtain the precise estimation of safety effects. Compared to crashes, traffic conflicts are easier to measure and more predictable. It can be expected that the conflict-predictive models can better capture the influence of detailed changes in contributing factors on the safety measure than traditional crash-predictive models do. For example, the conflict-predictive models developed in this study suggested that the effects of conflicting traffic volume on conflict frequency were different in different traffic conditions. A similar conclusion cannot be easily obtained using crash-predictive models. As a result, conflict-predictive models have potential to serve as important supplementations to traditional crash-predictive models to help us better understand the causes of crash occurrences. The possible uses of a conflict-predictive model in traffic safety studies include the following: 1. The conflict-predictive model can be used to predict the number of traffic conflicts occurring on an entity during a specific time period. Traffic conflicts as surrogate safety measures are usually collected in the field by trained observers. The methods used for identifying conflicts have been questioned due to the intensive involvement of observers’ subjective judgments. With a conflict-predictive model, traffic engineers do not have to collect traffic conflict data in the field, and the bias in the conflict data introduced by observers’ subjective judgments can be reduced; 2. The conflict-predictive model provides users with the information on the expected number of conflicts. Traditionally, the field-measured conflict counts were used to evaluate the safety of an entity. However, traffic conflicts are random events. The number of conflicts on an entity during a specific time interval may follow a particular distribution about its mean value, which is affected by various contributing factors such as traffic, geometric features, and traffic control. Theoretically, if traffic conflicts are to be used for safety assessment, the best safety measure should be the expected number of conflicts occurring on the entity during a specific period of time, not the observed conflict counts. 3. The conflict-predictive model can be used to evaluate the change in safety caused by a change in a contributing factor. Several existing studies have evaluated the safety effects of a treatment using traffic conflicts as safety measures (Autey et al. 2012; Hauer 1978; Johansson and Leden 2007; Liu et al. 2008; Princcioglu et al. 2006; Sayed et al. 2012; Zegeer and Deen 1978). Most of these studies were based on the na¨ıve before–after evaluation method in which the difference in the number of traffic conflicts counted during the before and after periods was used to measure the safety effects of a treatment. One of the limitations of the
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na¨ıve before–after evaluation method is that it mistakenly assumes that the factors affecting safety remain the same from the before to the after period. With conflict-predictive models, the before–after studies can be conducted with major confounding factors such as the traffic flow rate being controlled. The conflict-predictive model may also be used to estimate the empirical Bayesian-adjusted average conflict frequency to address the problem of regression to the mean. Following the present research, a more comprehensive study is needed to develop conflict-predictive models that can be directly used in practical engineering applications. Several issues need to be addressed. First, additional research is needed to develop more sophisticated models for different conflict types for various traffic facilities. The concerns may include, but are not limited to, the selection of explanatory variables, the functional forms of various conflict models, the possible spatial and temporal autocorrelation of traffic conflicts data, etc. Second, data need to be collected at more signalized intersections with heterogeneous traffic, geometric features, and control to testify the transferability of the conflict predictive models. Future studies may also consider comparing the crash-predictive model and conflict-predictive model developed using data collected from similar locations to further identify the validity of using conflict-predictive models for safety assessment.
Funding This research was sponsored by the National Natural Science Foundation of China (Grant Nos. 51322810 and 505908050).
Supplemental Material Supplemental data for this article can be accessed on the publisher’s website.
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651 Gettman D, Head L. 2008. Surrogate Safety Assessment Model and Validation. Washington, DC: Federal Highway Administration; 2008. FHWA-HRT-08-051. Glauz WD, Bauer BM, Migletz DJ. Expected traffic conflict rates and their use in predicting accidents. Transp Res Rec. 1985;1026:1–2. Glauz WD, Migletz DJ. Application of Traffic Conflict Analysis at Intersections. Washington, DC: Transportation Research Board, National Research Council; 1980. NCHRP Report 219. Harwood DW, Bauer KM, Potts IB, et al. Safety effectiveness of intersection left- and right-turn lanes. Paper presented at: 82nd Annual Meeting of the Transportation Research Board; 2003; Washington, DC. Hauer E. Design considerations of traffic conflict surveys. Transp Res Rec. 1978;667:57–66. Hauer E. Statistical road safety modeling. Transp Res Rec. 2004;1897:81–87. Hauer E, Ng J, Lovell J. Estimation of safety at signalized intersections. Transp Res Rec. 1988;1185:48–61. Johansson C, Leden L. Short-term effects of countermeasures for improved safety and mobility at marked pedestrian crosswalks in Boras, Sweden. Accid Anal Prev. 2007;39:500–509. Karim EB, Sayed T. Safety performance functions using traffic conflicts. Saf Sci. 2013;51:160–164. Liu P, Pan T, Lu J, Cao B. Estimating capacity of U-turns at unsignalized intersections: the conflicting traffic volume, the impedance effects, and the left-turn lane capacity. Transp Res Rec. 2008;2071:44–51. Maher MJ, Summersgill I. A comprehensive methodology for the fitting of predictive accident models. Accid Anal Prev. 1996;38:281–96. Meng Q, Qu XB. Estimation of rear-end vehicle crash frequencies in urban road tunnels. Accid Anal Prev. 2012;48:254–263. Miaou SP, Lum H. Modeling vehicle accidents and highway geometric design relationships. Accid Anal Prev. 1993;25:689–709. Minderhoud M, Bovy P. Extended time-to-collision measures for road traffic safety assessment. Accid Anal Prev. 2001;33:89–97. Pietrzyk M. Development of Expected Value Conflict Tables for FloridaBased Traffic Crashes. Washington, DC: U.S. Department of Transportation; 1996. USDOT WPI No. 0510721. Princcioglu F, Lu J, Liu P, Sokolow G. Right turn from driveways followed by U-turn on four-lane arterials: is it safer than direct left-turn? Transp Res Rec. 2006;1953:172–179. Roger PR, Elena SP, William RM. 2010. Traffic Engineering. 4th ed. Upper Saddle River, NJ: Prentice Hall; 2010. Salman NK, Al-maita KJ. Safety evaluation at three-leg, unsignalized intersections by traffic conflict technique. Transp Res Rec. 1995;1485:177–185. Sayed T. Estimating the safety of unsignalized intersections using traffic conflicts. Paper presented at: Third International Symposium on Intersections Without Traffic Signals; July 21–23, 1997; Portland, OR. Sayed T, Ismail K, Zaki MH, Autey J. Feasibility of computer visionbased safety evaluations: a case study of a signalized right-turn safety treatment. Paper presented at: 92nd Annual Meeting of the Transportation Research Board, 2012; Washington, DC. Sayed T, Zein S. Traffic conflict models and standards for signalized and unsignalized intersections. Paper presented at: CSCE 2nd Transportation Specialty Conference; June 10–13, 1998; Halifax, NS, Canada. Sayed T, Zein S. Traffic conflict standards for intersections. Transp Plann Technol. 1999;22:309–323. Tarko A, Davis G, Saunier N, Sayed T, Washington S. Surrogate Measures of Safety [white paper].Washington, DC: Subcommittee on Surrogate Measures of Safety and Committee on Safety Data Evaluation and Analysis, Transportation Research Board; 2009. Vogel K. A comparison of headway and time to collision as safety indicators. Accid Anal Prev. 2003;35:427–433. Washington S, Karlaftis M, Mannering F. Statistical and Econometric Methods for Transportation Data Analysis. London: Chapman & Hall/CRC; 2003. Zegeer CV, Deen RC. Traffic conflict as a diagnostic tool in highway safety. Transp Res Rec. 1978;667:48–55.
Traffic Injury Prevention Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gcpi20
Modeling the Frequency of Opposing Left-Turn Conflicts at Signalized Intersections Using Generalized Linear Regression Models a
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Xin Zhang , Pan Liu , Yuguang Chen , Lu Bai & Wei Wang
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School of Transportation, Southeast University, Nanjing, China Accepted author version posted online: 12 Nov 2013.Published online: 27 May 2014.
Click for updates To cite this article: Xin Zhang, Pan Liu, Yuguang Chen, Lu Bai & Wei Wang (2014) Modeling the Frequency of Opposing LeftTurn Conflicts at Signalized Intersections Using Generalized Linear Regression Models, Traffic Injury Prevention, 15:6, 645-651, DOI: 10.1080/15389588.2013.860526 To link to this article: http://dx.doi.org/10.1080/15389588.2013.860526
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Traffic Injury Prevention (2014) 15, 645–651 C Taylor & Francis Group, LLC Copyright ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2013.860526
Modeling the Frequency of Opposing Left-Turn Conflicts at Signalized Intersections Using Generalized Linear Regression Models XIN ZHANG, PAN LIU, YUGUANG CHEN, LU BAI, and WEI WANG School of Transportation, Southeast University, Nanjing, China
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Received 24 May 2013, Accepted 25 October 2013
Objective: The primary objective of this study was to identify whether the frequency of traffic conflicts at signalized intersections can be modeled. The opposing left-turn conflicts were selected for the development of conflict predictive models. Methods: Using data collected at 30 approaches at 20 signalized intersections, the underlying distributions of the conflicts under different traffic conditions were examined. Different conflict-predictive models were developed to relate the frequency of opposing left-turn conflicts to various explanatory variables. The models considered include a linear regression model, a negative binomial model, and separate models developed for four traffic scenarios. The prediction performance of different models was compared. Results: The frequency of traffic conflicts follows a negative binominal distribution. The linear regression model is not appropriate for the conflict frequency data. In addition, drivers behaved differently under different traffic conditions. Accordingly, the effects of conflicting traffic volumes on conflict frequency vary across different traffic conditions. Conclusions: The occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The use of conflict predictive models has potential to expand the uses of surrogate safety measures in safety estimation and evaluation. Keywords: safety, conflict, prediction, generalized linear model, signalized intersection
Introduction Traditionally, traffic safety assessment at signalized intersections has often been undertaken using crash data. In practical engineering applications, however, reliable crash data may not always be available. This is particularly true for developing countries such as China, where traffic engineers often rely on surrogate safety measures for safety assessment. Traffic conflict techniques are probably the most developed surrogate safety assessment method. A traffic conflict has been defined as an observable situation in which 2 or more road users approach each other in space and time to such an extent that there is a risk of collision if their movements remain unchanged (Tarko et al. 2009). Previous studies have suggested that there is a strong relationship between conflict frequency and crashes (Glauz et al. 1985; Karim and Sayed 2013; Meng and Qu 2012; Pietrzyk 1996;
Associate Editor Clay Gabler oversaw the review of this article. Address correspondence to Pan Liu, School of Transportation, Southeast University, Si Pai Lou #2, Nanjing, China 210096. E-mail: pan [email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gcpi.
Sayed 1997; Sayed and Zein 1998). It is then assumed that the change in the frequency of conflicts reflects the change in safety. Even though controversies still remain regarding the validity of this assumption, the traffic conflicts technique has attained a measure of popularity in road safety assessment (Autey et al. 2012; Glauz and Migletz 1980; Harwood et al. 2003; Johansson and Leden 2007; Liu et al. 2008). Over the past several decades, there have been numerous studies looking at various aspects of the traffic conflicts technique. However, little attention has been given to the analytical methods for safety evaluation using traffic conflicts as safety measures. Several researchers recently started using the simulated conflicts generated by microscopic traffic simulation models to automate the process of traffic conflicts analyses (Archer 2005; Cunto and Saccomanno 2008; Dijkstra et al. 2010; Duong et al. 2010; Gettman and Head 2008). However, controversies still remain regarding the validity of using simulated conflicts for safety assessment because many believe that microscopic traffic simulation models cannot accurately reproduce the complex behaviors of drivers in the real world. Traffic conflict data share some similar traits with crash data. Both conflicts and crashes are random events whose occurrences are affected by various external factors, such as traffic, geometric design, and traffic control. Clearly, the frequencies of both conflicts and crashes are nonnegative
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646 integers that follow a specific distribution. If we agree that traffic conflicts can be used as surrogate measures for safety, it is very likely that the methods developed for crash data analysis may also be applied to traffic conflicts data. For example, numerous existing studies have developed various statistical models to link the safety of an entity to explanatory variables. Theoretically, a similar relationship can also be established between the frequency of traffic conflicts and contributing factors. Several existing studies have investigated the relationship between conflict frequency and traffic volumes (Salman and Al-maita 1995; Sayed and Zein 1999). These studies used the conventional linear regression technique to evaluate the relationship between conflict frequency and traffic flow rate. One of the major assumptions of the classical linear regression model is that the dependent variable is continuous and normally distributed with a constant variance. The assumption may not be appropriate for conflict data that are nonnegative, random, and discrete in nature. The use of a continuous distribution, such as the normal distribution, is at best an approximate to a truly discrete process. Previous studies have suggested that using linear regression models to fit the count data may provide biased results (Cameron and Trivedi 1998; Hauer 2004; Hauer et al. 1988; Maher and Summersgill 1996; Miaou and Lum 1993). The primary objective of this study was to identify whether and how the frequency of traffic conflicts can be modeled. The focus of this study was on signalized intersections where the conflicts between various turning movements often constituted a safety concern. More specifically, the study sought answers to the following questions: (1) What was the underlying distribution of the conflict frequency during a specific period of time? (2) What kind of model should be selected given the underlying distributions of conflicts data? (3) Does the conflict-predictive model provide reasonable estimates for the frequency of traffic conflicts?
Data Field data collection was conducted at 30 four-leg signalized intersections in the Kunming area in China. The study area at each selected signalized intersection started from approximately 30 m upstream of the stop lines in different approaches. Four video cameras were set up in the field to cover the study area from different angles. The cameras were set up on top of roadside buildings to achieve adequate viewing height (see Figure A1, see online supplement). Field data collection was conducted during weekday peak periods under fine weather conditions. A total of 167 h of traffic data was recorded. The recorded videos were reviewed in the laboratory. The following information was extracted from videos: (1) the number and types of traffic conflicts, (2) the time to collision (TTC) for each conflict, and (3) the traffic volume for different movements. Data were counted in 5-min time intervals. A trained graduate student was designated to review all of the videos to ensure that consistent criteria were applied for identifying conflicts at different sites. The identification of traffic conflicts started from detecting the evasive actions between motor ve-
Zhang et al. hicles, such as braking, swerving, and noticeable deceleration. Once a noticeable evasive action was detected, the observer estimated the TTC associated with the maneuver to identify whether it can be considered a conflict. Only the evasive maneuvers with TTC less than 2 s were used for safety assessment (Minderhoud and Bovy 2001; Sayed and Zein 1999; Vogel 2003). Based on our field observation a conflict with TTC greater than two sec can be considered of low risk. A grid system was added in the video using the media software VideoStudio (Corel Video Studio, Version Pro X6.0, Ottawa, ON: Corel Corporation 2012) to help the observer estimate the TTC for each evasive action (see Figure A2, see online supplement). The following information was collected: (1) the time when the first vehicle took an evasive action to avoid a collision; (2) the distance between the vehicles to the conflict point; and (3) the speed of each conflicting vehicle. Speed of each conflicting vehicle was calculated by measuring the elapsed time for each vehicle to travel a particular distance in the video (V 1 and V 2 in Figure A2). VideoStudio was used to process the video files in a frame-by-frame way at a rate of 25 frames per second so that the observer can identify the speed of conflicting vehicles by comparing their locations in different frames. Field observation showed that the volume of the conflicting flows was the most important factor that affected the number of conflicts, and different conflict types were affected by different conflicting traffic flows. Thus, instead of developing an overall intersection level model, conflict predictive models should be developed for different conflict types from different approaches to better understand the effects of different combinations of conflicting traffic flows. In this study, the opposing left-turn conflicts were selected as an example for the development of conflict predictive models. The opposing leftturn conflicts accounted for 57.14 percent of the total conflicts at the selected signalized intersections. The data were divided into 2 groups, including a calibration group, which included 125 h of data collected from 20 approaches at 15 intersections, and a validation group, which include 42 h of data collected from 10 approaches at the other 5 intersections.
Distribution of Conflicts In total, 6063 traffic conflicts were observed and identified at the selected signalized intersections, including 3465 opposing left-turn conflicts, 390 right-turn-on-red conflicts, 296 opposing right-turn conflicts, 1802 rear-end conflicts, and 110 conflicts that cannot be easily defined as any conflict types. The TTC of each conflict varies from 0.5 to 2 s with a mean of 1.32 s. Chi-square and the Kolmogorov-Smirnov tests were conducted to test the hypothesis that the frequency of the opposing left-turn conflicts followed a particular probability distribution. The chi-square goodness-of-fit test was conducted to identify whether the conflict frequency followed a Poisson or negative binomial distribution. The Kolmogorov-Smirnov test was used to examine whether conflict frequency can be approximated by a normal distribution. The time intervals of 5, 15, and 30 min were used to identify whether the distribution of conflict frequency is also affected by the length of the time
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Opposing Left-Turn Conflicts interval in which conflicts were counted. We did not examine the distribution of conflict frequency in 1-h time intervals because the sample size was not sufficiently large. The conflict frequency data were divided into 3 categories, including a low, median, and high conflicting volume regime. Note that the conflicting volume was defined as the product of the left-turn volume and the opposing through traffic volume. The histogram and the cumulative distribution curves are illustrated in Figure 1. Results of the goodness-of-fit tests showed that the conflict frequency generally followed a negative binominal (NB) distribution (see Table A1, online supplement). The only exception was that the conflict frequency followed a Poisson distribution when data were counted in 5-min time intervals in the high-volume regime. In most cases normal distribution was not found to be a good approximation for the distribution of conflicts, except for the data counted in 30-min intervals in the medium- and high-volume regimes. The finding suggested that the linear regression model that assumed that the dependent variable was normally distributed was not appropriate for modeling conflict frequency. The time interval also affected the dependent variable that would be included in the conflict predictive model. In this study, the conflict frequency counted in 15-min intervals was selected as the dependent variable in a conflict-predictive model considering both the results of the distributional analysis and the requirements for sample size. Note that for many traffic engineering applications, 15 min is the standard time period used, primarily based on the belief that this is the shortest period of time over which flow rates are statistically stable (Roger et al. 2010).
647 Table 1. Descriptive statistics of candidate independent variables Variables
Min
Max
Mean
SD
Frequency (%)
Opposing through volume in 6 300 105 78.89 500 15 min Left-turn volume in 15 min 2 97 28 14.04 500 Median type 1 for raised median; 0 otherwise 139 (27.8) 1 for barrier; 0 otherwise 191 (38.2) 1 for double yellow line; 0 170 (34) otherwise Presence of white line extension 1 (Yes) 240 (48) 0 (No) 260 (52) Number of lanes on the opposing approach (n1 ) and cross street (n2 ) 1 if n1 a = 3, n2 b = 6; 0 otherwise 60 (12) 1 if n1 = 3, n2 = 4; 0 otherwise 57 (11.4) 1 if n1 = 2, n2 = 6; 0 otherwise 65 (13) 1 if n1 = 2, n2 = 4; 0 otherwise 88 (17.6) 1 if n1 = 2, n2 = 2; 0 otherwise 72 (14.4) 1 if n1 = 1, n2 = 4; 0 otherwise 85(17) n1 = 1, n2 = 2 73 (14.6) Average turning radius of left-turn 32 57 40.38 7.39 500 traffic Proportion of large cars in 0 0.28 0.036 0.062 500 left-turn traffic Proportion of large cars in 0 0.31 0.052 0.060 500 opposing through traffic Available green time allocated to 34 68 48 10 500 left-turn phase in seconds Percentage of green time allocated 0.35 0.57 0.45 0.062 500 to left-turn phase an bn
1 2
represents the number of lanes on the opposing approach. represents the number of lanes on the cross street.
Model Specification Linear Regression Model A linear regression model was developed to relate conflict frequency to various explanatory variables. The dependent variable of the model was the number of the opposing leftturn conflicts from one approach at a signalized intersection in 15 min. The data originally collected in 5-min time intervals were aggregated into 15-min levels, resulting in a sample size of 500 for 125 h of data in the calibration group. The number of the opposing left-turn conflicts in 15-min intervals varied from 0 to 15 with a mean of 4.98. Ten independent variables were initially considered for model specification. The research team did not consider the type of left-turn phase because all of the selected approaches had permitted left-turn phases. Descriptive statistics of the initially considered independent variables are given in Table 1. To linearize the relationship between the dependent and independent variables, different transformations, such as the logarithmic, exponential, power, and logistic transformations of the continuous independent variables, were tested. The stepwise regression technique was then used to determine the variables that should be included in the linear regression model. Results of the linear regression model are given in Table A2 (see online supplement). The best model had 6 independent variables. All of these variables were statistically significant with a 95 percent level of confidence. The model yielded a moderate adjusted R2 value of 0.490. All of the estimated co-
efficients can be considered intuitive. The final equation of the linear regression model was given by C F = 1.447 × ln(T) + 1.573 × ln(L) + 2.286 ×R1 + 1.455 × R2 + 0.982 × R3 + 0.075 ×RL − 1.325 × M − 0.030 × G − 8.234,
(1)
where CF represents the expected number of opposing leftturn conflicts per 15 min; T represents the opposing throughtraffic volume in 15 min; L represents the left-turn volume in 15 min; where R1 , R2 , and R3 are 3 indicator variables for the number of lanes on the opposing approach and the cross street (R1 = 1 if there are 3 lanes in the opposing approach and 6 lanes on the cross street in both directions and 0 otherwise; R2 = 1 if there are 3 lanes in the opposing approach and 4 lanes on the cross street in both directions and 0 otherwise; R3 = 1 if there are 2 lanes in the opposing approach and 6 lanes on the cross street in both directions and 0 otherwise). M is the binary variable for the presence of white line extension for the left-turn lane (see Figure A3, online supplement). RL represents the average turning radius provided for left-turn traffic. G represents the green time allocated to the left-turn movement. Residuals analysis was conducted to identify possible violations of the basic assumptions of the linear regression model. As shown in Figure A4 (see online supplement), the deviations of the residuals from zero became greater as the dependent variable became larger, indicating that the
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Fig. 1. Distributions of conflict frequency for different volume regimes in different time intervals.
disturbances were heteroscedastic (Washington et al. 2003). The results of the residual analysis suggested that a generalized linear regression model is more appropriate for modeling the conflict frequency data. Generalized Linear Regression Model Using the generalized linear regression technique, conflict modeling started with a Poisson model in which the dependent variable was the conflict frequency in 15 min from one approach at a signalized intersection. The 7 candidate variables given in Table 1 were considered. Different functional forms were tested using the cumulative residuals method (Maher and Summersgill 1996). Stepwise regression was used to determine the variables that should be included in the conflict-predictive model. The correlation matrix was estimated to ensure that there was no multicollinearity problem between the selected independent variables. The scaled deviance and Pearson’s χ 2 were used to detect the overdispersion or underdispersion in the Poisson regression model. Pearson’s χ 2 divided by the degrees of freedom for the Poisson model was 1.17. The scaled deviance divided by
the degrees of freedom was 1.27. The statistics suggested that the conflict data were overdispersed and an NB model should be used. The regression results of the best model are given in Table A3 (see online supplement). The final equation of the model was given as (2) C F = 0.068 × T 0.4482 × L0.4681 × exp(0.6270R1 +0.4767R2 + 0.3884R3 − 0.4939S1 − 0.2718S2 −0.1852M + 0.0083RL − 0.0060G), where S1 and S2 are 2 indicator variables for median type on main streets (S1 = 1 if there is a raised median on the main street and 0 otherwise; S2 = 1 for the presence of a barrier on the main street and 0 otherwise). The median types considered in this study are displayed in Figure A5 (see online supplement). The coefficients of the model suggest that the frequency of opposing left-turn conflicts increases as the left-turning radius increases and decreases with an increase in the green time that is allocated to the left-turn movement. The coefficients of the opposing through and left-turn volumes were positive,
Opposing Left-Turn Conflicts
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indicating that the conflict frequency increased with an increase in the conflicting traffic volume. The coefficients of the 2 indicator variables for median type were negative, implying that using a divided median was helpful to reduce the opposing left-turn conflicts. The coefficients of the categorical variables for the number of lanes generally indicated that conflict frequency increased with an increase in the number of lanes on the opposing approach and cross street. The cumulative residuals of the NB model were plotted against the opposing through volume and left-turn volume in Figure A6 (see online supplement). Generally, a good cumulative residuals plot is one that oscillates around 0 within the limits of ±2σ ∗ (n), which can be estimated as (Hauer 2004)
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∗
σ = σ (n) 1 −
σ 2 (n) , σ 2 (N)
(3)
where σ (n) represents the sum of the squared residuals from observation 1 to n and N represents the number of the observations used for model specification. The curves in Figure A6 show that the goodness-of-fit between the conflict frequency and the conflicting volumes were not so satisfactory. The curve for the opposing through volume showed that the conflict predictive model consistently underestimated the conflict frequency when the opposing through volume was small and overestimated the conflict frequency when the opposing through volume exceeded 55 vehicles in 15 min. The curve for the cumulative residuals also encroached the ±2σ ∗ (n) bands in 2 ranges of the opposing through volume. Field observation revealed that the relationship between the frequency of the opposing left-turn conflicts and conflicting volumes was actually quite complex and, accordingly, may not be modeled with an overall conflict predictive model. Almost all of the opposing left-turn conflicts were caused by the leftturning vehicles that did not yield to the right-of-way of the opposing through traffic during the permitted left-turn phases. Theoretically, a vehicle at the left-turn lanes with permitted left-turn phases had to wait until there was a suitable gap in the opposing through traffic flow to cross the intersection. The gap acceptance behavior of the drivers of left-turning vehicles was affected by both the opposing through traffic volume and the delay that the driver experienced at the leftturn lane. Generally, the drivers who experienced longer delays at the left-turn lane were more likely to accept small gaps to cross the intersection without yielding to the opposing through traffic. To better understand the effects of conflicting traffic volumes, the traffic conditions were divided into 4 scenarios based on the estimated average volume to capacity (v/c) ratio of the opposing through traffic (0.48) and the left-turn traffic (0.38). Note that the v/c ratio greatly affects delay at a signalized intersection. The definition of the 4 traffic scenarios was illustrated in Figure 2. Separate conflict predictive models were then developed for various traffic scenarios and the results are given in Table A4 (see online supplement). The NB models were found to be the best for most of the traffic scenarios except traffic scenario 3, for which the Poisson model was found to be the best.
Fig. 2. Definition of 4 traffic scenarios based on v/c ratio.
2
Both opposing through volume and left-turn volume were statistically significant in the models for traffic scenarios 1, 2, and 3. Even though the left-turn volume was not found to be significant for traffic scenario 4, the variable was still included for the purpose of comparison. The variables such as the number of lanes on the opposing approach and the cross street and the median types were not found to be significant. Inspection of the data showed that these variables were quite homogeneous in each traffic scenario. By analyzing the cumulative residuals of different conflict predictive models, it was found that the separate conflict predictive models provided better goodness-of-fit than did the overall NB model (see Figure A7, online supplement). The coefficients of the conflict predictive models showed that the conflicting traffic volumes had different effects on the occurrences of opposing left-turn conflicts under different traffic scenarios. The results of elasticity analysis showed that a 1 percent increase in the opposing through volume would increase the conflict frequency by 0.38, 0.53, 0.19, and 1.15 percent for traffic scenarios 1, 2, 3, and 4, respectively, given that other independent variables remain the same. Accordingly, a 1 percent increase in the left-turn volume would increase the conflict frequency by 0.59, 0.62, 0.44, and 0.26 percent for traffic scenarios 1, 2, 3, and 4, respectively. The lowest number of conflicts was predicted and observed in traffic scenario 2, which represented the condition in which the v/c ratios for both opposing through and left-turn traffic were relatively small. The opposing vehicles in this condition generally arrived in platoons. Left-turning vehicles can easily find suitable gaps between the platoons of the opposing through traffic to cross the intersection. The greatest number of conflicts was predicted and observed in traffic scenario 1, which represented the situation in which both opposing through and left-turn traffic had a relatively high v/c ratio. In this condition it was difficult for left-turning vehicles to find suitable gaps in the opposing through traffic. Drivers who experienced long delay at the left-turn lane may lose their patience and accept a small gap in the opposing through traffic
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to cross the intersection, forcing opposing through vehicles to apply brakes to avoid a collision. The effects of left-turn volume were not found to be significant in traffic scenario 4, which represented the condition in which the v/c ratio for left-turn traffic was relatively high and the v/c ratio for the opposing through traffic was relatively small. In this condition, the occurrence of conflicts was mainly dependent on the available gaps in the opposing through traffic because the left-turn traffic demand was always high. The number of available gaps would decrease as the opposing traffic volume increased. Drivers who experienced a long delay at the left-turn lane may select small gaps to cross the intersection, resulting in conflicts with the opposing traffic.
Comparison of the Prediction Performance The prediction performance of various conflict-predictive models was compared. The data used for model validation were collected from the 10 approaches at the 5 signalized intersections that were not used for model specification. A total of 168 observations in 15-min intervals were used for the validation of conflict predictive models. Two statistics were used for comparing the prediction performance, including the mean absolute deviation (MAD) and the mean squared prediction error (MSPE). These two statistics can be estimated as n 1 | yˆ i − yi | n
(4)
n 1 ( yˆ i − yi )2 , n
(5)
MAD =
i =1
MSPE =
i =1
where yˆ i and yi are the predicted and observed conflict frequency in 15-min, respectively, and n is the sample size used for model validation. The MAD and MSPE for different conflictpredictive models for different traffic scenarios are given in Table A5 (see online supplement). It was found that the generalized linear regression models generally provided smaller MAD and MSPE than the linear regression model. The conflict-predictive models developed for different traffic scenarios yielded the lowest MAD and MSPE. The conflicts predicted using different conflictpredictive models were then plotted against the observed conflicts (see Figure A8, online supplement). The linear regression model systematically overestimated the conflict frequency when the conflicting volumes were low and underestimated the conflict frequency when the conflicting volumes were high. In addition, the linear regression model provided some negative estimates for the conflict frequency, which was not realistic. The model validation results confirmed that the linear regression model was not appropriate for modeling the conflict frequency data. It was again found that the generalized linear regression models developed for different traffic scenarios outperformed the overall NB model because the data points for the separate models were more evenly distributed against the ideal line.
Discussion The major finding of the study is that the occurrences of traffic conflicts at signalized intersections can be modeled using generalized linear regression models. The traditional crashpredictive models relate the average crash frequency of an entity over a relatively long time period to some aggregated data such as AADT. The information lost in the process of aggregation sometimes makes it difficult to obtain the precise estimation of safety effects. Compared to crashes, traffic conflicts are easier to measure and more predictable. It can be expected that the conflict-predictive models can better capture the influence of detailed changes in contributing factors on the safety measure than traditional crash-predictive models do. For example, the conflict-predictive models developed in this study suggested that the effects of conflicting traffic volume on conflict frequency were different in different traffic conditions. A similar conclusion cannot be easily obtained using crash-predictive models. As a result, conflict-predictive models have potential to serve as important supplementations to traditional crash-predictive models to help us better understand the causes of crash occurrences. The possible uses of a conflict-predictive model in traffic safety studies include the following: 1. The conflict-predictive model can be used to predict the number of traffic conflicts occurring on an entity during a specific time period. Traffic conflicts as surrogate safety measures are usually collected in the field by trained observers. The methods used for identifying conflicts have been questioned due to the intensive involvement of observers’ subjective judgments. With a conflict-predictive model, traffic engineers do not have to collect traffic conflict data in the field, and the bias in the conflict data introduced by observers’ subjective judgments can be reduced; 2. The conflict-predictive model provides users with the information on the expected number of conflicts. Traditionally, the field-measured conflict counts were used to evaluate the safety of an entity. However, traffic conflicts are random events. The number of conflicts on an entity during a specific time interval may follow a particular distribution about its mean value, which is affected by various contributing factors such as traffic, geometric features, and traffic control. Theoretically, if traffic conflicts are to be used for safety assessment, the best safety measure should be the expected number of conflicts occurring on the entity during a specific period of time, not the observed conflict counts. 3. The conflict-predictive model can be used to evaluate the change in safety caused by a change in a contributing factor. Several existing studies have evaluated the safety effects of a treatment using traffic conflicts as safety measures (Autey et al. 2012; Hauer 1978; Johansson and Leden 2007; Liu et al. 2008; Princcioglu et al. 2006; Sayed et al. 2012; Zegeer and Deen 1978). Most of these studies were based on the na¨ıve before–after evaluation method in which the difference in the number of traffic conflicts counted during the before and after periods was used to measure the safety effects of a treatment. One of the limitations of the
Opposing Left-Turn Conflicts
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na¨ıve before–after evaluation method is that it mistakenly assumes that the factors affecting safety remain the same from the before to the after period. With conflict-predictive models, the before–after studies can be conducted with major confounding factors such as the traffic flow rate being controlled. The conflict-predictive model may also be used to estimate the empirical Bayesian-adjusted average conflict frequency to address the problem of regression to the mean. Following the present research, a more comprehensive study is needed to develop conflict-predictive models that can be directly used in practical engineering applications. Several issues need to be addressed. First, additional research is needed to develop more sophisticated models for different conflict types for various traffic facilities. The concerns may include, but are not limited to, the selection of explanatory variables, the functional forms of various conflict models, the possible spatial and temporal autocorrelation of traffic conflicts data, etc. Second, data need to be collected at more signalized intersections with heterogeneous traffic, geometric features, and control to testify the transferability of the conflict predictive models. Future studies may also consider comparing the crash-predictive model and conflict-predictive model developed using data collected from similar locations to further identify the validity of using conflict-predictive models for safety assessment.
Funding This research was sponsored by the National Natural Science Foundation of China (Grant Nos. 51322810 and 505908050).
Supplemental Material Supplemental data for this article can be accessed on the publisher’s website.
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