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Publication Number: FHWA-HRT-06-125
Date: November 2006
Pedestrian and Bicyclist Intersection Safety Indices
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CHAPTER 6. STATISTICAL ANALYSIS AND MODEL DEVELOPMENT
Three types of safety measures were collected for use in the development of the Ped ISI and Bike ISI—crashes, behavioral data (conflicts and avoidance maneuvers), and subjective intersection ratings. Of these measures, models were developed for ratings and behavioral data. The small amount of crashes precluded any model development on crash data. Models based on ratings were developed using multiple linear regression, since the ratings generally followed a normal distribution. Models based on behavioral data were developed using a generalized linear model, since the behavioral data generally followed a Poisson distribution.
The ratings-based models served as the core of the development of the Ped ISI and Bike ISI. The fact that these models predict a safety rating for a site on a scale of 1 to 6 conveniently leads to the development of a safety index. While these ratings-based models were the base of the safety indices development, the behavior-based models also had contributions to the ISI. The analyst noted which variables were significant in the avoidance maneuvers model and the direction of their effect on safety (positive or negative). It was of interest to identify those roadway and traffic variables that were most strongly associated with the occurrence of conflicts and avoidance maneuvers. In some situations, variables that were significant in the behavioral model, but not significant in the ratings model, were retained in the ratings model. This approach reflects the methodology of using multiple measures of safety in the development of the Ped ISI and Bike ISI.
BIKE ISI DEVELOPMENT
The Bike ISI consists of three separate models that were developed to evaluate the safety of the three possible bicycle movements at intersections—through, right-turn, and left-turn. The primary data file used in developing these models was a site-oriented file where each site was a particular approach leg of a specific intersection. The data file contained a number of variables describing the roadway geometry, traffic control, motor vehicle traffic, and bicycle facilities associated with each intersection. Table 9 shows the variables considered for inclusion in the model development and the full range of their values.
Table 9. Variables used in bicycle analysis.
Figure 12. Bicycle facility types.
Relationships between average ratings for the intersections and the variables listed in Table 9 were explored using various graphical methods, contingency tables, comparisons of means, and other methods to determine which variables were most strongly associated with the ratings. From these analyses, it could also be seen how best to categorize certain variables. For example, speed limits seemed most relevant when considered as two–level categorical variables indicating speed limits of 56 km/h (35 mi/h) or higher versus lower speed limits. Similarly, traffic control was used as a two–level variable indicating signalized intersections versus unsignalized intersections.
Statistical models for the average left–turn, right–turn, and through ratings were developed using regression analyses similar to those used in the development of the Bicycle Compatibility Index (Harkey, et al., 1998). These analyses lead to equations of the form:
The x1, …, xk are the variables listed in Table 9, modifications of these variables, or interactions of these variables. In particular, some interaction terms arose because the effects of some variables seemed to differ when a bike lane was present versus when it was not. The coefficients b0, b1, …, bk were estimated by a weighted least–squares procedure where each observation was weighted by the inverse of its variance. The resulting models are presented in the following tables.
The development of the ratings models went through an iterative process. For each version of a model, a comparison was made between the average evaluator rating given for a site and the rating predicted by the model. Sites with the greatest differences between the actual and predicted ratings were examined and reasons were found to explain most of the differences. Some differences were a result of factors that could not be incorporated into the model, since only one site of the group had the particular characteristic (i.e., high amounts of crossing pedestrian traffic, perpendicular on–street parking, high–speed channelized right–turn lane, etc.). Other factors did occur at enough sites to be added into the modeling process as separate factors. These factors included a more precise definition of the bike lane configuration (Figure 10), the number of vehicle lanes a bicyclist would cross to make a turn, and the presence of turning vehicles across a bicyclist’s through movement. The resulting ratings–based models are presented below in Table 10 through Table 12
Table 10. Through–movement bicycle ratings model.
Table 11. Right–turn bicycle ratings model.
Table 12. Left–turn bicycle ratings model.
For the analysis of behavioral data, a file was used that contained, for each bicyclist passing through the intersection, a count of avoidance maneuvers involving the cyclist and a motor vehicle, and the path taken by the cyclist (i.e., through, left, right). Unlike the pedestrian behavioral model, conflicts were not included in the bicycle behavioral model since there was a clearer distinction between bicycle conflicts and avoidance maneuvers. Appendix B contains information on observed bicycle conflicts.
The data file also contained the roadway and traffic variables listed in Table 9. Generalized regression models were used for these analyses where avoidance maneuvers were taken to follow a Poisson distribution with mean value µ such that the logarithm of µ could be expressed as a linear function of the roadway and traffic variables. The statistical significance of the estimated model coefficients thus determines which of the variables are associated with the likelihood of avoidance maneuvers between cyclists and motor vehicles. The resulting linear models, Tables 13 through 15, are displayed in the following tables in formats similar to the rating models in Table 10 through Table 12.
Table 13. Behavioral model for through bicyclists.
Table 14. Behavioral model for right–turning bicyclists.
Table 15. Behavioral model for left–turning bicyclists.
While the linear models shown in Table 13 through Table 15 are models for the logarithm of the mean of the respective Poisson distributions, the interpretation of the algebraic signs of the coefficients is similar to that for the ratings–based models in Table 10 through Table 12. Namely, a positive sign indicates an increase in the likelihood of an avoidance maneuver, while a negative sign indicates a decrease.
Final Bike ISI Models
The final Bike ISI models were a combination of the ratings models and behavioral models. They were built using the ratings models as a basis, but were modified according to input from the behavioral models. On–street parking on the approach is an important variable with respect to both through and left–turn avoidance maneuvers, but is a factor with respect to the rating models only for through cyclists when no bike lane is present. Given that parking was significant for the behavioral model and is known by bicycle researchers to cause potential safety hazards, parking was included as a variable in the final bicycle models. A relatively small effect for parking was included in the left–turn model and through model by directly inputting the specific effect and reestimating the other coefficients. There is no p–value for these parking variables since the effects were directly inputted. Table 16 and Table 17 show the final forms of the Bike ISI models.
Table 16. Final bike ISI models.
Table 17. Variables used in bike ISI models.
Bike ISI Adjustment Factors
Upon development of the Bike ISI, the research team compared the model-predicted rating for each site with the average rating it actually received in the survey. Some sites were found to have large differences between the predicted and actual ratings, most often due to a particular site characteristic that was not accounted for in the database. The rarity of these occurrences prevented an accurate modeling of their effect on the safety index value, but each characteristic was observed to have some negative effect on the rating of the site at which it was located (a negative effect on safety will increase the numeric safety index). While these factors are not included in the models, consideration should be given to sites with these characteristics with a iew to modifying the model-predicted safety index value to account for the effect of these factors.
PED ISI DEVELOPMENT
As with the Bike ISI, the Ped ISI was developed by using regression analysis to relate average rating scores and frequencies of conflicts and avoidance maneuvers to a number of variables describing the roadway geometries, pedestrian facilities, and motor vehicle traffic at those crossings. A list of these potential explanatory variables is shown in Table 18. For these analyses, the street being crossed is designated as the main street.
Table 18. Variables used in pedestrian analysis.
Ratings Model and Behavioral Model
Statistical models for average rating and behavioral data were developed in the same way as the Bike ISI. The main difference is that the bicycle behavioral model was based solely on avoidance maneuvers, whereas the pedestrian behavioral model is based on a combined group of conflicts and avoidance maneuvers. Results of these model developments are shown in Table 19 and Table 20.
Table 19. Pedestrian rating model.
Table 20. Pedestrian behavioral model.
Both the ratings and behavioral models have "signal control" and "number of through lanes" as common variables. In fact, signal control shows up as the variable with the most effect on safety in both models. Stop sign control does not show up as significant in the behavioral model, possibly because of the low amount of vehicle traffic through stop–controlled intersections. Main street ADT is significant in the behavioral model, but not in the ratings model, probably because the 40–s video clip was too short to give the evaluator anything but a general idea of the amount of traffic. The negative coefficient of the main street ADT variable is most likely a result of its correlation with signal control and number of through lanes.
Final Ped ISI Model
All significant variables in the ratings model—signal and stop control, number of through lanes, vehicle speed, and commercial area type—were retained and included in the final Ped ISI model. The inclusion of traffic control types in the model assumes that the signal or stop sign is located according to normal traffic engineering practice (i.e., signal at multi–lane, high–volume intersections; stop sign for low–volume movements). Although the ratings model did not include a variable for traffic volume, such a variable was added to the final Ped ISI model because of its significance in the behavioral model. The traffic volume (main street ADT) is included as an interaction with signal control.
The commercial area showed up as a significant factor in the ratings model and was included in the final Ped ISI model. The surrounding area was considered commercial if the predominant land use consisted of restaurants, retail shops, gas stations, banks, etc. Although not completely intuitive by itself, this factor generally correlates with other characteristics, such as greater number of lanes, which warrant higher ratings from the evaluators. The authors recognize that modifying the land use around an intersection is not within the normal realm of countermeasures. However, since the goal of the Ped ISI is to prioritize sites according to pedestrian or bicyclist safety, it is important for the tool to reflect factors that indicate where safety improvement efforts should be focused.
Table 21. Final Ped ISI model.
Table 22. Variables used in Ped ISI model.
Ped ISI Adjustment Factors
Some of the bicycle study sites had characteristics that negatively affected the site rating, but were so rare that they could not be modeled. Suggested adjustment factors were included for the benefit of the practitioner. In contrast, the comparison of the predicted rating to the actual rating for pedestrian study sites did not reveal specific characteristics that could account for differences in the ratings. Because of the larger area that can affect a bicyclist’s approach to an intersection and the three possible movements that a bicyclist can make, it is reasonable that a pedestrian crossing would have a simpler set of characteristics and have fewer characteristics that affect the safety of the crossing.
Somewhat surprisingly, the presence of a raised median was not found to be a significant factor in the results of the ratings or the avoidance maneuvers, even though past research has clearly found a significant safety benefit to pedestrians where raised medians or crossing islands are present on multi–lane roads. This may be explained by the fact that there were only 7 of 68 sites in the sample data where raised medians were present.
USING THE PED ISI AND BIKE ISI
This research report is accompanied by a User Guide, which succinctly presents the Ped ISI and Bike ISI and the data required to use them. It also contains several real–world examples where the Ped ISI and Bike ISI were used to determine safety index values for certain intersections.
DISCUSSION OF THE MODELS
The validity of the final Ped ISI and Bike ISI models may be judged largely by the variables included in the models and the known relationships between such variables and safety from what is known from previous safety literature.
Bike ISI Variables
Thus, all of the factors included in the final bicycle safety index models have been found in other studies to be related to bicycle safety and/or have a logical association with safety. It could be argued that additional variables should or could also have been included in the model. However, no single analysis can necessarily identify all possible variables of importance due to sample size, site selection, and other such limitations in a macro–level analysis. Other factors known to be problems at intersections can be accounted for by the local practitioner in a more micro–level analysis.
Ped ISI Variables
All of the factors included in the Ped ISI have been found in other studies to be related to pedestrian safety and/or have a logical association with safety. It could be argued that additional variables, such as "presence of raised medians," should also have been included in the model. However, no single analysis can necessarily identify all possible variables of importance due to sample size, site selection, and other such limitations. It is expected that the results of future pedestrian crash modeling (e.g., currently active project NCHRP 17–26) will be used to validate and enhance the Ped ISI.
COMPARISON OF SAFETY MEASURES
The methodology laid out in Chapter 3 describes how this research involved four measures of safety—crashes, conflicts, avoidance maneuvers, and safety ratings. An attempt to build a safety index model solely on any one of these safety measures would have certain drawbacks (Table 23). Thus, this research used multiple safety measures in the development of the Ped ISI and Bike ISI.
Table 23. Characteristics of pedestrian and bicyclist safety measures.
Combining these safety measures into one model is neither an easy nor clearly defined task. In this study, pedestrian crashes, bicycle crashes, and bicycle conflicts were few in number (Table 1), making it infeasible to perform detailed analyses on these data. Distribution differences between avoidance maneuvers (Poisson distribution) and ratings (normal distribution) did not allow for a simple combination of the regression results. In the end, the research team used the safety ratings data as the basis of the final Ped ISI and Bike ISI models and modified them according to the behavioral models.
The research team performed several tests to compare the four safety measures to each other for both the pedestrian and bicycle aspects of the study. This examination indicated how well the individual safety measures correlated with each other with respect to predicting the safety of a site. For the pedestrian ratings, sites were grouped into two or three categories based on each safety measure (i.e., sites with no crashes and sites with one or more crashes, etc.). Table 24 shows the results of categorical Chi–square tests performed between crashes, avoidance maneuvers, and ratings for the pedestrian analysis. There were no pedestrian conflicts to include in this comparative analysis. Results showed that crashes and avoidance maneuvers were not significantly different, but both measures were shown to be different from ratings. This difference might be explainable, since crash and avoidance frequencies are both likely related to traffic and pedestrian volumes, and therefore correlated with each other; on the other hand, ratings by observers focused on short (40 s) video clips of intersections where the raters saw the physical intersection features (e.g., number of lanes, presence of signal), but did not have time to gain a perspective on traffic (or pedestrian) volumes or speeds at the intersection.
Table 24. Comparison of pedestrian safety measures.
For comparisons on the bicycle analysis, an overall intersection rating was calculated as an average of the ratings for the three movements, and these average ratings were compared across the safety measures (Table 25). For the 15 sites where at least one conflict was observed, the average overall rating was 2.36, while for the 52 sites having no conflicts, the average value was 2.23. These average ratings did not differ significantly (p = 0.39).
Similarly, the average overall rating for the 16 sites where at least one crash occurred was 2.35 versus an average of 2.23 for sites where no crashes were recorded. Again, the difference was not significant (p = 0.39). While the numbers of sites having crashes and conflicts were almost the same, these events generally did not occur at the same locations.
The comparisons displayed in Table 25 that involved crashes and conflicts were performed for the site as a whole, irrespective of the individual movements. The comparison of avoidance maneuvers to ratings, however, was performed separately for through, right–turn, and left–turn movements.
Table 25. Comparison of bicycle safety measures.
The comparisons shown in Table 24 and Table 25 indicate that the measures of safety used in this study did not generally relate well to each other with respect to predicting site safety, whether pedestrian crosswalk or bicycle approach. This is not altogether unexpected. These measures of safety are very different in what they measure. Also, two of them, crashes and conflicts, had very low numbers of observed events. Thus, the safety measures for which there are adequate data were avoidance maneuvers and ratings. The following list presents some discussion on the similarities and differences in these two safety measures.
Similarities Between Avoidance Maneuvers and Ratings
Differences Between Avoidance Maneuvers and Ratings
It is evident that these safety measures differ from each other in their inherent definition and in their predictions of pedestrian and bicyclist intersection safety. Given these differences, the research team hopes that the use of multiple safety measures resulted in a more comprehensive safety index model than relying solely on one safety measure.
DISCUSSION OF VARIABLE INCLUSION
The process used in developing the final rating models accounted for associations between the various independent variables. In other words, the model development was an iterative process that involved the development of hundreds of contingency tables to determine which variables were most highly associated with the safety ratings. For example, intersections in commercial areas were more likely to be signalized and also generally had a greater number of lanes when compared to locations that were not in commercial areas. However, even after controlling for the type of signal control and the number of lanes, the variable "commercial area" still contributed significantly to the prediction of the pedestrian rating more than the use of those other independent variables alone. Therefore, the variable "commercial area" was also included in the pedestrian rating model.
At each stage of the model building process, numerous contingency tables were examined and potential models were estimated. This iterative process involved exploring the influence of adding additional variables in terms of explaining the variation in pedestrian or bicycle rating values. Variables that contributed significantly to the predictive power of the model were included in the model.
ACCOMPANYING LOCAL FIELD STUDIES
This research sponsored two studies on a local level that paralleled the goals of this research. Both studies were conducted in Chapel Hill, NC, in April 2005. The participants in these studies were local residents who were either familiar with walking in the general environment (for the pedestrian study) or experienced bicyclists (for the bicycle study). None of the participants were professional engineers, planners, or ped/bike advocates. Although these studies were not true validation analyses of the safety index models (i.e., they did not test the tool itself), the smaller scale of these studies provided additional insight to the results of the safety index study.
Pedestrian Local Field Study
Ten pedestrian participants gave subjective safety ratings of 23 intersection crossings, once from viewing a video clip of each crossing and again after visiting the crossing in person. The objective of this study was to compare video safety ratings to onsite ratings.
Similar to the larger Ped ISI study, the unit of analysis was a single crossing instead of a whole intersection. Twenty–three crossings were chosen to represent a variety of crossing characteristics. Participants viewed a 30–s video clip of each crossing and gave a rating from 1 to 6, according to how safe they felt about crossing the street at that location. The participants were then taken to the sites in the field, where they viewed the crossing from the curb (did not cross) and again provided a safety rating for each crossing. For both types of ratings, participants provided comments on the factors that affected their rating decision.
Statistical comparison of the video versus field ratings did not show a significant difference between the two types of ratings (Table 26). This result is encouraging for the Ped ISI, which based models on video ratings. However, the limited scale of this local study should prevent overgeneralization of this result.
Table 26. Field versus video ratings for pedestrian local study.
Bicyclist Local Field Study
Five bicyclist participants gave subjective safety ratings of 18 intersection approaches from a bicyclist’s point of view, once from viewing a video clip of each crossing and again after visiting the crossing in person. The objective of this study was to compare video safety ratings to onsite ratings.
Similar to the larger Bike ISI study, the unit of analysis was a single approach instead of a whole intersection. Eighteen intersection approaches were chosen to represent a variety of approach leg characteristics. Participants viewed a 30–s video clip of each approach and gave a rating from 1 to 6, according to how safe they felt about approaching and traveling through the intersection at that location. The participants were then taken to the sites in the field where they viewed the sites (did not ride a bicycle) and again provided a safety rating for each approach. For both types of ratings, participants provided brief comments on the factors that affected their rating decision.
In the same manner as the development of the Bike ISI, the analysis was done according to the separate movements a bicyclist can make at an intersection—through, right, and left. Statisticalcomparison of the video versus field ratings was performed for each of these movements and for the intersection as a whole (Table 27).
Table 27. Field versus video ratings for bicycle local study.
The analysis did not show a significant difference between field and video ratings for the through and left movements, as well as all movements averaged together at each intersection. There was a significant difference for the right-turn movement. The results of this analysis seem to indicate that field ratings will parallel video ratings for the majority of the study; however, there is some question about their association for right-turn ratings. However, low numbers of participants makes it difficult to generalize the findings of this local study. Recommendations are provided in Appendix D for conducting future online video surveys.