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Pedestrian Safety Prediction Methodology (2008)

Chapter: Chapter 4. Pedestrian Safety Modeling

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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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Suggested Citation:"Chapter 4. Pedestrian Safety Modeling." National Academies of Sciences, Engineering, and Medicine. 2008. Pedestrian Safety Prediction Methodology. Washington, DC: The National Academies Press. doi: 10.17226/23083.
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39 CHAPTER 4. PEDESTRIAN SAFETY MODELING This chapter presents the results for pedestrian safety modeling conducted with the available databases. MODELS FOR SIGNALIZED INTERSECTIONS IN TORONTO Candidate models in the following eight functional forms were considered: ( 8 ) ( 9 ) ( 10 ) ( 11 ) ( 12 ) ( 13 ) ( 14 ) ( 15 ) where: Nped = predicted number of vehicle-pedestrian collisions per year ADTmaj = average daily traffic volume (veh/day) for the major road ADTmin = average daily traffic volume (veh/day) for the minor road ADTtot = ADTmaj + ADTmin ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ +⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++= PedVold ADT ADTlncADTlnbaexpN maj min totped ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ +⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+= PedVold ADT ADTlncADTlnbexpN maj min totped ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ +⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++= PedVollnd ADT ADTlncADTlnbaexpN maj min totped ( )PedVolln d ADTln c ADTln b a exp N minmajped +++= ( )PedVolln d ADTln c ADTln b exp N minmajped ++= ( )PedVol d ADTln c ADTln b a exp N minmajped +++= ( )PedVol d ADTln c ADTln b exp N minmajped ++= ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ +⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+= PedVollnd ADT ADTlncADTlnbexpN maj min totped

40 PedVol = sum of the daily pedestrian volumes crossing all intersection legs (pedestrians/day) a,b,c,d = regression coefficients Table 15 illustrates the results obtained when the eight candidate model functional forms were applied to the data for three- and four-leg signalized intersections in Toronto. The models in which major-road ADT, minor-road ADT, and pedestrian volume were considered separately, as in Equations (8) through (11), generally showed that for three-leg signalized intersections, major-road ADT has an inverse effect on vehicle-pedestrian collisions and minor-road ADT and pedestrian volume both have direct effects. For four-leg signalized intersections, minor-road ADT and pedestrian volume have direct effects, while major-road ADT in most cases had an inverse effect on vehicle-pedestrian collisions. The statistical significance of the coefficients for pedestrian volume and minor-road ADT were always high; the relationship of major-road ADT to vehicle-pedestrian collisions was statistically significant, but was generally less strong (i.e., had a lower significance level) than did pedestrian volume or minor-road ADT. It seems natural that both vehicle and pedestrian volumes are related to the frequency of vehicle-pedestrian collisions and that, of these variables, pedestrian volume should have the strongest relationship. The inverse relationship of major-road ADT to vehicle-pedestrian collisions was investigated further. It was found that, while major-road ADT had an inverse effect on vehicle- pedestrian collisions, the ratio of minor-road to major-road ADT had a direct effect. In other words, when the minor-road ADT is relatively small compared to the major-road ADT, there are relatively few pedestrian-related collisions. However, when the minor-road ADT is larger (e.g., approaching a magnitude to the major-road ADT), there are generally a substantial number of vehicle-pedestrian collisions. Thus, the functional forms shown in Equations (12) through (15), which incorporate the ratio of minor- to major-road ADT, tend to fit the data the best and exhibit direct relationships between all three independent variables and the frequency of vehicle- pedestrian collisions. Equation (14) provides the most satisfactory model from among the alternative functional forms considered based on the goodness of fit of the models and the consistency of the observed effects of the independent variables with the expected effects. Table 16 presents the modeling results for the functional form shown in Equation (14). The goodness-of-fit measure, RLR2, for these models is known as the likelihood ratio R2 value. This value represents the extent to which the model explains more of the variation in the dependent variable (i.e., vehicle-pedestrian collisions) than an intercept-only model. Thus, the meaning of RLR2 differs from the meaning of R2 for an ordinary least squares regression model which represents the proportion of the variation in the dependent variable which is explained by the model. Several additional geometric design and traffic control variables were considered for addition to the models shown in Table 16. These additional variables are: • maximum number of lanes crossed by a pedestrian on any intersection leg • number of intersection legs with refuge islands

41 • maximum number of traffic lanes crossed by a pedestrian in any crossing maneuver at the intersection (considering presence of refuge islands) • number of intersection legs with marked crosswalks • presence of a skewed intersection leg The only one of these independent variables that was statistically significant with an effect in the expected direction was the maximum number of lanes crossed by a pedestrian on any intersection leg (considering presence of refuge islands). The resulting model incorporating maximum number of lanes crossed has the following functional form: ( 16 ) where: nlanesx = maximum number of lanes crossed by a pedestrian in any crossing maneuver at the intersection (considering presence of refuge islands) Table 17 presents the results for models in the form shown in Equation (16). The model in this form is very appropriate for potential application in the HSM. The model for 4SG intersections had a better fit than the model for 3SG intersections. All of the coefficients for the 4SG model are statistically significant at the 90 percent confidence level. The goodness-of-fit measure, RLR2, has a value of 0.46, indicating that the model explains substantially more of the variance in vehicle-pedestrian collision frequency than an intercept-only model. The results for this model indicate that the frequency of vehicle-pedestrian collisions increases with increasing pedestrian volume and with increasing total traffic volume. Vehicle-pedestrian collision frequencies also increase with the ratio of minor- to major-road traffic volume. As noted earlier, the frequency of vehicle-pedestrian collisions is highest when the minor- and major-road traffic volumes are nearly equal and is lowest when the minor-road traffic volume is much less than the major-road traffic volume. The model for 4SG intersections also includes a statistically significant effect of the maximum number of traffic lanes that must be crossed by a pedestrian in any crossing maneuver at the intersection. This variable has been defined to include both through and turning lanes that must be crossed by a pedestrian and to consider the presence of refuge islands along the crossing path. If the crossing path is broken by an island that provides a suitable refuge for the pedestrian such that the crossing may be accomplished in two (or more) stages, then the number of lanes crossed in each stage is considered separately. The model for 3SG intersections also has coefficients that are statistically significant at the 90 percent confidence level and has a goodness-of-fit measure, RLR2 equal to 0.23. While the goodness of fit is not as strong as for the 4SG-intersection model, the goodness of fit is still substantially better than an intercept-only model. The primary drawback of the model for 3SG intersections is that the coefficient for the total traffic volume term, while statistically significant, has a negative value. It appears counterintuitive to indicate that vehicle-pedestrian collisions would decrease as vehicle volumes increase. ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++= lanesx maj min totped nePedVollndADT ADTlncADTlnbaexpN

42 TABLE 15. Models in Various Functional Forms for Vehicle-Pedestrian Collisions at Toronto Intersections. Regression coefficient (standard error) Functional form in Equation a b c d Over- dispersion parameter (k) R2LR THREE-LEG SIGNALIZED INTERSECTIONS (3SG)a (8) –5.94 (1.45) –0.06 (0.12) 0.20 (0.07) 0.5402 (0.0581) 0.50 0.25 (9) – – –0.51 (0.06) 0.10 (0.06) 0.4738 (0.0566) 0.57 0.21 (10) –2.11 (1.46) –0.12 (0.13) 0.20 (0.07) 0.0003 (0.0001) 0.70 0.13 (11) – – –0.29 (0.05) 0.16 (0.07) 0.0003 (0.0001) 0.71 0.13 (12) 0.58 (1.80) –0.16 (0.17) 0.28 (0.07) 0.0003 (0.0001) 0.66 0.15 (13) – – –0.11 (0.01) 0.28 (0.07) 0.0003 (0.0001) 0.66 0.15 (14) –3.84 (1.78) –0.04 (0.16) 0.25 (0.07) 0.5197 (0.0579) 0.48 0.26 (15) – – –0.38 (0.04) 0.28 (0.07) 0.4804 (0.0548) 0.49 0.25 FOUR-LEG SIGNALIZED INTERSECTIONS (4SG) b (8) –8.57 (0.57) 0.11 (0.06) 0.37 (0.03) 0.4795 (0.0230) 0.22 0.48 (9) – – –0.66 (0.03) 0.37 (0.03) 0.3868 (0.0237) 0.31 0.38 (10) –5.38 (0.62) –0.03 (0.06) 0.52 (0.03) 0.0001 (0.0000) 0.38 0.32 (11) – – –0.53 (0.03) 0.51 (0.03) 0.0001 (0.0000) 0.43 0.27 (12) –5.71 (0.65) 0.51 (0.06) 0.42 (0.03) 0.0001 (0.0000) 0.38 0.32 (13) – – –0.02 (0.01) 0.51 (0.03) 0.0001 (0.0000) 0.43 0.27 (14) –8.82 (0.60) 0.48 (0.05) 0.26 (0.03) 0.4768 (0.0230) 0.22 0.48 (15) – – –0.28 (0.02) 0.43 (0.03) 0.3937 (0.0238) 0.32 0.38 NOTE: Coefficients shown in italics are not statistically significant at the 90% confidence level. a Based on data for 366 intersections. b Based on data for 1,166 intersections.

43 TABLE 16. Models for Vehicle-Pedestrian Collisions at Toronto Intersections. Regression coefficient (standard error) Intersection type No. of sites Intercept (a) ADTtot (b) ADTmin/ADTmaj (c) PedVol (d) Over- dispersion parameter (k) RLR2 3SG 366 –3.84 (1.78) –0.04 (0.16)a 0.25 (0.07) 0.52 (0.06) 0.48 0.26 4SG 1,166 –8.82 (0.60) 0.48 (0.05) 0.26 (0.03) 0.48 (0.02) 0.22 0.48 NOTE: All models are in the form shown in Equation (14). a Coefficient is not statistically significant at the 90% confidence level.

44 TABLE 17. Models for Vehicle-Pedestrian Collisions at Toronto Intersections Including Term for Number of Lanes Crossed by Pedestrians. Regression coefficient (standard error) Intersection type No. of sites Intercept (a) ADTtot (b) ADTmin/ADTmaj (c) PedVol (d) nlanesx (e) Over- dispersion parameter (k) R2LR 3SG 366 –2.06 (1.82) –0.32 (0.18) 0.30 (0.07) 0.54 (0.06) 0.20 (0.06) 0.44 0.28 4SG 1,166 –8.10 (0.67) 0.38 (0.07) 0.27 (0.03) 0.48 (0.02) 0.05 (0.02) 0.21 0.49 NOTE: All models are in the form shown in Equation (16).

45 The Toronto model for 4SG intersections shown in Table 17 could potentially be used in the HSM. The models for 3SG intersections in Table 17 would require further investigation because of the negative coefficient for total traffic volume. The model forms discussed above were applied to predict vehicle-pedestrian collisions for each intersection as a whole. Consideration was given to predicting vehicle-pedestrian collisions for individual intersection legs using traffic volumes, pedestrian volumes, and other characteristics of those intersection legs, but preliminary investigation found that the vehicle- pedestrian collision data by leg were too sparse to provide useful models. MODELS FOR CHARLOTTE INTERSECTIONS Tables 18 through 20 present modeling results for Charlotte intersections that are analogous to the results for Toronto intersections shown in Tables 15 through 17, respectively. The models in Table 18 show predictive relationships for Charlotte intersections for the functional forms in Equations (8) through (15). As in Toronto, the models with the best fit appear to be those for the functional form shown in Equation (14). Table 19 shows the Charlotte models in this functional form. With the exception of the pedestrian volume coefficient for 4SG intersections, neither the 3SG- or 4SG-intersection models shown in Table 19 have coefficients that are statistically significant at the 90 percent confidence level. Similarly, the Charlotte models shown in Table 20 for the functional form in Equation (16) consist primarily of coefficients that are not statistically significant at the 90 percent confidence level. This result is not unexpected because both the pedestrian volumes and the vehicle-pedestrian collision frequencies are substantially lower for Charlotte than for Toronto. Also, given the smaller sample sizes for the Charlotte intersections, it is much more difficult to find statistically significant effects for vehicle and pedestrian volumes. COMBINED MODELS FOR TORONTO AND CHARLOTTE INTERSECTIONS The Toronto and Charlotte databases were further combined to obtain a more widely applicable pedestrian accident model at intersections (in other words, a model not specific to just the Toronto and Charlotte areas). A random city factor was added to the model to account for potential differences between the two cities. This random effect was found not to be significant and the random city effect was then removed from the model estimation. The final models selected for the two intersection types are presented in Table 21. The model for 4SG intersections developed with the combined Toronto and Charlotte data and presented in Table 21 appears appropriate for use in the HSM. All of the coefficients are statistically significant at the 90 percent confidence level and the goodness-of-fit measure, RLR2, equal to 0.52 is the highest of any of the models developed. Models for 3SG intersections developed with the combined Toronto and Charlotte data suffered from the same problem of a negative coefficient for total traffic volume as the model for 3SG intersections shown in Table 17. Further investigation found that the negative coefficient

46 may result from multi-colinearity or correlation between the total traffic volume term (ADTtot) and the maximum number of lanes crossed term (nlanesx). Two alternative approaches to resolving this issue were considered, resulting in the two alternative models shown for 3SG intersections in Table 21. The Alternative 1 model for 3SG intersections omits the total traffic volume term. All of the remaining coefficients for this model are statistically significant. The drawback to the Alternative 1 model is that a model lacking the total traffic volume term does not show any change in vehicle-pedestrian collisions as traffic volumes increase or decrease, as would be expected. A further investigation was performed to determine how large the coefficient of total traffic volume could be made while maintaining the statistical significance of the other model terms, and especially the term for maximum lanes crossed at the 90 percent confidence level. The largest such coefficient for the total traffic volume term was found to be 0.05. A model for 3SG intersections fitted to the combined Toronto and Charlotte data, but including this 0.05 coefficient value, is shown as Alternative 2 in Table 21. It can be seen that the Alternative 2 model has a different intercept, but virtually the same coefficient values for other variables, as the Alternative 1 model. All of the coefficients in the Alternative 2 model are statistically significant at the 90% confidence level and the goodness-of-fit measure, RLR2, equal to 0.27 indicates that the model explains substantially more of the variance in vehicle-pedestrian collision frequency than an intercept-only model. This Alternative 2 model appears to be the best choice for application to 3SG intersections in the HSM. BASE MODELS FOR SIGNALIZED INTERSECTIONS The base models for signalized intersections for use in the HSM are the model for 4SG intersections and the Alternative 2 model for 3SG intersections presented in Table 21, which use the functional form shown in Equation (16). Specifically, the recommended model for 3SG intersections is: ( 17 ) The recommended model for 4SG intersections is: ( 18 ) ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanesx maj min totped n09.0PedVolln41.0ADT ADTln24.0ADTln05.002.5expN ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanesx maj min totped n04.0PedVolln45.0ADT ADTln26.0ADTln40.095.7expN

47 TABLE 18. Models in Various Functional Forms for Vehicle-Pedestrian Collisions at Charlotte Intersections. Regression coefficient (standard error) Functional form in Equation a b c d Over- dispersion parameter (k) R2LR THREE-LEG SIGNALIZED INTERSECTIONS (3SG)a (8) –10.53 (6.51) 0.87 (0.64) –0.14 (0.25) 0.1053 (0.0951) 1.69 0.04 (9) – – –0.09 (0.22) –0.23 (0.25) 0.1046 (0.0962) 1.85 0.01 (10) –11.34 (6.38) 0.88 (0.62) –0.05 (0.24) 0.0064 (0.0035) 1.49 0.07 (11) – – –0.15 (0.21) –0.16 (0.24) 0.0060 (0.0037) 1.68 0.03 (12) –10.73 (6.77) 0.72 (0.65) –0.16 (0.24) 0.0064 (0.0036) 1.52 0.07 (13) – – –0.30 (0.04) –0.11 (0.24) 0.0060 (0.0037) 1.66 0.04 (14) –9.69 (6.91) 0.62 (0.67) –0.24 (0.25) 0.1045 (0.0952) 1.72 0.04 (15) – – –0.31 (0.04) –0.18 (0.24) 0.1066 (0.0960) 1.83 0.02 FOUR-LEG SIGNALIZED INTERSECTIONS (4SG) b (8) –5.16 (1.98) 0.04 (0.20) 0.15 (0.11) 0.3359 (0.0530) 0.96 0.16 (9) – – –0.41 (0.10) 0.09 (0.11) 0.3097 (0.0517) 1.06 0.14 (10) –4.73 (2.11) 0.09 (0.21) 0.19 (0.12) 0.0006 (0.0002) 1.36 0.05 (11) – – –0.33 (0.10) 0.13 (0.12) 0.0005 (0.0002) 1.43 0.03 (12) –4.84 (2.23) 0.27 (0.21) 0.14 (0.11) 0.0006 (0.0002) 1.36 0.05 (13) – – –0.19 (0.02) 0.18 (0.11) 0.0005 (0.0002) 1.43 0.04 (14) –5.16 (2.09) 0.18 (0.20) 0.11 (0.11) 0.3354 (0.0503) 0.96 0.16 (15) – – –0.30 (0.03) 0.17 (0.11) 0.3115 (0.0517) 1.05 0.14 NOTE: Coefficients shown in italics are not statistically significant at the 90% confidence level. a Based on data for 84 intersections. b Based on data for 267 intersections.

48 TABLE 19. Models for Vehicle-Pedestrian Collisions at Charlotte Intersections. Regression coefficient (standard error) Intersection type No. of sites Intercept (a) ADTtot (b) ADTmin/ADTmaj (c) Ped Vol (d) Over- dispersion parameter (k) R2LR 3SG 84 –9.69 (6.91)a 0.62 (0.67)a –0.24 (0.25)a 0.10 (0.10)a 1.72 0.04 4SG 267 –5.16 (2.09) 0.18 (0.20)a 0.11 (0.11)a 0.34 (0.05) 0.96 0.16 NOTE: All models are in the form shown in Equation (14). a Coefficient is not statistically significant at the 90% confidence level.

49 TABLE 20. Models for Vehicle-Pedestrian Collisions at Charlotte Intersections Including Term for Number of Lanes Crossed by Pedestrians. Regression coefficient (standard error) Intersection type No. of sites Intercept (a) ADTtot (b) ADTmin/ADTmaj (c) PedVol (d) nlanesx (e) Over- dispersion parameter (k) R2LR 3SG 84 –10.58 (6.98)a 0.78 (0.70)a –0.20 (0.25)a 0.11 (0.10)a –0.18 (0.27)a 1.66 0.04 4SG 267 –5.43 (2.10) 0.26 (0.21)a 0.14 (0.11)a 0.33 (0.05) –0.11 (0.11)a 0.95 0.16 NOTE: All models are in the form shown in Equation (16). a Coefficient is not statistically significant at the 90% confidence level.

50 TABLE 21. Models for Vehicle-Pedestrian Collisions From Combined Data for Toronto and Charlotte Intersections. Regression coefficient (standard error) Intersection type No. of sites Intercept (a) ADTtot (b) ADTmin/ADTmaj (c) Ped Vol (d) nlanesx (e) Over- dispersion parameter (k) R2LR 3SG (Alt 1) 450 –4.04 (0.36) – 0.25 (0.06) 0.41 (0.04) 0.10 (0.05) 0.52 0.28 3SG (Alt 2) 450 –5.02 (0.36) 0.05 0.24 (0.06) 0.41 (0.04) 0.09 (0.05) 0.52 0.27 4SG 1,433 –7.95 (0.61) 0.40 (0.06) 0.26 (0.03) 0.45 (0.02) 0.04 (0.02) 0.24 0.52 NOTE: All models are in the form shown in Equation (16).

51 EFFECTS OF LAND USE AND DEMOGRAPHIC VARIABLES FOR SIGNALIZED INTERSECTIONS Basic Modeling With Data for Charlotte Intersections Data were available in Charlotte, but not in Toronto, for a range of land use and demographic variables including: • presence of bus stops within 300 m (1,000 ft) of the intersection • presence of schools (either public or private) with 300 m (1,000 ft) of the intersection • presence of parks within 300 m (1,000 ft) of the intersection • number of alcohol sales establishments within 300 m (1,000 ft) of the intersection • average per capita income of all census block groups within 300 m (1,000 ft) of the intersection • number of square feet of buildings on commercial land parcels partially or entirely within 0.8 km (0.5 mi) of the intersection • number of commercial structures on commercial land parcels within 0.8 km (0.5 mi) of the intersection • number of commercial land parcels within 300 m (1,000 ft) of the intersection A preliminary investigation of these data was conducted with the Charlotte data for 3SG and 4SG intersections. Of the land use and demographic variables considered, the ones that were found to have a statistically significant relationship to vehicle-pedestrian collisions are: • presence of bus stops within 300 m (1,000 ft) of the intersection (for 4SG intersections only) • presence of schools (either public or private) within 300 m (1,000 ft) of the intersection (at 80 percent confidence level for 4SG intersections only) • number of alcohol sales establishments within 300 m (1,000 ft) of the intersection (for 4SG intersections only) • average per capita income of all census block groups within 300 m (1,000 ft) of the intersection (higher income levels are associated with fewer crashes) (for both 3SG and 4SG intersections) • number of commercial structures on commercial land parcels within 0.8 km (0.5 mi) of the intersection (for 4SG intersections only) To further explore the effects of these land use and demographic variables on pedestrian safety, the model for 4SG intersections presented in Table 21 was expanded to include the variables listed above one at a time. The coefficients in the combined base model were fixed and the coefficients of each of the additional land use and demographic variables was estimated. This analysis was limited to 4SG intersections because the preliminary analysis results found few statistically significant effects for land use and demographic variables at 3SG intersections,

52 probably due to limited sample sizes and low accident counts. The results of the analysis for 4SG intersections in Charlotte are presented in Table 22. Accident modification factors (AMFs) were developed based on the results shown in Table 22 for number of bus stops, presence of schools, number of alcohol sales establishments, and neighborhood income level. No AMF was developed for presence of parks within 300 m (1,000 ft) of the intersection because the effect found was in a counterintuitive direction with fewer vehicle-pedestrian collisions at intersections near parks. No AMF was developed for commercial structures because the wide radius considered around the intersection, 0.8 km (0.5 mi), would make the AMF impractical to apply. The effect of alcohol sales establishments was determined in categories of zero, one to eight, and nine or more establishments within 300 m (1,000 ft) of an intersection. Table 22 indicates that the effect of this variable for one to eight establishments was not statistically significant, while the effect for nine or more establishments was statistically significant at the 80% confidence level. An AMF is provided for this effect because, overall, the alcohol sales establishment effect is statistically significant at the 84% confidence level. An AMF based on a continuous linear relationship between vehicle-pedestrian collisions and the number of alcohol sales establishments was considered, but was not used because this effect was not statistically significant as a continuous function. Accident Modification Factors The results shown in Table 22 have been expressed as accident modification factors (AMFs) for use in the HSM safety prediction methodology. Four AMFs are presented below; three of these AMFs are recommended for use in the HSM methodology. Number of Bus Stops Near an Intersection An AMF for bus stops, based on the regression coefficients in Table 22, can be presented as follows: Number of bus stops within 300 m (1,000 ft) of the intersection AMF 0 1.00 1 or 2 2.78 3 or more 4.15 To use this AMF, the base models shown in Equations (17) and (18) must be multiplied by 0.289. This multiplier translates the base model so that it corresponds to the base condition without bus stops. While no explicit effect of bus stops on pedestrian safety has been reported previously, Burner and Clifton (34) reported that pedestrian crash risk increases with transit accessibility and Hess (41) and Vernez-Mouden (42) reported that pedestrian crash risk increases with the number of transit uses within an area.

53 TABLE 22. Effects of Land Use and Demographic Variables for Charlotte Intersections Added to the 4SG Model Shown in Table 21. Land use or demographic variable Level Regression coefficient (standard error) Chi Sq Pr > Chi Sq Significant at 90% level? Number of bus stops 0 – – – – – 1-2 1.0222 (0.57) 3.27 0.0707 Yes 3 or more 1.4242 (0.50) 8.20 0.0042 Yes Presence of schools – 0.2963 (0.23) 1.64 0.1998 Noa Presence of parks – –0.3324 (0.24) 1.78 0.1822 Noa Number of alcohol sales establishments 0 – – – – – 1-8 0.1151 (0.23) 0.26 0.6122 No 9 or more 0.4413 (0.31) 1.97 0.1601 Noa Neighborhood average per capita income – –0.0301 (0.008) 15.25 0.0001 Yes Number of commercial structures – 0.0280 (0.009) 10.38 0.0013 Yes a Statistically significant at 80% level.

54 Schools Near an Intersection An AMF for intersections near schools, based on the regression coefficients in Table 22, can be presented as follows: Presence of school within 300 m (1,000 ft) of the intersection AMF No school present 1.00 School present 1.35 To use this AMF, the base models shown in Equations (17) and (18) should be multiplied by 1.005. This multiplier translates the base model so that it corresponds to the base condition with no nearby school. Alcohol Sales Establishments Near an Intersection An AMF for intersections near alcohol sales establishments based on the regression coefficients in Table 22 can be presented as follows: Number of alcohol sales establishments within 300 m (1,000 ft) of the intersection AMF 0 1.00 1-8 1.12 9 or more 1.56 To use this AMF, the base models shown in Equations (17) and (18) should be multiplied by 0.931. This multiplier translates the base model so that it corresponds to the base condition with no nearby alcohol sales establishments. This AMF confirms a relationship observed by LaScala (36, 38) (see Table 9). Neighborhood Income Level An AMF for intersections based on the per capita income for all census block groups within 300 m (1,000 ft) of the intersection was considered for inclusion in the HSM methodology. This AMF would have taken the following form based on Table 22: AMFinc = exp (-0.000030 (pci-25000)) ( 19 ) where: AMFinc = accident modification factor for pedestrian safety at intersections based on per capita income for the neighborhood pci = average per capita income for all census block groups within 300 m (1,000 ft) of the intersection

55 In applying this AMF, pci should be limited to the range from $9,000 to $85,000, which is the range of average per capita income in the data used to develop this relationship. This will result in a maximum range of AMFs from 0.17 to 1.62. The direction of the effect for this AMF confirms a relationship observed by Burnier and Clifton (34) (see Table 9). However, the magnitude of the effect is larger than would be expected if this truly represented an effect of pedestrian behavior alone. It is likely that this effect reflects, in part, an influence of neighborhood income level on pedestrian volume. Therefore, a decision was made not to include the neighborhood income level AMF in the HSM methodology. Other AMFs Consideration was given to adapting some of the findings reported in the literature (see Chapter 2 of this report) for use as AMFs. However, no satisfactory AMFs were found. In summary, while the direction of the effect of many factors on pedestrian safety is known from the literature, their effects have not been sufficiently quantified for incorporation in a predictive methodology. Adjustment of Base Model The base model adjustments shown above for each AMF should be combined as follows: (0.289) (1.005) (0.931) = 0.270 Combining the base model adjustments in this way involves the assumption that the effects of the AMFs are independent. This assumption has been made for all AMFs used in the HSM. FINAL BASE MODELS ADJUSTED FOR AMFS With the adjustments for the AMFs presented above, the base model for 3SG intersections should be modified as follows: ( 20 ) The base model for 4SG intersections should be similarly modified as: ( 21 ) These base models can be simplified by moving the 0.270 adjustment inside the exponential function and combining it with the intercept term. In this final form, the base model for 3SG intersections is: ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanes maj min totped n09.0PedVolln41.0ADT ADTln24.0ADTln05.002.5exp270.0N ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanes maj min totped n04.0PedVolln45.0ADT ADTln26.0ADTln40.095.7exp270.0N

56 ( 22 ) Similarly, the base model for 4SG intersections in final form is: ( 23 ) These base models apply to signalized intersections with the following base conditions: • no bus stops within 300 m (1,000 ft) of the intersection • no schools within 300 m (1,000 ft) of the intersection • no alcohol sales establishments within 300 m (1,000 ft) of the intersection • average per capita income of $25,000 for the surrounding neighborhood Figure 1 illustrates the sensitivity of vehicle-pedestrian collision frequency to each parameter in the model for 3SG intersections shown in Equation (22). The vertical axis in each sensitivity plot is the expected annual vehicle-pedestrian collision frequency, Nped (collisions/intersection/year). The first plot in the figure shows the sensitivity of collision frequency to pedestrian crossing volume, PedVol (pedestrians/day), for specific values of the maximum number of lanes crossed at an intersection. The middle row of plots show the sensitivity of vehicle-pedestrian collision frequency to traffic volume ratio, ADTmin/ADTmaj for two representative values of PedVol, a low activity level (20 pedestrians/day) and a medium-high activity level (750 pedestrians/day). The bottom row of plots shows that for the same two values of PedVol, there is very little sensitivity of vehicle-pedestrian collision frequency to total traffic volume, ADTtot. This low sensitivity results from the small coefficient value (0.05) for the ADTtot term. Figure 2 illustrates a sensitivity analysis analogues to Figure 1 for the model for 4SG intersections shown in Equation (23). The sensitivity plots were prepared for representative values for PedVol for 4SG intersections, including a low activity level (50 pedestrians/day) and a medium-high activity level (1,500 pedestrians/day). These pedestrian activity levels for 4SG intersections are higher than those observed for 3SG intersections. The coefficient of the ADTtot term (0.40) in the base model for 4SG intersections is substantially higher than the coefficient for 3SG intersections, as illustrated by the greater sensitivity shown in the plots in the bottom row of Figure 2. MODELS FOR ROADWAY SEGMENTS The use of the Minnesota roadway segment database to develop a replacement for pedestrian safety adjustment factor [see Equation (6) and Table 8] used in the current draft of HSM Chapter 12 was explored. This was recognized as a substantial challenge because of the lack of pedestrian volume data. Further analyses confirmed that divided roadways have lower vehicle-pedestrian collision frequencies than undivided roadways, presumably because of the presence of a median that can serve as a refuge for pedestrians crossing the arterial. However, as expected, given the lack of pedestrian volume data, no alternative methodology could be developed. ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanesx maj min totped n09.0PedVolln41.0ADT ADTln24.0ADTln05.060.6expN ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ ++⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛++−= lanesx maj min totped n04.0PedVolln45.0ADT ADTln26.0ADTln40.053.9expN

57 Figure 1. Sensitivity analysis of pedestrian safety base models for 3SG intersections.

58 Figure 2. Sensitivity analysis of pedestrian safety base models for 4SG intersections.

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TRB's National Cooperative Highway Research Program (NCHRP) Web-Only Document 129, Phase 3: Pedestrian Safety Prediction Methodology explores development of improved pedestrian safety prediction models for use in the Highway Safety Manual.

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