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Pedestrian and Bicycle Safety Performance Functions (2023)

Chapter: Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data

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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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Suggested Citation:"Section 5 - Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data." National Academies of Sciences, Engineering, and Medicine. 2023. Pedestrian and Bicycle Safety Performance Functions. Washington, DC: The National Academies Press. doi: 10.17226/27294.
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276 This section of the report documents models developed to estimate the potential of a pedes- trian or bicycle crash occurring in the absence of having pedestrian or bicycle exposure data. Many agencies do not collect pedestrian or bicycle exposure data, so such models may be of particular interest to those agencies. Models were developed to estimate the potential of a pedes- trian or bicycle crash occurring on various roadway segment and intersection types when the associated pedestrian or bicycle exposure data are not available. The results of this analysis could be considered for potential use in the forthcoming new chapters on pedestrians and bicyclists and systemic safety management planned for HSM2. The remainder of this section describes the data used for model development, the model devel- opment process, and final models used to estimate the potential of a pedestrian or bicycle crash occurring in the absence of having pedestrian or bicycle exposure data. 5.1 Data and Data Preparation Models to estimate the potential of a pedestrian or bicycle crash occurring, without directly incorporating pedestrian or bicycle exposure data into the models, were developed for rural road- way segments, urban and suburban roadway segments, and urban and suburban intersections. Models were not developed for rural intersections, as the pedestrian and bicycle crash data were too limited to develop meaningful models. 5.1.1 Data Used for Rural Roadway Segments The data used for the models of rural roadway segments were collected from Ohio using Safety Analyst and the available census information. The models aimed at determining the probability that a crash occurred involving a pedestrian or a bicyclist on any given rural two-lane, two- way road; rural multilane undivided highway; and rural multilane divided highway. Freeways (i.e., highways with full access control) were not considered in the analysis. A summary of the independent variables available for each rural roadway segment considered in the models is described in Table 180. As appropriate, the average width of the inside and outside shoulders was used for model- ing. In the modeling process, only a subset of these variables was significant in predicting the crashes involving a pedestrian or bicyclist. Summary statistics of the significant predictor vari- ables included in the models to estimate the potential of a pedestrian or bicycle crash occurring on rural roads are shown in Table 181. S E C T I O N 5 Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data

Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data 277   Variable Description Data Source: Safety Analyst Road type Type of segment Lane width Average width of through lanes Median type Indication of type and characterization of the area separating opposing traffic lanes [0: undivided; 1: rigid-barrier system (divided); 3: flexible barrier system (divided); 4: raised median with curb (divided); 5: depressed median (divided); 9: other divided] Median width Average width of the portion of a divided highway separating the opposing traffic lanes Outside shoulder width Average width of the outside shoulder Inside shoulder width Average width of the inside shoulder Posted speed Posted speed limit AADT Annual daily traffic (determined as the average number of vehicles passing a segment from both directions of the mainline route) averaged over observations between 2008 and 2017 Percent heavy vehicles Percentage of heavy vehicles (determined as the count of commercial vehicles divided by the count of all vehicles) averaged over observations between 2008 and 2017 Total years The total years of data that were averaged to obtain the avgAADT and avgPercentHeavyVehicles variables Ped crash Presence of a pedestrian crash between 2008–2017 (indicator variable) Bike crash Presence of a bike crash between 2008–2017 (indicator variable) Data Source: Census popTotal Total population of people residing in the census tract of the segment ageMedian Median age of people residing in the census tract of the segment ageMedianMale Median age of males residing in the census tract of the segment ageMedianFemale Median age of females residing in the census tract of the segment houseSize Total number of residential houses in the census tract of the segment Table 180. Description of independent variables considered in the models to estimate the potential of a pedestrian or bicycle crash occurring on rural roads. Continuous Variable Mean Std. Dev. Min. Max. Average AADT (veh/day) 3,590.300 3,226.100 69.80 40,708.50 Population (people) 118.900 160.900 0.00 4,321.00 Segment length (mi) 0.821 1.141 0.01 11.44 Lane width (ft) 11.600 2.700 4.50 35.00 Average shoulder width (ft) 3.500 2.700 0.00 19.50 Categorical Variable Category Percent Road type Rural two-lane highway segment 92.40 Rural multilane undivided highway segments 3.10 Rural multilane divided highway segments 4.60 Table 181. Summary statistics for variables included in the models to estimate the potential of a pedestrian or bicycle crash occurring on rural roads.

278 Pedestrian and Bicycle Safety Performance Functions 5.1.2 Data Used for Urban and Suburban Roadway Segments The data used to develop models of urban and suburban roadway segments were obtained from the dataset used to develop pedestrian and bicycle SPFs, incorporating pedestrian and bicy- clist exposure data into the models but excluding pedestrian and bicyclist exposure for purposes of this effort. Details on this dataset are provided in Section 3. 5.1.3 Data Used for Urban and Suburban Intersections The data used to develop models of urban and suburban intersections were obtained from the dataset used to develop pedestrian and bicycle SPFs, incorporating pedestrian and bicyclist exposure data into the models but excluding pedestrian and bicyclist exposure for purposes of this effort. Details on this dataset are provided in Section 3. 5.2 Model Development In the absence of having pedestrian or bicycle exposure data, binary logistic regression was used to develop models to estimate the potential of a pedestrian or bicycle crash occurring. In other words, no direct estimate of pedestrian and bicycle volume along the roadway or at an intersection (e.g., AADP, AADB, peak-hour pedestrian volume, peak-hour bicycle volume, or 2-hr count) was included in the model. However, other indirect measures of pedestrian and bicycle exposure (such as population) were included in model development. The model is applied when the dependent variable takes a binary form—for example, success or failure. In the models devel- oped here, “success” was considered as a pedestrian or bicycle crash occurring during a particular observational unit (i.e., segment) during some predefined time period. The binary logistic regression model takes the following form: + y 1 Pr i U U i i = e e ` j (5-1) where Pr (yi) is the probability of observation i being a success. The term Ui is a utility function that is related to the independent (explanatory) variables in the following linear form: xb= + jUi ijj0 b/ (5-2) where βj are coefficients to be estimated and xij are observed explanatory variables associated with observation i. The coefficient estimates reveal the effects of independent variables on the dependent outcome. The change in the likelihood of a successful outcome due to a change in the independent variable is provided by the odds ratio of that parameter. For indicator variables or variables entered into the model in a continuous form with no transformation, the odds ratio associated with changing the indicator variable from “not selected” to “selected” or a one-unit change in the continuous variable is: jOdds Ratio e= b (5-3) For continuous variables entered into the model in a log form, the odds ratio associated with k-times change in that variable is: jOdds Ratio k= b (5-4) For example, a doubling of that variable (e.g., 2 times changes) would be associated with a change in the odds ratio of 2βj.

Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data 279   Odds ratios greater than 1 suggest an increased likelihood of a successful outcome (in this case, higher likelihood of a pedestrian or bicycle crash occurring on a segment), while odds ratios less than 1 suggest a decreased likelihood (reduced likelihood of a pedestrian or bicycle crash occurring). Thus, positive model coefficients are associated with an increased likelihood of pedestrian or bicycle crash occurrence, while negative model coefficient estimates are associated with a decreased likelihood of a pedestrian or bicycle crash occurrence. A forward-selection process was used to estimate the model parameters. In this method, each potential independent variable was tested to examine its impact on the dependent variable and the most impactful variable selected. Nonlinear transformations were considered for the con- tinuous independent variables when such transformation improved the overall model fit and to identify the best functional form for each of the potential independent variables. Then, all other variables were sequentially added to determine the best pair. This process was repeated until the addition of no other variables significantly improved the overall model fit. Categorical variables were combined as necessary so that a sufficient number of observations were included within each group in the models. 5.3 Analysis Results This section presents the final models to estimate the potential of a pedestrian or bicycle crash occurring in the absence of having pedestrian or bicycle exposure data. 5.3.1 Rural Roadway Segments The dependent variable for the rural roadway segments was the occurrence of a pedestrian (or bicycle) crash within a 10-year period from 2008 to 2017 on a given roadway segment. Table 182 provides the results of models to estimate the potential of a pedestrian or bicycle crash occurring on all rural roadway segments combined. In the model, indicator variables were used to denote if the segment was a rural multilane undivided roadway segment or rural multilane divided road- way segment, compared to a baseline condition of the segment being a rural two-lane roadway segment. As shown, the indicator variables are either statistically insignificant at the 95% confi- dence level or nearly so. The number of multilane roadway segments (either divided or undivided) Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total traffic volume (veh/obs period) Log 0.8207 < 0.001 0.4884 < 0.001 Population (people) Log (X+1) 0.2458 < 0.001 0.2192 0.002 Segment length (mi) Log 0.8477 < 0.001 0.6692 < 0.001 Lane width greater than 11 ft Indicator −0.2479 0.0460 — — Lane width greater than or equal to 12 ft Indicator — — −0.2597 0.115 Average shoulder width greater than 3 ft Indicator −0.1720 0.11.08 — — Average shoulder width greater than 1 ft Indicator — — -0.1740 0.347 Undivided rural multilane segment Indicator 0.3590 0.2675 0.8678 0.015 Divided rural multilane segment Indicator −0.3449 0.1893 −0.7273 0.109 Constant — −12.0601 < 0.0010 −9.3037 < 0.001 AIC 3152.4 2062.9 NOTE: The observation (obs) period differed for each segment in the database (e.g., 2–9 years). The time period and traffic volume were combined to account for the “total traffic volume” during the time period of interest (e.g., veh/day x 365 x no. of years = veh/obs period). AIC = Akaike’s Information Criterion; — = Not applicable. Table 182. Models to estimate the potential of a pedestrian or bicycle crash occurring on rural roads.

280 Pedestrian and Bicycle Safety Performance Functions was also very small compared to the two-lane rural roadway segments. For these reasons, a sepa- rate model was estimated using only data on rural two-lane roads. The model for rural two-lane roadway segments is provided in Table 183. The models presented in Table 182 and Table 183 are consistent, perhaps due to the low number of multilane roadway segment observations and statistically insignificant (or nearly so) indica- tors for multilane roadway segments. The potential of either a pedestrian crash occurring or a bicycle crash occurring increases with vehicular traffic volume, population within the census tract, and segment length. The potential of a pedestrian (or bicycle) crash occurring is lower on roadway segments with lanes greater than 11 ft (or greater than or equal to 12 ft for bicycle crashes). The potential of a pedestrian (or bicycle) crash occurring is lower on roadway segments with shoulders greater than 3 ft (or greater than 1 ft for bicycle crashes). These findings are all generally consistent with engineering expectations. Note that the segment length is included in the form of the natural logarithm to account for the different impacts a unit increase in segment length could have since the values can range from small (0.01 mi) to relatively large (11.44 mi). Furthermore, population is included in the model in the form of the natural logarithm of one plus the total population in the associated census tract. The natural log transform was used since it greatly improved the overall fit of the model to the observed data. However, the one plus component was required as numerous observations had a population value of zero and thus the natural logarithm could not be computed. Odds ratios provide an indication of the change in the potential of a pedestrian (or bicycle) crash occurring as a function of the independent variables included in the model. Table 184 pro- vides the odds ratios for the rural two-lane road model associated with a change in the indicator variable or a doubling of each of the continuous variables included in the model in log form. For example, roadway segments with lanes greater than 11 ft are 0.792 times as likely to have a pedes- trian crash compared to roadway segments with lanes less than or equal to 11 ft wide. Roadway segments with lanes greater than or equal to 12 ft are 0.773 times as likely to have a bicycle crash compared to roadway segments with lanes less than 12 ft wide. Other indicator variables can be interpreted similarly. A pedestrian or bicycle crash is 1.753 or 1.390 times as likely, respectively, as the average AADT is doubled for that segment. Notice that a doubling of segment length is only associated with a 1.772 and 1.568 times increase in the potential for pedestrian and bicycle crashes, respectively. This likely indicates that segment length in the database captures unobserved effects, perhaps related to intersection or driveway locations. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total traffic volume (veh/obs period) Log 0.8100 < 0.001 0.4752 < 0.001 Population (people) Log (X+1) 0.2622 < 0.001 0.2209 0.004 Segment length (mi) Log 0.8257 < 0.001 0.6488 < 0.001 Lane width greater than 11 ft Indicator −0.2335 0.065 — — Lane width greater than or equal to 12 ft Indicator — — −0.2578 0.128 Average shoulder width greater than 3 ft Indicator −0.1524 0.177 — — Average shoulder width greater than 1 ft Indicator — — −0.1431 0.458 Constant — −12.0493 < 0.001 −9.2107 < 0.001 AIC 2902.7 1920.1 NOTE: The observation (obs) period differed for each segment in the database (e.g., 2–9 years). The time period and traffic volume were combined to account for the “total traffic volume” during the time period of interest (e.g., veh/day x 365 x no. of years = veh/obs period). AIC = Akaike’s Information Criterion; — = Not applicable. Table 183. Models to estimate the potential of a pedestrian or bicycle crash occurring on rural two-lane roads.

Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data 281   5.3.2 Urban and Suburban Roadway Segments The dependent variable for the urban roadway segments was the occurrence of a pedestrian (or bicycle) crash over the observed analysis period. Like the models presented in Section 3, the analysis of urban and suburban roadway segments focused on two-lane roads, four-lane undivided and divided roads, and one-way roads. In many cases, the analysis period differed for each unique roadway segment. To account for this, the observation period was incorporated into the exposure measurement as the product of the AADT volume and the number of years in the observation period. Table 185 provides the results of the models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban two-lane undivided roads. The models presented in Table 185 suggest that the potential of either a pedestrian crash or a bicycle crash occurring increases with vehicular traffic volume, population in adjacent census tract, segment length, number of intersections, and school density (for bicycle crashes). Both pedestrian and bicycle crash potential decrease with outside shoulder width. These findings are all consistent with engineering expectations. Table 186 provides the associated odds ratios that provide the magnitudes of the change in crash potential associated with either increasing the continuous variables by one unit or doubling the continuous variables included in the model in log form. Variables Pedestrian Model Bicycle Model Indicator Variables Lane width greater than 11 ft 0.792 — Lane width greater than or equal to 12 ft — 0.773 Average shoulder width greater than 3 ft 0.859 — Average shoulder width greater than 1 ft — 0.867 Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 1.753 1.390 Population (people) + 1 1.200 1.165 Segment length (mi) 1.772 1.568 NOTE: — = Not applicable. Table 184. Odds ratios associated with the model to estimate the potential of a pedestrian or bicycle crash occurring on rural two-lane roads. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total traffic volume (veh/obs period) Log 0.3539 0.050 0.8252 < 0.001 Population (people) Log (X+1) 0.3572 0.021 0.2067 0.190 Segment length (mi) Log 0.6968 < 0.001 0.6872 < 0.001 Number of intersections None 0.2698 < 0.001 0.0733 0.298 Outside shoulder width (ft) None −0.2102 0.313 −0.2610 0.230 School density None — — 0.0150 < 0.001 Constant −5.9705 0.070 −10.2394 < 0.001 AIC 646.63 579.37 NOTE: The observation (obs) period differed for each segment in the database (e.g., 2–9 years). The time period and traffic volume were combined to account for the “total traffic volume” during the time period of interest (e.g., veh/day x 365 x no. of years = veh/obs period). AIC = Akaike’s Information Criterion; — = Not applicable. Table 185. Models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban two-lane undivided roads.

282 Pedestrian and Bicycle Safety Performance Functions Table 187 provides the results of the models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban four-lane undivided and divided roads. The models suggest that pedestrian and bicycle crash potential increases with total traffic volume, segment length, and the number of intersections along the segment. Pedestrian crash potential is lower on divided roadways compared to undivided roadways and decreases with the outside shoulder width but increases with the population in the adjacent census tract. Bicycle crash potential decreases as roadway width increases, as expected. Table 188 provides odds ratios associated with these explanatory variables. Table 189 provides the results of the models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban one-way roads. The models suggest that pedestrian crash potential increases with total traffic volume, segment length, the number of intersections along the segment, and total roadway width. Bicycle crash potential increases with total traffic volume, segment length, on higher speed limit roads (30 mph and above, compared to lower than 30 mph) and with school density. Odds ratios associated with these explanatory variables are provided in Table 190. 5.3.3 Urban and Suburban Intersections The dependent variable for the urban and suburban intersection models was the occurrence of a pedestrian (or bicycle) crash over the observed analysis period at a given intersection location. Variables Pedestrian Model Bicycle Model Continuous Variables (effects of one-unit increase) Number of intersections 1.310 1.076 Outside shoulder width (ft) 0.810 0.770 School density — 1.015 Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 1.278 1.772 Population (people) + 1 1.281 1.154 Segment length (mi) 1.621 1.610 Table 186. Odds ratios associated with the model to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban two-lane undivided roads. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total traffic volume (veh/obs period) Log 0.7623 0.006 0.7366 0.006 Population (people) Log (X+1) 0.3926 0.056 — — Segment length (mi) Log 0.4101 0.233 0.4071 0.154 Divided roadway Indicator −1.2613 0.004 — — Number of intersections None 0.1895 0.031 0.1233 0.191 Outside shoulder width (ft) None −0.4026 0.301 — — Total roadway width (ft) None — — −0.0231 0.097 Constant −10.7810 0.003 −7.2943 0.030 AIC 249.39 268.8 NOTE: The observation (obs) period differed for each segment in the database (e.g., 2–9 years). The time period and traffic volume were combined to account for the “total traffic volume” during the time period of interest (e.g., veh/day x 365 x no. of years = veh/obs period). AIC = Akaike’s Information Criterion; — = Not applicable. Table 187. Models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban four-lane undivided and divided roads.

Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data 283   Variables Pedestrian Model Bicycle Model Continuous Variables (effects of one-unit increase) Number of driveways along segment 1.028 — Total roadway width (ft) 1.051 — Speed limit greater than or equal to 30 mph — 4.193 School density — 1.004 Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 1.556 1.317 Segment length (mi) 2.692 1.697 Table 190. Odds ratios associated with models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban one-way roads. Variables Pedestrian Model Bicycle Model Indicator Variables Divided roadway 0.283 — Continuous Variables (effects of one-unit increase) Number of intersections 1.209 1.131 Outside shoulder width (ft) 0.669 — Total roadway width (ft) — 0.977 Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 1.696 1.666 Population (people) + 1 1.313 — Segment length (mi) 1.329 1.326 Table 188. Odds ratios associated with models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban four-lane undivided and divided roads. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total traffic volume (veh/obs period) Log 0.6379 0.023 0.3976 0.150 Segment length (mi) Log 1.4285 0.002 0.7632 0.096 Number of driveways along segment None 0.0280 0.435 — — Total roadway width (ft) None 0.0501 < 0.001 — — Speed limit greater than or equal to 30 mph None — — 1.4334 0.005 School density None — — 0.0043 0.327 Constant −7.7617 0.009 −5.5954 0.064 AIC 209.19 219.12 NOTE: The observation (obs) period differed for each segment in the database (e.g., 2–9 years). The time period and traffic volume were combined to account for the “total traffic volume” during the time period of interest (e.g., veh/day x 365 x no. of years = veh/obs period). AIC = Akaike’s Information Criterion; — = Not applicable. Table 189. Models to estimate the potential of a pedestrian or bicycle crash occurring on urban and suburban one-way roads.

284 Pedestrian and Bicycle Safety Performance Functions Similar to the modeling approach for intersections presented in Section 3, datasets were com- bined for the analysis of three-leg stop control intersections with two-way/two-way operations; four-leg stop control intersections with two-way/two-way operations; and three-leg signal con- trol intersections with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations combined. However, only models for three-leg signal control intersections with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations are provided as no meaningful models were developed for three- and four-leg stop control intersections. Models were also developed and are presented below for four-leg signal control intersections with two-way/two-way operations. In many cases, the analysis period differed for each unique intersection. To account for this, the observation period was incorporated into the exposure measurement as the product of the AADT volume entering the intersection (i.e., sum of AADT on major approach and AADT on minor approach) and the number of years in the observation period. Table 191 provides the results of the models to estimate the potential of a pedestrian or bicycle crash occurring at three- leg signal control intersections with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations. The models presented in Table 191 suggest that the potential of either a pedestrian crash or a bicycle crash occurring increases with vehicular traffic volume and population in adjacent census tract. For pedestrian crashes, the crash potential is higher for four-leg intersections than for three- leg intersections, but this was not observed at a statistical level for bicycle crashes. These findings are all consistent with engineering expectations. Table 192 shows the associated odds ratios that provide the magnitudes of the change in crash potential associated with doubling the continuous variables included in the model in log form. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total entering AADT (vehicles entering intersection during observation period) Log 1.2680 0.009 0.7842 0.1180 Population (people) Log (X+1) 0.9997 0.028 1.1114 0.0120 Indicator for four-leg intersection Indicator 0.6781 0.272 — — Indicator for roadway segment within Pennsylvania Indicator 1.0918 0.072 −0.1888 0.7118 Constant −31.4434 0.002 −24.2984 0.0210 AIC 134.59 130.68 NOTE: AIC = Akaike’s Information Criterion; — = Not applicable. Table 191. Models to estimate the potential of a pedestrian or bicycle crash occurring at three-leg signal control intersections with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations. Pedestrian Model Bicycle Model Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 2.408 1.722 Population (people) + 1 2.000 2.161 Table 192. Odds ratios associated with models to estimate the potential of a pedestrian or bicycle crash occurring at three-leg signal control intersection with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations.

Development of Pedestrian and Bicycle Models in the Absence of Pedestrian and Bicyclist Exposure Data 285   Table 193 provides the results of models to estimate the potential of a pedestrian or bicycle crash occurring at four-leg signal control intersections with two-way/two-way operations. The models suggest that pedestrian and bicycle crash potential increases with vehicular traffic volume and population in adjacent census tract. Table 194 provides odds ratios associated with these explanatory variables. 5.4 Summary Several models were developed to estimate the potential of a pedestrian or bicycle crash occur- ring on roadway segments and at intersections, without directly incorporating pedestrian or bicycle exposure data such as AADP, AADB, peak-hour pedestrian volume, peak-hour bicycle volume, 2-hr count, etc. into the models. However, other indirect measures of pedestrian and bicycle exposure (population, for example) were included in model development. Models were developed for rural roadway segments, urban and suburban roadway segments, and urban and suburban intersections. Data from Ohio are used to develop models for rural roads, and data from Minneapolis and Philadelphia were used to develop models for urban and suburban roadway segments and intersections. No models were developed for rural intersections. Results of the analysis indicate the following: • Rural roadway segments – Rural two-lane undivided roads: ◾ The potential of either a pedestrian or a bicycle crash occurring increases with vehicular traffic volume, population within the census tract, and segment length. ◾ The potential of a pedestrian crash occurring is lower on roadway segments with lanes greater than 11 ft. ◾ The potential of a pedestrian crash occurring is lower on roadway segments with shoulders greater than 3 ft. Pedestrian Model Bicycle Model Continuous Variables (effects of doubling) Total traffic volume (veh/obs period) 3.320 3.355 Population (people) + 1 2.519 1.598 Table 194. Odds ratios associated with models to estimate the potential of a pedestrian or bicycle crash occurring at four-leg signal control intersections with two-way/two-way operations. Variable Transformation Pedestrian Model Bicycle Model Coefficient p-Value Coefficient p-Value Total entering AADT (vehicles entering intersection during observation period) Log 1.7314 < 0.001 1.7461 < 0.001 Population (people) Log (X+1) 1.3328 0.008 0.6764 0.153 Indicator for roadway segment within Pennsylvania Indicator 1.1486 0.043 -0.2682 0.613 Constant -41.6746 < 0.001 -36.7443 < 0.001 AIC 147.36 156.92 NOTE: AIC = Akaike’s Information Criterion. Table 193. Models to estimate the potential of a pedestrian or bicycle crash occurring at four-leg signal control intersections with two-way/two-way operations.

286 Pedestrian and Bicycle Safety Performance Functions ◾ The potential of a bicycle crash occurring is lower on roadway segments with lanes greater than or equal to 12 ft. ◾ The potential of a bicycle crash occurring is lower on roadway segments with shoulders greater than 1 ft. • Urban and suburban roadway segments – Two-lane, undivided roads ◾ The potential of either a pedestrian or bicycle crash occurring increases with vehicular traffic volume, population in adjacent census tract, segment length, number of intersec- tions, and school density (for bicycle crashes). ◾ Both pedestrian and bicycle crash potential decrease with outside shoulder width. – Four-lane undivided and divided roads ◾ The potential of either a pedestrian and bicycle crash occurring increases with total traf- fic volume, segment length, and the number of intersections along the segment. ◾ The potential of a pedestrian crash is lower on divided roadways compared to undivided roadways and decreases with the outside shoulder width but increases with the popula- tion in the adjacent census tract. ◾ The potential of a bicycle crash decreases with roadway width. – One-way roads ◾ The potential of a pedestrian crash increases with total traffic volume, segment length, the number of intersections along the segment, and total roadway width. ◾ The potential of a bicycle crash increases with total traffic volume, segment length, on higher speed limit roads (30 mph and above, compared to lower than 30 mph) and with school density. • Urban and suburban intersections – Three-leg signal control intersections with two-way/two-way operations and four-leg signal control intersections with one-way/two-way operations ◾ The potential of either a pedestrian or bicycle crash occurring increases with vehicular traffic volume and population in adjacent census tract. ◾ The potential of a pedestrian crash is higher for four-leg intersections than for three-leg intersections. – Four-lane signal control intersections with two-way/two-way operations ◾ The potential of either a pedestrian or bicycle crash occurring increases with vehicular traffic volume and population in adjacent census tract.

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Each year, national crash studies have estimated that while overall traffic fatalities are decreasing, the percentages of those fatalities among pedestrians and cyclists are increasing.

NCHRP Research Report 1064: Pedestrian and Bicycle Safety Performance Functions, from TRB's National Cooperative Highway Research Program, presents state departments of transportation and other transportation professionals with an update of pedestrian and bicycle safety performance functions (SPFs).

Supplemental to the report are three spreadsheet tools that address SPFs on rural multilane roads, rural two-lane roads, and urban/suburban arterials.

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