Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments (2017)

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24 C H A P T E R 4 Crash Modification Factor Development for Pedestrian Treatments The aim of the analytical work was to use the most appropriate techniques for estimating CMFs or CMFunctions for pedestrians involved and all crashes, by type, for various treatments and treatment combinations. As defined in the FHWA’s Guide to Developing Quality Crash Modification Factors (64), a crash modification factor (CMF) is a multiplicative factor used to compute the expected number of crashes after implementing a given countermeasure at a specific site. The CMF is multiplied by the expected crash frequency without treatment. A CMF greater than 1.0 indicates an expected increase in crashes, while a value less than 1.0 indicates an expected reduction in crashes after implementation of a given countermeasure. For example, a CMF of 0.8 indicates an expected safety benefit, specifically, a 20 percent expected reduction in crashes. A CMF of 1.2 indicates an expected degradation in safety, specifically, a 20 percent expected increase in crashes. A crash modification function (CMFunction) is a formula used to compute the CMF for a spe- cific site based on its characteristics. It is not always reasonable to assume a constant reduction in crashes for all sites with different characteristics (e.g., safety improvements may be greater for high traffic volumes). A countermeasure may also have several levels or potential values (e.g., improving intersection skew angle). A crash modification function allows the CMF to change over the range of a variable or combination of variables. Where possible, it is preferable to develop CMFunctions as opposed to a single CMF value since safety effectiveness most likely varies based on site characteristics, at least to some extent. In practice, however, this is often difficult since more data are required to detect such differences. This is particularly so for pedestrian counter- measures. It is also possible that the CMF for all pedestrian crashes might be different than the CMF for fatal and incapacitating pedestrian crashes. The same limitation related to the need for a larger crash set also applies to this issue. It was quickly realized that the preferred before-after study would be limited in scope and robustness because of the relatively small sample sizes, especially for pedestrian crashes. Thus, considerable effort was made to assemble a database for the alternative methodology, cross- sectional regression analysis, while recognizing the well-known limitations of this approach. Because of those limitations, it was still necessary to conduct a before-after study, however lim- ited, to corroborate the results of the cross-sectional analysis. The results of the before-after study could also be used to reinforce the results of the cross-sectional regression analysis by providing combined results that could be used with more confidence. This chapter is organized as follows. The before-after study is described, followed by a section on the cross-sectional analysis. Each of these main sections provides information on the data Data Analysis

Data Analysis 25 and methodology used, followed by a presentation and discussion of the results. The chapter closes with a section that compares the results of the two sets of analyses and a final section with conclusions and recommendations. Before-After Evaluation The intent of the study was to conduct a before-after evaluation for the following treatments (initially, it appeared there were sufficient samples to facilitate such a study): • Refuge island alone (68 sites) • Advanced YIELD or STOP markings and signs alone (69 sites) • Refuge island with advanced YIELD or STOP markings and signs (9 sites) • PHB alone (10 sites) • PHB with advanced YIELD or STOP markings and signs (27 sites) • RRFB alone (9 sites) • RRFB with advanced YIELD or STOP markings and signs (7 sites) However, it was clear that samples of sites for PHB alone, RRFB alone, and the refuge island and advanced YIELD or STOP markings and signs and RRFB and advanced YIELD or STOP markings and signs combinations were limited (less than or equal to 10 sites). These samples were too small to obtain any reliable CMFs for pedestrian crashes. Hence, the before-after evaluation was pursued for refuge islands, advanced YIELD or STOP markings and signs, and PHB and advanced YIELD or STOP markings and signs. Four crash types were investigated in the before-after evaluation: total, rear-end, sideswipe, and pedestrian. Before-After Study Methodology The Empirical Bayes (EB) methodology for observational before-after studies was used to develop CMFs. In the EB approach, the CMF is estimated based on the parameters p and l, where p is the expected number of crashes that would have occurred in the after period with- out the treatment and l is the number of reported crashes in the after period. This methodol- ogy is rigorous in that it properly accounts for regression to the mean and has been included in the first edition of the HSM as the state-of-the-art for conducting observational before-after studies (67). To estimate p (expected number of crashes), the research team 1. Identified a group of untreated sites that were otherwise similar to the treatment group. This is called the reference group. 2. Using data from the reference group, estimated safety performance functions (SPFs) (math- ematical equations) relating crashes to the characteristics of the site including traffic volume, pedestrian volume, number of through lanes, location type (intersection or non-intersection), area (urban or suburban), presence and type of crosswalk, one-way or two-way street, and presence or absence of school crossing. The SPFs are documented in Appendix E of this report. 3. Calibrated annual SPF multipliers, in estimating SPFs, to account for the temporal effects (e.g., variation in weather, demography, and crash reporting) on safety. 4. Estimated the number of crashes that would be expected in each year of the before period for each treatment site using the SPFs, the annual SPF multipliers, and data on the site char- acteristics for each year in the before period for each treatment site. The sum of these annual estimates was called P. The year of the treatment installation was not included in the before and after periods.

26 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments 5. Used the following equations to calculate the EB estimate of the expected crashes in the before period at each site, where x is the count of crashes in the before period at a treatment site and m is the expected number of crashes in the before period after correcting for possible bias due to RTM: , (1)1 2m w x w P( ) ( )= + where the weights w1 and w2 were estimated from the mean and variance of the SPF estimate as: 1 , (2)1w Pk Pk = + 1 1 , (3)2w Pk = + where k was estimated from the SPF calibration process with the use of a maximum likelihood procedure. In that process, a negative binomial distributed error structure was assumed with k being the overdispersion parameter of this distribution. 6. Estimated p as the product of m and the sum of the annual SPF predictions for the after period divided by P, the sum of these predictions for the before period (for each treatment site). The EB procedure also produced an estimate of the variance of p. The estimate of p was then summed over all sites in treatment groups of interest (to obtain psum) and compared with the count of crashes during the after period in that group (lsum). The vari- ance of p was also summed over all sites in the strategy group. The CMF was estimated as: ( )( )= λ pi + pi pi1 (4) 2 CMF Var sum sum sum sum The standard deviation of the estimated CMF was the following: 1 (5) 2 2 2 2 2StDev CMF Var Var Var sum sum sum sum sum sum ( ) ( ) ( ) ( )= θ pi pi + λ λ   + pi pi   The percent change in crashes is calculated as 100(1 - CMF); thus a value of CMF = 0.7 with a standard deviation of 0.12 indicates a 30 percent reduction in crashes with a standard deviation of 12 percent. Further discussion of the EB procedure can be found in Hauer (65). Data for Before-After Study The before-after evaluation included data from the following cities: • Alexandria and Arlington, Virginia • Cambridge, Massachusetts • Charlotte, North Carolina • Chicago, Illinois • Eugene and Portland, Oregon • Miami and St. Petersburg, Florida

Data Analysis 27 • Milwaukee, Wisconsin • New York, New York • Phoenix, Scottsdale, and Tucson, Arizona Tables 4-1 through 4-3 show the summary statistics for the following treatment groups: • Refuge island (68 sites) • Advanced YIELD or STOP markings and signs (69 sites) • PHB in combination with advanced YIELD or STOP markings and signs (27 sites) Tables 4-1 through 4-3 show summary statistics on the following variables: AADT on the major road, pedestrian volumes, number of years before and after, and crashes per site-year before and Variable Minimum Maximum Mean Standard Deviation Major road AADT 1245 46000 12599 9897 Pedestrian volume (24 hours) 3 5354 434 935 Years before 1 5 2.37 1.2 Years after 1 8 5.84 1.7 Total crashes per site-year before 0 21.5 1.61 3.14 Total crashes per site-year after 0 15.75 1.52 2.71 Rear-end crashes per site-year before 0 9 0.63 1.4 Rear-end crashes per site-year after 0 9 0.50 1.34 Sideswipe crashes per site-year before 0 3 0.20 0.58 Sideswipe crashes per site-year after 0 1.25 0.12 0.24 Pedestrian crashes per site-year before 0 1.5 0.04 0.2 Pedestrian crashes per site-year after 0 0.67 0.04 0.11 Variable Minimum Maximum Mean Standard Deviation Major road AADT 340 52892 15735 14271 Pedestrian volume (24 hours) 5 6812 644 1224 Years before 1 5 1.9 1.23 Years after 1 8 4.51 1.88 Total crashes per site-year before 0 27 2.92 5.17 Total crashes per site-year after 0 21.5 2.08 3.02 Rear-end crashes per site-year before 0 20 1.49 3.46 Rear-end crashes per site-year after 0 9 0.80 1.43 Sideswipe crashes per site-year before 0 1.5 0.17 0.36 Sideswipe crashes per site-year after 0 3 0.22 0.45 Pedestrian crashes per site-year before 0 3 0.13 0.47 Pedestrian crashes per site-year after 0 1.5 0.09 0.27 Table 4-1. Summary statistics for sites with refuge islands (68 sites). Table 4-2. Summary statistics for sites with advanced YIELD or STOP markings and signs (69 sites).

28 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments after for the four different crash types that were considered. These statistics are included to pro- vide the reader with some basic information about the sample size and the range of the different variables. The before and after crash statistics from Tables 4-1 through 4-3 are for information only and cannot be directly used to estimate CMFs because such a comparison does not take account into the possible bias due to RTM and other trends. This comparison can be done with the EB estimates presented later. Before-After Study Results—Estimates of Crash Modification Factors Table 4-4 shows the estimated CMFs for refuge island, advanced YIELD or STOP markings and signs, and the PHB and advanced YIELD or STOP markings and signs combination. The columns that are included in Table 4-4 are as follows: • Treatment and number of sites. This is the number of treated sites included in the evaluation. Only sites that had at least 1 year of before period data and 1 year of after period data were included in the before-after evaluation. The number of sites includes both intersections and non-intersections. The sample size was not sufficient to provide reliable CMFs for inter sections and non-intersections separately. • Crash type. As mentioned earlier, four crash types were included. The results for sideswipe and rear-end crashes were combined to be consistent with the approach used in the cross- sectional modeling method and other CMF evaluations conducted in recent times. • Number (#) of crashes per year (before). This is the actual number of crashes per year in the before period at the treatment sites. • Number (#) of crashes per year (after). This is the actual number of crashes per year in the after period at the treatment sites. • Number (#) of crashes (before). This is the actual number of crashes in the before period at the treated sites. • Number (#) of crashes (after). This is the actual number of crashes in the after period at the treated sites. Variable Minimum Maximum Mean Standard Deviation Major road AADT 6634 48791 20673 12221 Pedestrian volume (24 hours) 6 1647 334 353 Years before 1 5 3.26 1.72 Years after 3 8 5.41 1.93 Total crashes per site-year before 0.2 11.8 3.62 3.6 Total crashes per site-year after 0 7.25 2.14 1.89 Rear-end crashes per site-year before 0 7 1.43 2.15 Rear-end crashes per site-year after 0 3.88 0.92 0.91 Sideswipe crashes per site-year before 0 2.2 0.41 0.63 Sideswipe crashes per site-year after 0 1.5 0.18 0.36 Pedestrian crashes per site-year before 0 1 0.10 0.22 Pedestrian crashes per site-year after 0 0.33 0.03 0.07 Table 4-3. Statistics for sites with PHBs and advanced YIELD or STOP markings and signs (27 sites).

Table 4-4. Estimated crash modification factors from the before-after evaluation. Treatment and number of sites Crash type # of crashes per year (before) # of crashes per year (after) # of crashes (before) # of crashes (after) EB estimates (before) Variance of EB (before) EB estimates (after) Variance of EB (after) CMF S.E. of CMF p- value Refuge island: 68 sites Pedestrian 2.53 2.23 6 13 7.9 2.0 18.8 11.2 0.671 0.215 0.126 Advanced YIELD or STOP markings and signs: 69 sites Total 163.16 148.78 310 671 304.6 233.7 754.7 2254.5 0.886 0.065 0.079 Rear-end and Sideswipe 83.68 74.28 159 335 155.5 101.0 416.2 1068.8 0.800 0.076 0.008 Pedestrian 9.47 4.66 18 21 14.3 5.4 32.2 27.4 0.636 0.169 0.031 Pedestrian hybrid beacons & Advanced YIELD or STOP markings and signs: 27 sites Total 87.73 63.03 286 341 275.1 232.3 413.2 1078.5 0.820 0.078 0.021 Rear-end and Sideswipe 38.65 33.64 126 182 117.5 84.0 205.4 460.9 0.876 0.111 0.264 Pedestrian 3.07 0.74 10 4 8.0 2.9 15.6 13.3 0.244 0.128 <0.001

30 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments • EB estimates (before). This is the EB estimate of the crashes in the before period after correct- ing for RTM. Generally, this is expected to be lower than the actual number of crashes in the before period if sites with high accidents had been selected for treatment. • Variance of EB (before). This is the variance of the EB estimates for the before period. • EB estimates (after). This is the estimate of the crashes in the after period had the treatment not been implemented. • Variance of EB (after). This is the variance of the EB estimates for the after period. • CMF. This column shows the CMF. • S.E. of CMF. This is the standard error of the CMF. • p-value. This indicates the level of significance for the CMF. With lower p values (or the level of significance), we have more confidence that the CMF is truly statistically different from 1.0. Typically, most researchers use p values of 0.05 (i.e., 5%) or lower as a benchmark. However, due to the relative rarity of pedestrian crashes (compared to vehicle crashes), CMFs associated with pedestrian treatments have p values that are higher than 0.05. Hence, we also discuss p values higher than 0.05 in the discussion below. The following observations can be made based on the results in Table 4-4: • Refuge islands. For pedestrian crashes, the results indicate a reduction of approximately 33%, which was significant at about the 13% level. The results for the vehicle-vehicle involved crash types were not considered reliable enough for inclusion. • Advanced YIELD or STOP markings and signs. The results indicate, approximately, an 11 percent reduction in total crashes, a 20 percent reduction in rear-end and sideswipe crashes, and a 36 percent reduction in pedestrian crashes. The reduction in total crashes is statistically significant at about the 8 percent level, and the reduction in the other two crash types is statistically significant at the 5 percent level or lower. • PHB and Advanced YIELD or STOP markings and signs. The results indicate, approxi- mately, an 18 percent reduction in total crashes and a 76 percent reduction in pedestrian crashes. Both these results are statistically significant at the 5 percent level or lower. The changes in rear-end and sideswipe crashes are not statistically significant at any reasonable significance level. The result for pedestrian crashes is quite consistent with the 69 percent reduction reported by Fitzpatrick and Park (32) for the same treatment at intersections in Tucson. Fitzpatrick and Park (32) also used the EB before-after evaluation method. It should be mentioned that two of the columns in Table 4-4 indicate the pedestrian crashes per site per year that occurred on average before and after the various countermeasures were installed. Even though there is a reduction in pedestrian crashes/site/year in the after period (compared to the before period) for each countermeasure, these crash rates do not account for possible bias due to RTM, overall trends, and changes in traffic volume between the before and after periods. For this reason, the rates shown in Table 4-4 alone should not be used to deter- mine the precise level of the CMF. The CMFs were estimated based on the EB procedure, which accounts for the possible variation in crashes due to RTM, overall trends, and changes in traffic volumes. Table 4-4 also provides the total sample of crashes that was included in the before and after periods. The greater number of crashes in the after period as compared to the before period is the result of there being a larger time frame in the after period than the before period. Crash Modification Factor Estimation from Cross-Sectional Regression Analysis As mentioned earlier, although the EB before-after methodology is preferred for estimating CMFs, and it was possible to do a limited EB study for this research, a cross-sectional analysis was necessary because the data before and after a treatment was actually implemented were too

Data Analysis 31 limited for a robust before-after study. The results from the two approaches are compared in a later section. Analysis Purpose The purpose of the cross-sectional regression analysis, as for the before-after study, was to estimate CMFs or CMFunctions for each of the four pedestrian treatments under study. These four treatments are: • Refuge islands • Advanced YIELD or STOP markings and signs • PHBs • RRFBs It was also of interest to estimate CMFs for combinations of treatments. In fact, at many of the sites one treatment was installed initially, followed by installation of one or more additional treatments in later years. For most combination treatments, however, the sample size was too limited to provide robust results. The exceptions were PHBs and RRFBs—most sites with these treatments also have advanced YIELD or STOP markings and signs present. Several crash types were analyzed separately for each treatment, including • Pedestrian crashes • Rear-end plus sideswipe crashes • Total crashes • (KABC) injury rear-end plus sideswipe crashes • (KABC) injury total crashes KABC refers to crashes classified as K (fatal), A (incapacitating injury), B (non-incapacitating injury) or C (possible injury) on the KABCO injury severity scale (O stands for property damage only). While the target crash of the four pedestrian treatments is the small subset of vehicle-pedestrian crashes, vehicle-vehicle crashes were added to the analysis to investigate whether they were affected as well. If the treatments alter driver behavior, this is a logical possibility. Rear-end and sideswipe crashes were combined as it was hypothesized that these types of vehicle-vehicle crashes may be the crash types most likely to be affected by pedestrian treatments and would be similar in this regard. The combined category was considered the target vehicle-vehicle crash category. Approach for Crash Modification Factor Cross-Sectional Regression Analysis CMFs derived from cross-sectional panel data are based on a single time period under the assumption that the ratio of average crash frequencies for sites with and without a feature is an estimate of the CMF for implementing that feature. Known confounding factors, such as traffic volume or geometric characteristics, can be controlled for in principle by estimating a multiple variable regression model and/or matching sites based on these variables. However, the basic problem with the cross-sectional design is that an unknown portion of the observed difference in crash experience can be due to factors that cannot be controlled for (e.g., if data are non-existent) or are unknown. For this reason, caution needs to be exercised in making infer- ences about CMFs on the basis of cross-sectional designs. Corroboration with insights from before-after studies, however limited, other cross-section studies and/or logical reasoning tends to mitigate this difficulty.

32 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments The cross-sectional analysis applied Generalized Linear Modeling (GLM). Because each site- year of data was used as an observation, it was necessary to resolve the issue of repeated measures of the data in specifying the models. This is termed “repeated measures” because for each site multiple observations of crash counts are used, and the errors between these observations are correlated. In addition, the model specification considered that the data are nested both by site location (multiple years of observed data for each site) and by city. The approach taken within the GLM framework to account for the repeated measures and the nested nature of the data was Generalized Estimation Equations (GEE). This ensures that the correlation between within-site observations is accounted for as well as allowing for unobserved heterogeneity between cities. Regression models for crash data typically adopt an error distribution from the Poisson family, which is suited for non-negative count data. The negative binomial model has been used exten- sively for crash data modeling because these data are frequently overdispersed, meaning the vari- ance of observed crash frequencies is greater than the mean. In preliminary model development, it was observed that the pedestrian crash data were not overdispersed. For this reason, the regres- sion models for pedestrian crashes used a Poisson error distribution with repeated measures. For the other crash types considered, the negative binomial distribution with repeated measures specification was found to be appropriate because those data did exhibit overdispersion. Cumulative Residual (CURE) plots and the Integrate-Differentiate (ID) method (discussed in Appendix F) were used to investigate different model forms. The assessment of model fit included, in addition to the CURE plot, several goodness-of-fit statistics and considerations, including: • The logic of the direction of effect and magnitude of estimated parameters • The p values of estimated parameters • For negative binomial models, the value of the overdispersion parameter • CURE plots for each variable included in the model • Akaike’s Information Criteria (AIC) When comparing two or more potential models, the AIC penalizes for the addition of param- eters and thus selects a model that fits well but has a minimum number of parameters. AIC is not typically used as a goodness-of-fit measure in itself, but can be used to compare the relative fit of alternate models. The lower value of AIC is preferred. AIC = -2(log-likelihood) + 2K, where K is the number of estimated parameters included in the model (i.e., number of variables + the intercept). The log-likelihood of the model, given the data, is readily available in statistical output and reflects the overall fit of the model (smaller values indicate worse fit). Description and Data Preparation Considerations for Cross-Sectional Model Databases This section describes the preparation of the datasets used to develop the regression models for each of the four treatments and provides summary statistics. Definitions of the variables are given in Table 4-5. Data Preparation Considerations Data Observations for Modeling. The structure of the data used to estimate the regression models included each individual site-year of data as an observation. Each site-year was used instead of aggregating all years of data for each site because many sites experienced changes over time other than the treatment of interest. For example, at one midblock site in Phoenix, a refuge island was installed in 2003, an advanced STOP sign with markings was installed in 2005, and

Data Analysis 33 a PHB was installed in 2009. Because of the multiple changes, the data for all years cannot be combined. Data for any year in which one of the four treatments of interest was installed were discarded from the calibration dataset so that a full year of data could be used where no changes took place. Additionally, for a few sites, one or more years of data were discarded when major construction took place, e.g., a lane addition. Influence Area. The influence area defines the areas upstream and downstream from each pedestrian crossing within which crashes are included in the crash data for the site. Preliminary models were developed using the full influence area (350 ft) used for each jurisdiction to assign crashes related to the crossing and using areas of 50 ft, 150 ft, and 250 ft in either direction of the treatment. No significant difference was found for varying the size of the influence area, so the full influence area data provided by jurisdictions were used for developing the final models to maximize the number of crashes under study. This is consistent with the strategy adopted for the data used for the before-after study. Zero Pedestrian Volume Sites. Some sites had a count of zero pedestrians during the time a traffic count was done. It is unlikely that the crossing volume is truly zero for the average daily count, but it is likely that the pedestrian volume is low. In developing preliminary models, it was investigated whether these sites should be dropped from the data or whether a value of 0.5 should be assigned as a daily pedestrian volume so that the GLM approach could be used on these sites in estimating the regression models. It was found that there were no substantial dif- ferences in the parameter estimates or goodness-of-fit for the models estimated under either approach. Thus, the sites with a count of zero pedestrians were included with a daily crossing volume of 0.5 in the final dataset used, in order to maximize the data available. Aggregation/Disaggregation of Data. Because some sites had more than one of the four pedestrian treatments under study, it was considered preferable to eliminate sites with one of Variable Definition Lanes Number of lanes on road being crossed Crosswalk Length Crosswalk length in feet AADT Average annual daily traffic on mainline road PEDAADT Pedestrian average annual daily volume Midblock_Int M if midblock location I if unsignalized intersection BusStop Y if bus stop is present N if bus stop is not present Lighting Y if lighting is present N if lighting is not present Refuge Island Presence Y if refuge island is present N if refuge island is not present School Crossing Y if school crossing is present N if school crossing is not present Median Y if median is present on road being crossed N if median is not present on road being crossed AreaType Suburban or urban area type TraffDir One-way or two-way traffic on road being crossed PEDCRASH Frequency of pedestrian–vehicle crashes TOTCRASH Frequency of total crashes INJCRASH Frequency of fatal+injury crashes TARGETCRASH Frequency of rear-end plus sideswipe crashes INJTARGETCRASH Frequency of fatal+injury rear-end plus sideswipe crashes Table 4-5. Definitions for analysis variables.

34 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments the other three treatments present when looking at the safety effects of a single treatment. This approach sought to reduce the number of confounding variables that the regression modeling needed to account for. Where possible this approach was undertaken. However, for the PHB and RRFB treatments it was not possible to take this approach because it would have left very few site-years of observed data for the single treatment. Where this could not be done, one or more of the other treatments was included in order to increase the sample size. Details on which data were included for each model are discussed in the cross-sectional model results section. The results are presented and interpreted with the appropriate caveats. Data Summary Refuge Islands. The dataset for developing CMFs for refuge islands did not include any site that had advanced YIELD or STOP markings and signs, PHB, or RRFB installed at any time during the study period. Table 4-6 and Table 4-7 provide descriptive statistics by treatment and reference group. The reference group sites do not have any of the four main treatments installed. Advanced YIELD or STOP markings and signs. The dataset used for developing CMFs for advanced YIELD or STOP markings and signs did not include any site that had a refuge island, PHB, or RRFB installed at any time during the study period. Table 4-8 and Table 4-9 provide descriptive statistics by treatment and reference group. The reference group sites do not have any of the four main treatments installed. PHBs. The dataset for developing CMFs for PHBs did not include any site that had a refuge island or RRFB installed at any time during the study period. Because many sites with a PHB also have an advanced YIELD or STOP marking and sign, sites with these signs were included in the dataset. The sites were also limited to cities in which a PHB existed: Charlotte, Portland, Phoenix, Scottsdale, Tucson, and St. Petersburg. Table 4-10 and Table 4-11 provide descriptive statistics by treatment and reference group. The reference group sites do not have any of the four main treatments installed. RRFBs. For pedestrian crash models, the dataset for developing CMFs for RRFBs included all locations. This was needed to allow for a sufficient sample of pedestrian crashes. For the other crash types, the dataset for RRFBs did not include any site that had a refuge island or PHB installed at any time during the study period. Because many sites with an RRFB also have an advanced YIELD or STOP marking and sign, sites with these signs were included in the dataset. For the non-pedestrian crash models, the sites were also limited to cities in which an RRFB existed: Chicago, Eugene, Miami, Phoenix, Portland, and St. Petersburg. Table 4-12 and Table 4-13 provide descriptive statistics by treatment and reference group. The reference group sites do not have any of the four main treatments installed. Cross-Sectional Model Results This section presents and discusses the final models developed and the CMFs implied by the relevant parameter estimates. The following considerations were applied in making decisions on variables to include in the models and presenting the results: 1. The typical multiplicative crash prediction model form was eventually applied with pedes- trian and total AADT as separate power model terms and the categorical variables for each city in which a crossing is located, presence of a treatment, area type (urban or suburban), and crossing location (midblock or intersection) as exponential terms. The exponential model form for categorical variables implies a percent change to the crash prediction for each level of the variable, leading to a CMF for the presence of treatment variables.

Data Analysis 35 Site Type Variable Frequency Percentage Reference Midblock_Int Intersection – 2,970 Midblock – 897 Intersection – 76.8 Midblock – 23.2 BusStop No – 2,047 Yes – 1,820 No – 52.9 Yes – 47.1 Lighting No – 840 Yes – 3,027 No – 21.7 Yes – 78.3 Refuge Island Presence Yes – 0 No – 3,867 Yes – 0.0 No – 100.0 SchoolCrossing No – 3,529 Yes – 338 No – 91.3 Yes – 8.7 Median No – 3,867 Yes – 0 No – 100.0 Yes – 0.0 AreaType Suburban – 3,522 Urban – 345 Suburban – 91.1 Urban – 8.9 TraffDir One-Way – 97 Two-Way – 3,770 One-Way – 2.5 Two-Way – 97.5 Treatment Midblock_Int Intersection – 813 Midblock – 341 Intersection – 70.5 Midblock – 29.5 BusStop No – 626 Yes – 528 No – 54.3 Yes – 45.7 Lighting No – 135 Yes – 1,019 No – 11.7 Yes – 88.3 Refuge Island Presence No – 0 Yes – 1,154 No – 0.0 Yes – 100.0 CrossingGuard No – 1,147 Yes – 7 No – 99.4 Yes – 0.6 SchoolCrossing No – 1,079 Yes – 75 No – 93.5 Yes – 6.5 Median No – 492 Yes – 662 No – 42.6 Yes – 57.4 AreaType Suburban – 956 Urban – 198 Suburban – 82.8 Urban – 17.2 TraffDir One-Way – 49 Two-Way – 1,105 One-Way – 4.2 Two-Way – 95.8 Table 4-7. Frequency tallies for refuge island dataset. Site Type Statistic Lanes Crosswalk Length AADT PEDAADT PEDCRASH TOTCRASH INJCRASH TARGET CRASH INJ TARGET CRASH Control N 3867 3867 3867 3867 3867 3867 3867 3867 3867 Control MIN 2 21 810 0.5 0 0 0 0 0 Control MAX 7 142 48000 7825 4 31 15 22 8 Control MEAN 4.0 56.4 17603.2 343.1 0.1 2.4 0.9 1.0 0.3 Control STD 1.2 13.6 9507.8 721.0 0.3 3.4 1.5 1.9 0.8 Treatment N 1154 1154 1154 1154 1154 1154 1154 1154 1154 Treatment MIN 2 22 340 0.5 0 0 0 0 0 Treatment MAX 7 112 47500 20388 2 19 7 8 4 Treatment MEAN 3.6 60.3 15634.9 607.8 0.1 1.2 0.4 0.5 0.2 Treatment STD 1.3 17.8 10335.7 1829.9 0.2 2.0 0.9 1.0 0.4 Table 4-6. Summary statistics for refuge island dataset.

36 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments Site Type Variable Frequency Percentage Reference Midblock_Int Intersection – 2,970 Midblock – 897 Intersection – 76.8 Midblock – 23.2 BusStop No – 2,047 Yes – 1,820 No – 52.9 Yes – 47.1 Lighting No – 840 Yes – 3,027 No – 21.7 Yes – 78.3 Presence of Advanced YIELD or STOP Markings and Signs Yes – 0 No – 3,867 Yes – 0 No – 100.0 SchoolCrossing No – 3,529 Yes – 338 No – 91.3 Yes – 8.7 Median No – 3,867 Yes – 0 No – 100.0 Yes – 0.0 AreaType Suburban – 3,522 Urban – 345 Suburban – 91.1 Urban – 8.9 TraffDir One-Way – 97 Two-Way – 3,770 One-Way – 2.5 Two-Way – 97.5 Treatment Midblock_Int Intersection – 417 Midblock – 123 Intersection – 77.2 Midblock – 22.8 BusStop No – 347 Yes – 193 No – 64.3 Yes – 35.7 Lighting No – 32 Yes – 508 No – 5.9 Yes – 94.1 Presence of Advanced YIELD or STOP Markings and Signs Yes – 540 No – 0 Yes – 100.0 No – 0 CrossingGuard No – 537 Yes – 3 No – 99.4 Yes – 0.6 SchoolCrossing No – 517 Yes – 23 No – 95.7 Yes – 4.3 Median No – 413 Yes – 127 No – 76.5 Yes – 23.5 AreaType Suburban – 388 Urban – 152 Suburban – 71.9 Urban – 28.1 TraffDir One-Way – 30 Two-Way – 510 One-Way – 5.6 Two-Way – 94.4 Table 4-9. Frequency tallies for advanced YIELD or STOP markings and signs dataset. Site Type Statistic Lanes Crosswalk Length AADT PEDAADT PEDCRASH TOTCRASH INJCRASH TARGET CRASH INJ TARGET CRASH Ref N 3867 3867 3867 3867 3867 3867 3867 3867 3867 Ref MIN 2 21 810 0.5 0 0 0 0 0 Ref MAX 7 142 48000 7824.6 4 31 15 22 8 Ref MEAN 4.0 56.4 17603.2 343.1 0.1 2.4 0.9 1.0 0.3 Ref STD 1.2 13.6 9507.8 721.0 0.3 3.4 1.5 1.9 0.8 Treat N 540 540 540 540 540 540 540 540 540 Treat MIN 2 20 533 0.5 0 0 0 0 0 Treat MAX 8 122 49402.0 5128.8 2 14 10 13 9 Treat MEAN 3.4 53.2 12979.0 494.5 0.1 1.1 0.4 0.4 0.2 Treat STD 1.4 19.7 12364.6 937.0 0.3 1.7 1.0 1.2 0.7 Table 4-8. Summary statistics for advanced YIELD or STOP markings and signs dataset.

Data Analysis 37 Site Type Variable Frequency Percentage Reference Midblock_Int Intersection – 2,349 Midblock – 780 Intersection – 75.1 Midblock – 24.9 BusStop No – 1,828 Yes – 1,301 No – 58.4 Yes – 41.6 Lighting No – 630 Yes – 2,499 No – 20.1 Yes – 79.9 PHB Presence Yes – 0 No – 3,129 Yes – 0.0 No – 100.0 SchoolCrossing No – 2,979 Yes – 150 No – 95.2 Yes – 4.8 Median No – 3,012 Yes – 117 No – 96.3 Yes – 3.7 AreaType Suburban – 2,920 Urban – 209 Suburban – 93.3 Urban – 6.7 TraffDir One-Way – 105 Two-Way – 3,024 One-Way – 3.4 Two-Way – 96.6 Treatment Midblock_Int Intersection – 345 Midblock – 21 Intersection – 94.3 Midblock – 5.7 BusStop No – 274 Yes – 92 No – 74.9 Yes – 25.1 Lighting No – 4 Yes – 362 No – 1.1 Yes – 98.9 PHB Presence Yes – 359 No – 7 Yes – 98.1 No – 1.9 CrossingGuard No – 344 Yes – 22 No – 94.0 Yes – 6.0 SchoolCrossing No – 211 Yes – 155 No – 57.7 Yes – 42.3 Median No – 356 Yes – 10 No – 97.3 Yes – 2.7 AreaType Suburban – 312 Urban – 54 Suburban – 85.3 Urban – 14.7 TraffDir One-Way – 27 Two-Way – 339 One-Way – 7.4 Two-Way – 92.6 Table 4-11. Frequency tallies for PHB dataset. Site Type Statistic Lanes Crosswalk Length AADT PEDAADT PEDCRASH TOTCRASH INJCRASH TARGET CRASH INJ TARGET CRASH Ref N 3129 3129 3129 3129 3129 3129 3129 3129 3129 Ref MIN 2 20 533 0.5 0 0 0 0 0 Ref MAX 8 122 49402 7824.6 3 31 15 22 9 Ref MEAN 4.2 56.4 18446.6 240.0 0.1 2.6 1.0 1.2 0.4 Ref STD 1.1 14.5 10334.2 592.1 0.3 3.6 1.6 2.0 0.9 Treat N 366 366 366 366 366 366 366 366 366 Treat MIN 2 20 510 0.5 0 0 0 0 0 Treat MAX 7 130 46000 1647.2 1 27 13 21 9 Treat MEAN 3.9 60.8 17625.7 303.2 0.1 2.9 1.3 1.6 0.6 Treat STD 1.5 22.5 11766.1 262.7 0.2 3.5 1.6 2.4 1.1 Table 4-10. Summary statistics for PHB dataset.

38 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments Table 4-12. Summary statistics for RRFB dataset. Site Type Statistic Lanes Crosswalk Length AADT PEDAADT PEDCRASH TOTCRASH INJCRASH TARGET CRASH INJ TARGET CRASH Ref N 1798 1798 1798 1798 1798 1798 1798 1798 1798 Ref MIN 2 20 533 0.5 0 0 0 0 0 Ref MAX 8 142 49402 7824.6 3 19 12 16 9 Ref MEAN 4.1 56.0 15958.2 322.0 0.1 1.4 0.6 0.6 0.2 Ref STD 1.3 16.8 10477.8 739.7 0.3 2.1 1.1 1.2 0.6 Treat N 130 130 130 130 130 130 130 130 130 Treat MIN 2 34 1386.5 9.99 0 0 0 0 0 Treat MAX 6 108 46000 1403.8 1 6 3 4 1 Treat MEAN 3.5 56.7 16250.2 235.2 0.0 0.9 0.3 0.3 0.1 Treat STD 1.3 14.3 12112.7 323.9 0.2 1.3 0.6 0.7 0.2 Table 4-13. Frequency tallies for RRFB dataset. Site Type Variable Frequency Percentage Reference Midblock_Int Intersection – 1,325 Midblock – 473 Intersection – 73.7 Midblock – 26.3 BusStop No – 801 Yes – 997 No – 44.6 Yes – 55.4 Lighting No – 289 Yes – 1,509 No – 16.1 Yes – 83.9 RRFB Presence Yes – 0 No – 1,798 Yes – 0.0 No – 100.0 SchoolCrossing No – 1,695 Yes – 103 No – 94.3 Yes – 5.7 Median No – 1,681 Yes – 117 No – 93.5 Yes – 6.5 AreaType Suburban – 1,587 Urban – 211 Suburban – 88.3 Urban – 11.7 TraffDir One-Way – 61 Two-Way – 1,737 One-Way – 3.4 Two-Way – 96.6 Treatment Midblock_Int Intersection – 87 Midblock – 43 Intersection – 66.9 Midblock – 33.1 BusStop No – 49 Yes – 81 No – 37.7 Yes – 62.3 Lighting No – 18 Yes – 112 No – 13.9 Yes – 86.2 RRFB Presence Yes – 115 No – 15 Yes – 88.5 No – 11.5 CrossingGuard No – 90 Yes – 40 No – 69.2 Yes – 30.8 SchoolCrossing No – 62 Yes – 68 No – 47.7 Yes – 52.3 Median No – 74 Yes – 56 No – 56.9 Yes – 43.1 AreaType Suburban – 117 Urban – 13 Suburban – 90.0 Urban – 10.0 TraffDir One-Way – 5 Two-Way – 125 One-Way – 3.9 Two-Way – 96.1

Data Analysis 39 2. Interaction terms were attempted to account for, for example, the effect of presence of treat- ment and crossing location, but these did not improve the model’s ability to explain the varia- tion in crashes between sites. 3. Multi-level models were attempted to develop CMFunctions by investigating whether the implied CMFs for presence of treatment varied by vehicle and pedestrian AADT and other variables, but these too did not improve the results. 4. The “City” factor variable was included in the models to account for differences in expected crashes between jurisdictions that are not related to the treatment, which could include crash reporting practices, weather, cultural issues, etc. Inclusion of this variable estimates a unique intercept term for each city in a model. The same logic applies to the inclusion of the area type variable. Models with and without the city variable and the area type were attempted before deciding to include these variables in the final models. (For the most part, these variables were included.) Cities were also grouped according to the coefficients when they were used individually, but the groups did not result in improvements and in any case did not have logical characteristics to define them. 5. For PHB and RRFB, almost all site-years of data had advanced YIELD or STOP markings and signs as well. For pedestrian crashes, where a satisfactory CMF was estimated for advanced YIELD or STOP markings and signs, a model with separate coefficients for each treatment was first estimated. The results for advanced YIELD or STOP markings and signs presence were consistent with the previous results, so the model for PHB or RRFB was then run using the advanced YIELD or STOP markings and signs presence parameter estimated for that treatment on its own as an offset. In the modeling process, the value of the offset is subtracted from the value of the dependent variable (crashes). This approach was adopted only for the pedestrian crash models since the models for the other crash types did not support the esti- mation of CMFs. 6. With the exception of refuge islands, CMFs are not reported for non-pedestrian crash types since the estimated models do not support the estimation of a valid CMF for those crash types. In such cases, an effect for non-pedestrian crashes also cannot be logically or anecdotally supported. 7. The estimates for the city variable are not provided in the interest of brevity and because, in any case, they do not impact the estimated CMFs. Refuge Islands The following model forms pertain to each crash type. The models predict the expected num- ber of crashes per year. _ _ _ _ PEDCRASH exp AADT PEDAADT TOTCRASH exp AADT PEDAADT INJCRASH exp AADT PEDAADT TARGETCRASH exp AADT PEDAADT INJTARGETCRASH exp AADT PEDAADT a City b Refuge Island Presence+c AreaType e f a City b Refuge Island Presence+d Midblock int e f a City b Refuge Island Presence+d Midblock int e f a City b Refuge Island Presence+d Midblock int e f a City b Refuge Island Presence+d Midblock int e f           = = = = = ( ) ( ) ( ) ( ) ( ) + + + + + + + + + + Target crashes include rear-end and sideswipe crashes. where AADT = total AADT on roadway being crossed AreaType = 1 if Suburban, 0 if Urban City = an intercept term specific for each city Midblock_Int = 1 if intersection, 0 if midblock PEDAADT = total pedestrian AADT for midblock or intersection Refuge Island Presence = 1 if present, 0 if not present

40 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments Parameter estimates for all models are shown in Table 4-14. As noted above, the estimates for the city variable are not provided in the interest of brevity and because, in any case, they do not impact the estimated CMFs. With the exception of the parameter estimates for refuge island presence and area type in the pedestrian crash model, all parameter estimates are statistically significant at the 5 percent level (i.e., a value of no effect is not within 1.96 standard errors). Those two estimates are, however, statistically significant at the 10 percent level (a value of zero is not within 1.64 standard errors). The estimated parameters indicate that fewer crashes of all types are expected when a refuge island is present and, for pedestrian crashes, in suburban areas versus urban areas. Greater num- bers of crashes of all types are expected at higher levels of vehicle and pedestrian AADT. With the exception of pedestrian crashes, the models also indicate that more crashes are expected at intersections than at midblock crossings. The CMFs implied by the parameter estimates for refuge island presence (expb) are provided in Table 4-15, along with the p values that indicate the level of significance. These indicate crash reductions for all crash types with statistically significant CMFs (p < 0.10) consistently of the order of 0.7 (crash reductions of 0.7). Note that the refuge island may be provided by a continuous median or a smaller island pro- vided at the crossing. Additional models were attempted that allowed the safety effects to differ by continuous median versus short refuge island, but the results were inconclusive. Parameter Estimate (standard error) Parameter Pedestrian Total Injury RE+SS* Injury RE+SS a −10.4246 (1.6409) −5.5953 (0.7761) −6.4572 (0.8886) −8.3157 (0.9754) 9.7130 (1.2009) b −0.3578 (0.2153) −0.2981 (0.0956) −0.3369 (0.1148) −0.2999 (0.1258) −0.3254 (0.1460) c −0.5715 (0.3127) n/a n/a n/a n/a d n/a 0.4730 (0.1083) 0.4312 (0.1183) 0.4140 (0.1224) 0.3728 (0.1395) e 0.6977 (0.1694) 0.5192 (0.0756) 0.5375 (0.0846) 0.7235 (0.0947) 0.7780 (0.1157) f 0.3295 (0.0486) 0.1224 (0.0247) 0.1141 (0.0260) 0.1041 (0.0237) 0.0986 (0.0263) overdispersion n/a 0.7608 (0.0305) 0.7075 (0.0482) 0.9149 (0.0521) 0.9837 (0.1075) *RE = Rear-end; SS = Sideswipe Table 4-14. Parameter estimates for refuge island regression models. Table 4-15. CMFs for refuge islands. Crash Type CMF (standard error) p-value PEDCRASH 0.699 (0.152) 0.0965 TOTCRASH 0.742 (0.071) 0.0018 INJCRASH 0.714 (0.082) 0.0033 TARGETCRASH 0.741 (0.093) 0.0171 INJTARGETCRASH 0.722 (0.106) 0.0258

Data Analysis 41 Advanced YIELD or STOP Markings and Signs The following model forms pertain to each crash type. The models predict the expected num- ber of crashes per year. = = = = = ( ) ( ) ( ) ( ) ( ) + + + + + + + + + + _ _ _ _ PEDCRASH exp AADT PEDAADT TOTCRASH exp AADT PEDAADT INJCRASH exp AADT PEDAADT TARGETCRASH exp AADT PEDAADT INJTARGETCRASH exp AADT PEDAADT a b Advance StopYield Sign Presence+c AreaType e f a City b Advance StopYield Sign Presence+c AreaType d Midblock int e f a City b Advance StopYield Sign Presence+d Midblock int e f a City b Advance StopYield Sign+d Midblock int e f a City b Advance StopYield Sign Presence+d Midblock int e f            where AADT = total AADT on roadway being crossed AreaType = 1 if Suburban, 0 if Urban City = an intercept term specific for each city Midblock_Int = 1 if intersection, 0 if midblock PEDAADT = total pedestrian AADT for midblock or intersection Advance Stop Yield Sign Presence = 1 if present, 0 if not present Parameter estimates for all models are shown in Table 4-16. The estimates for city are not provided in the interest of brevity, and they do not impact the estimated CMFs. The city variable was included in the models to account for differences in expected crashes between jurisdictions that are not related to the treatment. For pedestrian crashes, the city variable was not included in the final model because the parameter estimates became unstable. The parameter estimates for presence of an advanced YIELD or STOP marking and sign are of low statistical significance, as is the parameter estimate for AADT in the pedestrian crash model. All other parameters are statistically significant at the 5 percent level. The AADT term in the pedestrian crash model is consistent with the other models in terms of the direction of effect, however. For the presence of advanced YIELD or STOP markings and signs, the estimated parameters indicate that fewer pedestrian, total, and injury crashes are expected when a sign is present, and Table 4-16. Parameter estimates for advanced YIELD or STOP markings and signs models. Parameter Estimate (standard error) Parameter Pedestrian Total Injury RE+SS* Injury RE+SS a −6.5485 (1.6715) −5.1484 (0.6466) −5.5571 (0.7427) −7.8277 (0.7854) −8.7847 (1.0780) b −0.1470 (0.3295) −0.0195 (0.2240) −0.1367 (0.2714) 0.3520 (0.3284) 0.2801 (0.4228) c −0.9656 (0.4798) −0.2668 (0.1462) n/a n/a n/a d n/a 0.6124 (0.1172) 0.6039 (0.1265) 0.5200 (0.1283) 0.4786 (0.1550) e 0.2501 (0.2041) 0.5021 (0.0634) 0.4384 (0.0705) 0.6752 (0.0767) 0.6761 (0.1044) f 0.4003 (0.1011) 0.0949 (0.0257) 0.1006 (0.0270) 0.0880 (0.0248) 0.1026 (0.0287) overdispersion n/a 0.7151 (0.0307) 0.6908 (0.0488) 0.9038 (0.0530) 1.1215 (0.1149) *RE = Rear-end, SS = Sideswipe

42 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments more crashes are expected for target and target injury crashes. For total crashes, the estimate is extremely close to 0, which would indicate no effect. For the non-pedestrian crash types, the sample sizes are sufficiently large that the large standard errors of these estimates as well as the inconsistent direction of effect can be used to question their reliability in estimating a CMF. For this reason, it is concluded that the models do not support a CMF for vehicle-vehicle crashes. For pedestrian crashes, which have much smaller sample sizes, regardless of the large standard error, the results appear logical in direction of effect and magnitude. Greater numbers of crashes of all types are expected at higher levels of vehicle and pedestrian AADT. For pedestrian and total crashes, fewer crashes are expected in suburban areas versus urban areas. With the exception of pedestrian crashes, the models also indicate that more crashes are expected at intersections than are expected at midblock crossings. The CMF implied for pedestrian crashes by the parameter estimate for advanced YIELD or STOP markings and signs is provided in Table 4-17. As calculated, the p-value is large, implying low significance. However, because the direction of the effect is intuitive (CMF < 1), the point estimate of the CMF for pedestrian crashes is still recommended for application since the high p-value is likely to be a result of the scarcity of these crashes. For the other crash types, for which the sample size of crashes is not small, the large p values and, in some cases, illogically large magnitudes of effect implied led to no CMF being recommended. Pedestrian Hybrid Beacons The following model forms pertain to each crash type. The models predict the expected num- ber of crashes per year. For the PEDCRASH model, the CMF estimated for advanced YIELD or STOP markings and signs was included in the model as an offset.                = = = = = ( ) ( ) ( ) ( ) ( ) + + + + + + + + + + + _ _ _ _ PEDCRASH exp AADT PEDAADT TOTCRASH exp AADT PEDAADT INJCRASH exp AADT PEDAADT TARGETCRASH exp AADT PEDAADT INJTARGETCRASH exp AADT PEDAADT a City b PHB Presence+d AreaType f g a City b PHB Presence+c Advance Stop Yield Sign Presence+d AreaType e Midblock int f g a City b PHB Presence+c Advance StopYield Sign Presence+e Midblock int f g a City b PHB Presence+c Advance StopYield Sign Presence+e Midblock int f g a City b PHB Presence+c Advance StopYield Sign Presence+e Midblock int f g where AADT = total AADT on roadway being crossed Advance Stop Yield Sign Presence = 1 if present, 0 if not present AreaType = 1 if Suburban, 0 if Urban City = an intercept term specific for each city Midblock_Int = 1 if intersection, 0 if midblock PEDAADT = total pedestrian AADT for midblock or intersection PHB Presence = 1 if present, 0 if not present Table 4-17. CMFs for advanced YIELD or STOP markings and signs. Crash Type CMF (standard error) p-value PEDCRASH 0.863 (0.290) 0.6555 TOTCRASH Models do not support the recommendation of a CMF. INJCRASH TARGETCRASH INJTARGETCRASH

Data Analysis 43 Parameter estimates for all models are shown in Table 4-18. The estimates for city are not provided in the interest of brevity, and they do not impact the estimated CMFs. The city variable was included in the models to account for differences in expected crashes between jurisdictions that are not related to the treatment. The parameter estimates for presence of PHB are of low statistical significance with the excep- tion of the estimate for injury crashes. With the exception of the parameter estimate for area type in the pedestrian crash model and the estimates for advanced YIELD or STOP markings and signs, all parameters are statistically significant at the 5 percent level. The area type term in the pedestrian crash model is consistent with the other models in terms of the direction of effect, however, and is statistically significant at the 10 percent level. For the presence of PHB, the estimated parameters indicate that fewer pedestrian crashes are expected when a PHB is present, and all other crash categories increase. Greater numbers of crashes of all types are expected with increases in vehicle and pedestrian AADT. With the excep- tion of pedestrian crashes, the models also indicate that more crashes are expected at inter sections than at midblock crossings. The CMF implied for pedestrian crashes by the parameter estimates for PHBs is provided in Table 4-19. The p-value for pedestrian crashes is on the high side, but, as with advanced YIELD or STOP markings and signs, because the direction of the effect is intuitive (CMF < 1), the point esti- mate of the CMF for pedestrian crashes is still recommended for application. No CMFs are recom- mended for the other crash types due to the statistical significance and/or illogical effects implied. Table 4-18. Parameter estimates for PHB models. Parameter Estimate (standard error) Parameter Pedestrian Total Injury RE+SS* Injury RE+SS a −7.1959 (1.2593) −3.5996 (0.6295) −4.1974 (0.7043) −5.8685 (0.7804) −7.9532 (0.93400 b −0.3930 (0.3013) 0.5446 (0.3288) 0.6080 (0.2510) 0.6450 (0.5089) 0.5600 (0.4275) c n/a −0.4191 (0.2341) −0.4275 (0.2313) −0.3189 (0.4036) −0.1172 (0.4124) d −0.5695 (0.3110) −0.2967 (0.1640) n/a n/a n/a e n/a 0.7576 (0.1287) 0.6913 (0.1400) 0.5589 (0.1448) 0.4390 (0.1505) f 0.3802 (0.1337) 0.3436 (0.0645) 0.2945 (0.0669) 0.4779 (0.0761) 0.5948 (0.0907) g 0.3141 (0.0522) 0.1003 (0.0269) 0.1126 (0.0282) 0.1107 (0.0260) 0.1266 (0.0283) overdispersion n/a 0.7213 (0.0319) 0.6791 (0.0477) 0.9983 (0.0555) 1.1413 (0.1063) *RE = Rear-end, SS = Sideswipe Table 4-19. CMFs for PHBs. Crash Type CMF (standard error) p-value PEDCRASH 0.675 (0.206) 0.1921 TOTCRASH Models do not support the recommendation of a CMF. INJCRASH TARGETCRASH INJTARGETCRASH

44 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments Rectangular Rapid Flashing Beacons The following model forms pertain to each crash type. The models predict the expected num- ber of crashes per year. The model for pedestrian crashes used the CMFs estimated for pedes- trian refuge islands, advanced YIELD or STOP markings and signs, and PHBs as offsets in the PEDCRASH model because the data included sites with these treatments. For the other crash types, the data did not include sites with pedestrian refuge islands or PHBs, and the presence of advanced YIELD or STOP markings and signs was also included in the model. _ _ _ _ PEDCRASH exp AADT PEDAADT TOTCRASH exp AADT PEDAADT INJCRASH exp AADT PEDAADT TARGETCRASH exp AADT PEDAADT INJTARGETCRASH exp AADT PEDAADT a City b RRFB Presence f g a City b RRFB Presence+c Advance StopYield Sign Presence+d AreaType e Midblock int f g a City b PHB Presence+c Advance StopYield Sign Presence+e Midblock int f g a City b RRFB Presence+c Advance StopYield Sign Presence+e Midblock int f g a City b RRFB Presence+c Advance StopYield Sign Presence+e Midblock int f g               = = = = = ( ) ( ) ( ) ( ) ( ) + + + + + + + + + + + where AADT = total AADT on roadway being crossed Advance Stop Yield Sign Presence = 1 if present, 0 if not present AreaType = 1 if Suburban, 0 if Urban City = an intercept term specific for each city Midblock_Int = 1 if intersection, 0 if midblock PEDAADT = total pedestrian AADT for midblock or intersection RRFB Presence = 1 if present, 0 if not present Parameter estimates for all models are shown in Table 4-20. The estimates for city are not provided in the interest of brevity and they do not impact the estimated CMFs. The city variable was included in the models to account for differences in expected crashes between jurisdictions that are not related to the treatment. Parameter Estimate (standard error) Parameter Pedestrian Total Injury RE+SS* Injury RE+SS a −7.0997 (1.5901) −3.5339 (0.6395) −3.9171 (0.7733) −5.0199 (0.7179) −5.5874 (1.1623) b −0.6427 (0.6672) −0.1053 (0.1960) −0.0661 (0.2183) 0.2145 (0.2044) −0.6618 (0.5498) c n/a −0.2768 (0.2062) −0.2855 (0.2662) 0.2899 (0.1835) −0.0798 (0.4304) d n/a −0.3214 (0.1803) n/a n/a n/a e n/a 0.4602 (0.1611) 0.4155 (0.1697) 0.4216 (0.1467) 0.3952 (0.2333) f 0.2336 (0.1386) 0.3188 (0.0685) 0.2401 (0.0771) 0.2693 (0.0730) 0.2534 (0.1094) g 0.4198 (0.0876) 0.1111 (0.0442) 0.1029 (0.0451) 0.1041 (0.0366) 0.0947 (0.0598) overdispersion n/a 0.8504 (0.0618) 1.0210 (0.1167) 1.3313 (0.1007) 2.0417 (0.3518) *RE = Rear-end, SS = Sideswipe Table 4-20. Parameter estimates for RRFB models.

Data Analysis 45 The parameter estimates for presence of RRFB are of low statistical significance. With the exception of the parameter estimate for area type in the total crash model and the estimates for advanced YIELD or STOP markings and signs, all parameters are statistically significant at the 5 percent level. The area type term in the total crash model is consistent with the other models in terms of the direction of effect, however, and is statistically significant at the 10 per- cent level. The estimated parameters indicate that if RRFB is present, fewer pedestrian, total, and target injury crashes are expected, but at the same time, more target crashes are expected. Greater num- bers of crashes of all types are expected at higher levels of vehicle and pedestrian AADT. With the exception of pedestrian crashes, the models also indicate that more crashes are expected at intersections than at midblock crossings. For total crashes, fewer crashes are expected in sub- urban areas versus urban areas. The CMF for pedestrian crashes implied by the parameter estimates for RRFBs is provided in Table 4-21. As was the case for advanced YIELD or STOP markings and signs, because the direction of the effect is intuitive (CMF < 1), the point estimate of the CMF for pedestrian crashes is still recommended for application since the high p-value is likely a result of the scar- city of these crashes. No CMFs are recommended for the other crash types due to the statistical significance and/or illogical effects implied. For example, the parameter estimate for presence of RRFBs for target crashes would indicate an increase in crashes of 24 percent, which seems large and hard to explain by logical considerations. Comparison of Before-After and Cross-Sectional Study Results Table 4-22 summarizes the results from the before-after and cross-sectional analyses for treat- ments and crash type cases where the analyses support a CMF recommendation. As is evident, a comparison of results from the two studies is only possible for pedestrian crashes, the main target crash type. In general, the before-after results, where they could be obtained, corroborate the direction of effect for pedestrian crashes from the cross-sectional analysis and, in the case of refuge islands, the order of magnitude. For the other treatments, advanced YIELD or STOP markings and signs, PHB, and PHB + advanced YIELD or STOP markings and signs, the CMF point estimates are larger (the benefits smaller) for the cross-sectional study, which might be expected on theoretical grounds as a result of the issues with cross-sectional studies. However, given the large standard errors, in particu- lar for the CMFs for the cross-sectional analysis, it cannot be concluded that the estimates are different statistically. Crash Type CMF (standard error) p-value PEDCRASH 0.526 (0.377) 0.3354 TOTCRASH Models do not support the recommendation of a CMF. INJCRASH TARGETCRASH INJTARGETCRASH Table 4-21. CMFs for RRFBs.

46 Development of Crash Modification Factors for Uncontrolled Pedestrian Crossing Treatments Consolidation of Analysis Results As presented in Table 4-22, credible CMFs for pedestrian crashes and vehicle-involved crashes were estimated by either cross-sectional or before-after analysis, or both, for refuge islands, advanced YIELD or STOP markings and signs, PHB, and PHB + advanced YIELD or STOP mark- ings and signs. The CMF for RRFB was based on a very limited sample, and hence should be used with caution. As noted above, results from the before-after and cross-sectional analyses are only reported for treatments and crash type cases where the analyses support a CMF recommendation. The two methods have strengths and limitations. Although the before-after analysis is pre- ferred, especially the EB approach used for this research, the limited sample size of sites and crashes limits the robustness of the results. By contrast, the well-known limitations of deriving CMFs from cross-sectional regression analysis suggest that results obtained from that analysis, albeit from a substantial sample, should be interpreted and used with caution. It is encouraging, however, that the results of the limited before-after study corroborate those from the cross- sectional study for pedestrian crashes, the main crash type of interest. On balance, it is difficult to choose one approach over another where two sets of results are obtained, as was the case for pedestrian crashes, which logically suggests that equal weighting of the CMFs is not unreasonable for recommending CMFs for practical application. With this in mind, where there are two CMFs in Table 4-22, the median point values are presented in Table 4-23 as a final recommendation for practical application. Where there is a CMF value from only one study, that value is recommended. In each case, there is an appropriate annotation indicating the basis of the recommendation. For practical applications where a conservative benefit estimate is desired for a contemplated treatment, the higher of two CMF values from Table 4-22 is recom- mended. However, as a general caution, in the application of the CMFs, users should consider the Treatment Crash type Cross-sectional study Before-after study Estimate Standard error Estimate Standard error Refuge Island Pedestrian 0.699 0.152 0.671 0.215 Total 0.742 0.071 All Injury 0.714 0.082 Rear-End/Sideswipe Total 0.741 0.093 Rear-End/Sideswipe Injury 0.722 0.106 Advanced YIELD or STOP Markings and Signs Pedestrian 0.863 0.290 0.636 0.169 Total 0.886 0.065 Rear-End/Sideswipe Total 0.800 0.076 PHB Pedestrian 0.526 0.206 0.38* n/a PHB + Advanced YIELD or STOP Markings and Signs Pedestrian 0.62** 0.140 0.244 0.128 Total 0.820 0.078 Rear-End/Sideswipe Total 0.876 0.111 RRFB Pedestrian 0.526 0.377 *As mentioned earlier, the sample size for the PHB alone treatment was very limited for conducting a before-after evaluation. However, the before-after evaluation estimated CMFs for advanced YIELD or STOP markings and signs and PHB + advanced YIELD or STOP markings and signs combinations. Using these results and assuming that CMFs are multiplicative for treatment combinations, the CMF for PHB alone was calculated as the CMF for PHB + advanced YIELD or STOP markings and signs divided by the CMF for advanced YIELD or STOP markings and signs, i.e., 0.244/0.636 = 0.38. **Estimated for comparison purposes Table 4-22. CMFs from before-after and cross-sectional analyses.

Data Analysis 47 summary statistics in Tables 4-6 to 4-13 to see how closely the site under consideration for one of the treatments resembles the sites used to develop the CMF. As mentioned earlier, CMFunctions were explored in order to determine the effectiveness of the treatments under study in relation to different levels of AADT, posted speed limit, area type, number of lanes, and other factors. However, the CMFunctions did not provide useful results. Future research could focus on developing CMFunctions and, at the very least, investi- gate whether the treatments considered in this study are more or less effective under different conditions. Table 4-23. Recommended CMFs. Treatment Crash Type Recommended CMF Study Basis Estimate Standard Error Refuge Island (RI) Pedestrian 0.685 0.183 Median from two studies Total 0.742 0.071 Cross-section All Injury 0.714 0.082 Cross-section Rear-End/Sideswipe Total 0.741 0.093 Cross-section Rear-End/Sideswipe Injury 0.722 0.106 Cross-section Advanced YIELD and STOP Markings and Signs Pedestrian 0.750 0.230 Median from two studies Total 0.886 0.065 Before-after Rear-End/Sideswipe Total 0.800 0.076 Before-after PHB Pedestrian 0.453 0.167 Median from two studies PHB + Advanced YIELD and STOP Markings and Signs Pedestrian 0.432 0.134 Median from two studies Total 0.820 0.078 Before-after Rear-End/Sideswipe Total 0.876 0.111 Before-after RRFB Pedestrian 0.526 0.377 Cross-section