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NCHRP 3-78b: Final Project Report April 2016 117 8 APPENDIX B: YIELD MODEL DETAILS This appendix summarizes the yield modeling results for the combined data for TOPR-34 and NCHRP 3-78b. In order to create models to predict driver yielding rates for blind and sighted pedestrians, Stata was used to analyze data collected at two-lane roundabouts in Ohio, Maryland, Michigan, North Carolina, Washington, Oregon, Indiana, Wisconsin, and New York. 8.1 Introduction A contributing factor to the accessibility concerns of many multi-lane roundabouts is believed to be the low yielding rates at these sites. Yielding rate is one of the critical performance measures for accessibility identified by members of this team in NCHRP Report 674 (Schroeder et al., 2011). There is strong evidence from research that RRFBs increase yielding at single-lane roundabouts, but it is unclear if a similar increase in yielding would be seen at multi-lane roundabouts. This question is explored in this task through empirical research at various two-lane roundabouts with and without RRFBs in the United States. In addition, the effect of geometric variables, such as fastest path radius, and behavioral variables, such as average vehicle speed at crosswalk, on yielding will also be investigated. This study seeks to better understand driver yielding behavior and what behavioral and site attributes affect driver yielding probability. 8.2 Methodology 8.2.1 Data Collection A naturalistic yielding study was performed to determine the driver yielding rate using randomly generated pedestrian events at the crosswalk with and without the use of a long white cane. Because the analysis focuses on the probability of yielding, the research team derived the dependent variable, yielding rate, from observed active yields at each site. Active yields are defined as those events where the motorist slowed or stopped for a crossing pedestrian or a pedestrian waiting on the curb to cross and the pedestrian was the only reason the motorist stopped or slowed. Yield probability is calculated by dividing the total number of active yields by the sum of active yields and no yields. ððððð ðððððððððð¡ð¦ = # ðð ð´ðð¡ðð£ð ðððððð ðð¢ð ðð ð´ðð¡ðð£ð ðððððð ððð ðð ðððððð The research team did not consider passive yields, or those events where the motorist yielded to the pedestrian, but was already stopped for another reason, since passive yields are typically primarily a function of traffic volume and not related to geometric factors. Data collection was planned for periods during which the occurrence of passive yields was limited (times without excessive congestion). In the experiment, the pedestrian waited at the edge of the curb facing the direction of travel across the crosswalk with their head turned toward oncoming traffic to indicate their intention to make the crossing. The pedestrian accepted (completed the crossing from the curb to the splitter island) a yield or a gap. Vehicles in both lanes in the direction of interest were considered when classifying driver behavior. To avoid confusing drivers and the collection of inaccurate data, the pedestrian continued to walk beyond the end of the crosswalk before beginning another trial. To avoid any unusual reactions by motorists, the pedestrian wore no unusually bright or distracting attire. Trials were performed at the entry or exit leg in a randomized order. Approximately half of the trials employed the use of a long white cane, to simulate the arrival of a blind pedestrian. In all of the trials, the
NCHRP 3-78b: Final Project Report April 2016 118 pedestrian took one step âintoâ the crosswalk in accordance with most statesâ yielding laws. Variables collected are shown in Table 9-1. Table 8-1: Variables of Interest in Yielding Study Factor Description Value Independent Variables EXT Exit or entry approach of roundabout Exit=1, Entry=0 RDS Fastest path radius of roundabout in feet Continuous variable XSPD_AVE Average vehicle speed at crosswalk in mph Continuous variable RRFB Presence of RRFB at crosswalk Yes=1, No=0 SIGHT_D Pedestrian crossing sight distance Not provided=1, Provided=0 OL_DEC Overlapping driver decision points 1=Present, 0=Not Present Dependent Variable YIELDR Yielding rate for all subjects Continuous variable 8.2.2 Modeling Approach Stata was used to analyze the data collected in order to create a model to predict the probability of a driver yielding to a pedestrian or pedestrians on a crossing event. In preparation for modeling, observations were removed if yielding information was missing. Sites with one or three lanes at the crosswalk and sites with slip lanes were not included in this analysis. The sample sizes for each state and overall are provided in Table 8-2, and a table with detailed site information can be found in Appendix A. Each observation represents one site for each state with a yielding rate derived from no less than 15 trial crossings (Max=27; Min=15; Average=21) at the site. The results of a Student T-Test for Independent Means (T-value=0.590; p-value=0.557) indicate no significant difference between yielding rates for âblindâ pedestrians and yielding rates for âsightedâ pedestrians, so the yielding rates were combined as the response variable, YIELDR. Table 8-2: Sample Sizes by State State # of Observations (With Cane-âBlindâ) # of Observations (Without Cane-âSightedâ) Total # of Observations for Study Ohio 3 3 6 Maryland 1 1 2 Michigan 3 3 6 North Carolina 4 4 8 Washington 5 5 10 Oregon 4 4 8 Indiana 2 2 4 Wisconsin 2 3 5 New York 3 3 6 TOTAL 27 28 55 In the first step of modeling, a correlation table was created to determine if any variables are significantly related to each other, or intercorrelated. In the next step, multivariable linear regression models were generated to predict the driver yielding rates, taking into account macroscopic site conditions. Predicted yielding rates were produced based on two variable selection processes:
NCHRP 3-78b: Final Project Report April 2016 119 â¢ Full Model â uses all independent variables regardless of p-value. â¢ Manual Selection â a custom model that is informed by the first modeling result and examination of correlation and collinearity, and considers practical significance and feasibility of implementing variables in simulation rather than focusing on statistical fit. 8.3 Results 8.3.1 Descriptive Statistics Data analysis began with finding the mean, standard deviation, maximum, and minimum for all variables used in the modeling process. The descriptive statistics help characterize the geometric and treatment features at each study site based on the data collected, and offer a better understanding of data trends and variability. Values are provided in relation to the dependent variable of interest, YIELDR. The average yielding rate for âblindâ pedestrians was 72.3% while the average yielding rate for âsightedâ pedestrians was 67.5%. The average yielding rate for all pedestrians was 69.9%. The average speed at crosswalk for the sites was 21 mph. Data showed that half the sites were located at roundabout exits. Over 70% (18) of the sites featured RRFBs, while three sites (11%) featured raised crosswalks and two sites (7%) featured sound strips or rumble strips. Raised crosswalks, sound strips, and rumble strips were not included as explanatory variables in the analysis due to the small sample size. Further descriptive statistics are provided below. Table 8-3: Descriptive Statistics for Roundabout Sites All Data Variable N Mean StdDev Max Min Dependent Variables YIELDR 55 69.9 29.5 100 0 Independent Variables EXT 55 0.49 0.50 1 0 RDS 55 311 280 1000 73 XSPD_AVE 55 20.9 3.7 29 13 RRFB 55 0.64 0.5 1 0 SIGHT_D 55 0.33 0.47 1 0 OL_DEC 55 0.42 0.50 1 0 8.3.2 Correlation A summarized version of the Pearson correlation table showing the correlation between the yielding rate for all pedestrians and the explanatory variables is shown in Table 8-4. Correlation coefficients are provided with the significance level indicated by superscripted asterisks. The following variables show a significant negative or inverse correlation with the YIELDR variable, suggesting a decrease in yielding with an increase in the variable (or binary variable change from 0 to 1): EXT, RDS, XSPD_AVE, SIGHT_D, and OL_DEC. No significant correlation was found between RRFB and the dependent variable. Several of the independent variables are intercorrelated, which affects their suitability to be included in the same models due to multicollinearity. These intercorrelations will be addressed in the recommended models section to follow.
NCHRP 3-78b: Final Project Report April 2016 120 Table 8-4: Correlation Table for Roundabout Sites n=55 YIELDR EXT RDS XSPD_AVE RRFB SIGHT_D OL_DEC YIELDR 1.0000 Pe ar so n Co rr el at io n EXT -0.2494* 1.0000 RDS -0.5949* 0.5826* 1.0000 XSPD_AVE -0.3863* 0.6974* 0.7017* 1.0000 RRFB 0.1191 -0.0137 0.1252 -0.0187 1.0000 SIGHT_D -0.3639* 0.4002* 0.5098* 0.5235* 0.0439 1.0000 OL_DEC -0.2494** 0.1997 0.4232* 0.2718* 0.1811 0.1943 1.0000 *p<0.05, **p<0.10 8.4 Model Development The yielding rate is a continuous variable that is constrained to be between 0% and 100%, making it suitable for use in multivariable linear regression modeling. Regression diagnostics were applied to the dependent and explanatory variables to verify that the data met the assumptions of linear regression. The form of the multivariable linear regression model for yielding rate is: Y=a + b1X1 + b2X2 + b3X3 (â¦) Where: Y is the value of the dependent variable, what is being predicted or explained; a is the constant or intercept; b1 is the slope for X1, the first independent variable that is explaining the variance in Y; b2 is the slope for X2, the second independent variable that is explaining the variance in Y; b3 is the slope for X3, the third independent variable that is explaining the variance in Y; and b4 and onwards are the slopes for additional independent variables that explain the variance in Y. Based on this equation, if the values of all variables except one independent variable (Xi) are kept constant, one unit increase in the value of Xi will increase the value of the response variable Y by the slope of Xi. The R2 statistic is generally used in regression models to describe how much variability of the data is explained by the model. For multivariable linear regression models, the variability of the model can be evaluated by the adjusted R2 statistic, which is an adjustment of the R2 based on the number of observations and predictors in the model. Higher adjusted R2 is an indicator of a better fit of the model to the data and the proportion of the data that can be explained by the model. Final models were developed using a manual selection process informed by the results of modeling with all independent variables regardless of p-value, as well as the results of the correlation analysis. Significantly associated independent variables were not included in the same model. Two models were investigated to predict driver yielding behavior: 1) a geometric model including explanatory variables for approach, fastest path radius, treatment, pedestrian sight distance, and overlapping decision points, and 2) a behavioral model including explanatory variables for approach, average vehicle speed at crosswalk, and treatment. The full multivariable linear regression model results for each dependent variable are shown in Table 5. The parameter significance level is indicated by superscripted asterisks. Table 8-5 shows that factor RDS is significant to the model with p-value<0.05, and factor RRFB is significant to the model with p- value<0.10. The adjusted R2 value is 0.34.
NCHRP 3-78b: Final Project Report April 2016 121 Table 8-5: Full Model to Predict Yielding Rates to âBlindâ and âSightedâ Pedestrians All Sites Regression Coefficient Std Error p 95% Conf Interval EXT 4.652 9.218 0.616 -13.882 23.186 RDS -0.070 0.018 0.000* -0.107 -0.033 XSPD_AVE 0.761 1.477 0.609 -2.209 3.730 RRFB 13.074 6.941 0.066** -0.882 27.030 SIGHT_D -6.815 8.344 0.418 -23.591 9.962 OL_DEC -1.545 7.337 0.834 -16.298 13.207 Constant 68.111 27.016 0.015 13.792 122.430 Prob > F 0.000 R2 0.409 Adj. R2 0.335 *p<0.05, **p<0.10 After generating the full model, the data were examined for strong correlations and significant linear relationships between the independent variables. Strong collinearity effects were additionally corroborated by performing VIF (variance inflation factor) tests in Stata. Any two explanatory variables that were found to be significantly linearly related were not included in the same final model, but were evaluated as controls in the model building process. Significant linear relationships and strong significant correlations were found between: â¢ RDS and EXT â¢ XSPD_AVE and EXT â¢ XSPD_AVE and RDS â¢ SIGHT_D and EXT â¢ SIGHT_D and RDS â¢ OL_DEC and RDS Table 8-6 presents a summary of the model building process for the geometric model. The model with the highest adjusted R2 value includes fastest path radius and RRFB as explanatory factors for driver yielding behavior. Controlling for approach, pedestrian sight distance, and overlapping decision points, the factors fastest path radius and RRFB remain significant to the model (p<0.10) and their effect on yielding remains nearly the same as in the model that includes only fastest path radius and RRFB as variables of interest. Because the effects of the significant factors remain nearly the same when controlling for additional explanatory variables, it is reasonable to recommend Model 2. Table 8-6: Model Building Process for Geometric Yielding Model Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 RDS -0.063* -0.065* -0.072* -0.068* -0.071* -0.066* RRFB 11.947** 12.508** 12.471** 12.689** 12.664** EXT 6.132 6.977 6.056 6.901 SIGHT_D -5.796 -5.825 OL_DEC -1.410 -1.502 Constant 89.331 82.535 81.207 81.432 81.376 81.613
NCHRP 3-78b: Final Project Report April 2016 122 R2 0.354 0.392 0.399 0.406 0.400 0.406 Adj. R2 0.342 0.369 0.364 0.358 0.352 0.345 *p<0.05, **p<0.10 Table 8-7 presents a model for predicting driver yielding behavior based on geometric features of the roundabouts under study. The recommended geometric model estimates an 11.9% increase in the yielding rate in the presence of RRFB, and a 0.07% decrease in the yielding rate for every one foot increase in the fastest path radius. Table 8-7: Recommended Geometric Model to Predict Yielding Rates to âBlindâ and âSightedâ Pedestrians YIELDR Regression Coefficient Std Error p 95% Conf Interval RDS -0.065 0.011 0.000* -0.088 -0.042 RRFB 11.947 6.619 0.077** -1.335 25.229 Constant 82.535 6.057 0.000 70.380 94.690 Prob > F 0.000 R2 0.392 Adj. R2 0.369 *p<0.05, **p<0.10 Table 8-8 presents a summary of the model building process for the behavioral model. The model with the highest adjusted R2 value includes average speed at crosswalk in mph as an explanatory factor for driver yielding behavior. Controlling for approach and RRFB, average speed at crosswalk in mph remains significant to the model (p<0.05) with the same effect on yielding. Because average speed at crosswalk in mph is collinear with and acts as a proxy for approach, it is reasonable to recommend Model 2 for predicting driver yielding behavior based on driver behavior and the presence of treatments at the roundabouts under study. Table 8-9 presents a centered version of Model 2 using the average speed at crosswalk in mph and RRFB as predictors for yielding. Average speed at crosswalk in mph was centered to its mean (21 mph), which involved subtracting the mean from and dividing by the standard deviation (3.647) for each yielding value. Centering to the mean makes it simpler to interpret the constant, but gives the same result for predicting yielding by speed as the uncentered model. For the centered model, the mean yielding rate is 64% for the mean average speed at crosswalk, 21 mph. For every one mile per hour increase in the mean average speed at crosswalk, the yielding rate is estimated to decrease by approximately 12.0%. The model also estimates an 8.1% increase in the yielding rate in the presence of RRFB. Table 8-8: Model Building Process for Behavioral Yielding Model Model 1 Model 2 Model 3 XSPD_AVE -3.071* -3.055* 2.778** RRFB 6.799 6.797 EXT -2.919 Constant 134.077 129.402 125.046 R2 0.149 0.162 0.163 Adj. R2 0.133 0.130 0.114 *p<0.05, **p<0.10
NCHRP 3-78b: Final Project Report April 2016 123 Table 8-9: Recommended Behavioral Model to Predict Yielding Rates to âBlindâ and âSightedâ Pedestrians YIELDR Regression Coefficient Std Error p 95% Conf Interval centeredXSPD_AVE -11.996 3.518 0.001 -19.055 -4.937 RRFB 8.093 7.563 0.290 -7.084 23.270 Constant 64.050 6.040 0.000 51.929 76.171 Prob > F 0.004 R2 0.194 Adj. R2 0.163 *p<0.05, **p<0.10 8.5 Summary Multivariable linear regression models were generated to predict driver yielding rates to âblindâ and âsightedâ pedestrians at two-lane roundabouts in nine states in the United States. Since no significant difference was found between yielding rates to âblindâ and âsightedâ pedestrians, final models were created through manual selection informed by full modeling efforts and correlation analysis using the dependent variable of interest, driver yielding rate to all pedestrians (YIELDR). Separate models were created focusing on geometric and behavioral predictors for driver yielding behavior. Fastest path radius (RDS), presence of RRFB (RRFB), and average vehicle speed at crosswalk (XSPD_AVE) were found, in their respective models, to be significant explanatory factors for driver yielding to pedestrians at the two-lane roundabout sites. The recommended geometric model estimates an 11.9% increase in the yielding rate in the presence of RRFB, and a 0.07% decrease in the yielding rate for every one foot increase in the fastest path radius. The recommended behavioral model estimates an 8.1% increase in the yielding rate in the presence of RRFB, and estimates the yielding rate to decrease by approximately 12.0% for every one mile per hour increase in the mean average speed at crosswalk (21 mph). Table 8-10: Detailed Site Information for Yield Models # State City Intersection Name Approach Location 1 OH Hilliard Cemetery/Main East Entry 2 OH Hilliard Cemetery/Main East Exit 3 OH Hilliard Cemetery/Main West Exit 4 MD Greenbelt Cherrywood/Metro West Entry 5 MI Ann Arbor Ellsworth/State West Entry 6 MI Ann Arbor Ellsworth/State West Exit 7 MI Novi Maple/Farmington South Entry 8 MI Novi Maple /Farmington North Exit 9 NC Davidson Davidson Gateway-Harbour Place/Griffith East Entry 10 NC Davidson Davidson Gateway-Harbour Place/Griffith East Exit 11 NC Davidson Davidson Gateway-Harbour Place/Griffith West Entry
NCHRP 3-78b: Final Project Report April 2016 124 12 NC Davidson Davidson Gateway-Harbour Place/Griffith West Exit 13 WA Olympia 4th/Olympic East Entry 14 WA Olympia 4th/Olympic North Entry 15 WA Olympia 4th/Olympic North Exit 16 WA Olympia 14th/Jefferson East Entry 17 WA Olympia 14th/Jefferson East Exit 18 OR Springfield Pioneer/Hayden Bridge East Entry 19 OR Springfield Pioneer/Hayden Bridge East Exit 20 OR Springfield Pioneer/Hayden Bridge South Entry 21 OR Springfield Pioneer/Hayden Bridge South Exit 22 IN Carmel Clay Terrace/Clay Terrace North Entry 23 IN Carmel Clay Terrace/Clay Terrace North Exit 24 WI Oshkosh Jackson/Murdock South Entry 25 WI Oshkosh Jackson/Murdock South Exit 26 WI Oshkosh Jackson/Murdock East Entry 27 WI Oshkosh Jackson/Murdock East Exit 28 NY Albany Fuller/Washington North Exit 29 NY Albany Fuller/Washington South Entry 30 NY Albany Fuller/Washington South Exit