Development of Decision Support Tools to Assess Pedestrian and Bicycle Safety: Development of Safety Performance Function Valerian Kwigizile, Jun Oh, Ron Van Houten, & Keneth Kwayu
INTRODUCTION 2
OVERVIEW v Introduction v Objectives v Literature review v Preliminary data collection and site selection v Detailed data collection v Development of surrogate measure of non-motorized exposure v Development of safety performance functions v Conclusions 3
INTRODUCTION v Walking and biking are forms of transportation that offers basic mobility for all people. v In communities were walking and biking is encouraged, it improve quality of life Reduce obesity and other health related problems Reduce air pollution and congestion Boost local economy by inviting retail merchant to invest in places near homes and working places 4
INTRODUCTION v In USA, trips that are done by walking and bicycling rose from 9.5% in 2001 to 11.9% in 2009 (National Household Travel Survey, 2009) v Bicyclist and pedestrian are 2.3 and 1.5 times, respectively, more likely be killed in a crash for each trip as compared to vehicle occupants(beck et al, 2007) v Therefore there is a need for developing framework for identifying locations with the highest risk for non-motorized road users and propose appropriate countermeasures. 5
INTRODUCTION v Non-motorized Safety Performance Functions(SPFs) is one of the good approach for quantifying non-motorized risk v However there are challenges in developing robust SPFs such as Lack of non-motorized counts Non-motorized crashes are rare event, therefore poses some difficulties in applying modeling techniques 6
OBJECTIVE Develop a methodology for developing statewide safety performance function for pedestrian and bicyclist at intersection Specifically the methodology addressed the following v Proper sampling procedure in coming up with unbiased sample size for model development v Developing proxy measure of pedestrian and bicyclist exposure using data that are readily available at statewide level v Assessment of SPF performance using cross-validation technique 7
SITE SELECTION 8
SITE SELECTION Sampling Strategy and Preliminary Data Collection Aggarwal(1988) 9
SITE SELECTION Identifying target population Urban intersections with collector and arterial roads. 10
SITE SELECTION Subdividing the target population into Subgroup Parameters Subcategory Road function Intersection connecting arterial roads Intersection connecting arterial road and collector road Intersection connecting collector roads. Intersection type Three leg intersection Four leg intersection Urban population 5000-49,999 50,000-199,999 200,000-more Non-motorized crashes: Pedestrians and No crash observed Bicyclists crashes(2004-2014) 1-5 crashes 6-10 crashes >10 crashes 11
SITE SELECTION Sample size computation Whereby w " = N " N %&% S " = w " N w " = Weighted factor for intersections in group i N " = Number of intersections in group i N %&% =Total number of intersections for all groups S " = Number of intersections withdrawn from group i N = Required total sample size from all groups 12
SITE SELECTION Site selection for Arterial-Arterial intersections Similar procedure was applied for arterialcollector and collector-collector intersections Intersection type 3 leg 4 leg no/wi Urban population no/wi no Nonmotorized Crashes No. Weight (Wi) Sample size (N) Sample size(si) Wi xn 1 0 228 0.0203 500 11 5000-49,999 262 2 1-5 34 0.0030 500 2 0.023 3 6-10 0 0.0000 500 0 4 11-16 0 0.0000 500 0 1 0 285 0.0254 500 13 1890 50,000-337 2 1-5 51 0.0045 500 3 0.169 199,9999 0.030 3 6-10 1 0.0001 500 1 4 11-16 0 0.0000 500 0 1 0 1072 0.0956 500 48 200,000-more 1291 2 1-5 219 0.0195 500 10 0.115 3 6-10 0 0.0000 500 0 4 11-16 0 0.0000 500 0 1 0 293 0.0261 500 14 5000-49,999 448 2 1-5 149 0.0133 500 7 0.0400 3 6-10 6 0.0005 500 1 4 11-16 0 0.0000 500 0 1 0 401 0.0358 500 18 3273 50,000-702 2 1-5 293 0.0261 500 14 0.292 199,9999 0.063 3 6-10 8 0.0007 500 1 4 11-16 0 0.0000 500 0 1 0 1034 0.0922 500 47 200,000-more 2123 2 1-5 1019 0.0909 500 46 0.189 3 6-10 64 0.0057 500 3 13 4 11-16 6 0.0005 500 1
DATA COLLECTION 14
DATA COLLECTION Data that were collected; v Non-motorized crash data(2010-2014) v Demographic data v Land use data v Traffic volume data v Road Geometry data v Walk score index 15
DATA COLLECTION Non-motorized crash data 16
DATA COLLECTION Landuse data 17
DATA COLLECTION Geometric Characteristics v Signal information v Intersection type v Lane use information v Bicycle and pedestrian facilities information v On-street parking information v Presence/absence of median v One way or two way Top view Lane use information Bike and pedestrian facility Street view Signal information Signal configuration All the data were collected manually from Google Earth Pro 18
DATA COLLECTION Census data v Population v Race v Poverty status v Educational level v Means of transportation to work Public transit, walking and biking 19
DATA COLLECTION Walk score data v Walk score Index measures walkability of a given point or area on a scale of one to one hundred v Distance decay function is used to model score index v Amenity that have 5min walk get the maximum points and the point keep on diminishing up to zero after 30 min walk Score Definition 90-100 Walkers Paradise Daily trips do not require a car 70-89 Very Walkable Most trip can be accomplished on foot 50-69 Somewhat Walkable Some trips can be accomplished on foot. 25-49 Car Dependent Most trips require a car 0-24 Car Dependent almost all trips require a car 20
DEVELOPING SURROGATE MESURE FOR NON-MOTORIZED EXPOSURE 21
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis v This is the multivariate technique which aims at explaining the joint variation and covariation of observed variables using latent variables. Using matrix notation, factor analysis can be presented as Whereby y +,- y - y + +,- = = Observed variables matrix y +,- = Σ +,/ F /,- + e +,- λ -- λ -+ F - F λ +- λ / /,- +/ +,/ Σ +,/ = variance-covariance matrix which comprises of factor loadings, λ +/ F /,- = Factor Matrix e +,- = Error term + e - e + +,- 22
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis v Estimation procedure utilized Maximum Likelihood approach by minimizing the following function Γ /9 = ln Σ ln S + trace (S)(Σ D- ) p Where Γ /9 = Log likelihood function Σ = Determinant of predicted covariance-variance matrix S = Determinant of observed covariance-variance matrix p = Number of input indicators/observed variables Trace= Sum of the diagonal values in the covariance-variance matrix 23
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Computation of factor score Whereby f " = (Σ D- Λ) "K+ Factor score = J fi (x " x ") "K- f " = the factor score weight for observed variable i Σ D- = Inverse of observed variable covariance matrix Λ = Factor-observed variable covariance matrix x " = the observed variable i x " = the mean of observed variable i 24
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model specification-pedestrian level score 25
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model Estimation-Pedestrian level score Variable Standardized Coef. Std. Err. z P>z Percent using public transport 0.5397 0.0440 12.26 0 Population per square mile 0.6959 0.0345 20.17 0 Percent of poverty below 0.6131 0.0392 15.65 0 Walking per square mile 0.5299 0.0448 11.82 0 Pedestrian facility 0.2568 0.0545 4.72 0 Walk score 0.8347 0.0288 29.01 0 Proportion of commercial land use 0.3244 0.0518 6.26 0 26
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model specification-bicyclist level level score 27
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model Estimation-Bicycle level score Variable Standardized Coef. Std. Err. z P>z Bike facility 0.3713 0.0547 6.79 0 Poverty level below 0.4860 0.0507 9.59 0 Population per square mile 0.5454 0.0496 11.01 0 Speed limit major -0.7318 0.0415-17.61 0 Speed limit minor -0.6646 0.0423-15.7 0 Proportion of commercial land use 0.1358 0.0601 2.26 0.024 28
NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Factor score Pedlevel = 0.0707 perc VWX9 0.974 + 0.0008 pop \]/"9^ 420.178 + 0.0153cpov %&%efg 13.473h + 0.0011 walking ]/"9^ 36.32 + 0.1233 ped mno9%p 0.586 + 0.0244(walkscore 35.772) + 0.2828 pro o&// 0.146 Bikelevel = 0.0415 bike mno"9"%p 0.598 + 0.0021 pov %&%efg 13.44 + 0.0001(pop_sqmile 419.052) 0.0086(speedlmt_min 34.893) 0.0063(speedlmt_maj 42.828) + 0.0231(pro_comm 0.146) 29
DEVELOPING SPFs 30
DEVELOPING SPFs Introduction v Parameter were estimated using maximum likelihood approach v The counts model that were considered for the analysis are listed below: Poisson Regression Model (NRM) Negative Binomial Regression Model (NBRM) Zero Inflated Poisson Regression Model (ZIP) Zero Inflated Negative Binomial Model (ZINB) 31
DEVELOPING SPFs Goodness of fit tests Goodness of fit measure for comparing the competing count data models Akaike s Information Criterion (AIC) AIC = 2L + 2k n Bayesian Information Criterion (BIC) BIC = 2L + klog(n) k=number of predictors including the intercept n= number of observation L= model log-likelihood. 32
DEVELOPING SPFs Introduction to classical approach Residual probability plot Difference between residual and predicted probability Root Mean Square Error(RMSE) RMSD = "K- (y " y " ) ƒ N y " = predicted pedestrian/bicyclist crashes for intersection i y " = observed pedestrian/bicyclist crashes for intersection i N= total number of intersections 33
DEVELOPING SPFs Data Description Density 0.1.2.3.4.5.6.7 Density 0.1.2.3.4.5.6.7.8 0 1 2 3 4 5 6 Pedestrian crashes 0 1 2 3 4 5 6 7 8 Bicycle crashes v Total number of intersection=240 v 85%of intersection-model estimation and 15%- Model validation 34
DEVELOPING SPFs Model estimation-pedestrian SPFs Variable PRM NBRM ZIP ZINB AADT major approach 0.0352 (3.84) 0.0361 (3.3) 0.0234 (2.14) 0.0234 (2.13) AADT minor approach 0.0433 (3.02) 0.0454 (2.6) 0.0405 (2.51) 0.0409 (2.49) Pedestrian level score 0.5204 (9.19) 0.5627 (7.81) 0.2329 (2.69) 0.2392 (2.59) Constant term -1.912 (10.36) -1.965 (-9.45) -1.094 (-4.46) -1.1117 (-4.27) Over dispersion parameter alpha 0.319 0.027 Inflate(For zero-inflated models) Pedestrian level score -2.375 (-4.31) -2.403 (-4.18) Constant -0.9181 (-1.88) -0.972 (-1.73) 35
DEVELOPING SPFs Model estimation-bicycle SPFs Variable PRM NBRM ZIP ZINB AADT major approach 0.0334 (3.72) 0.0406 (2.69) 0.0217 (2.15) 0.0347 (2.37) AADT minor approach 0.0801 (6.29) 0.0870 (3.63) 0.0730 (5.15) 0.087 (3.91) Bicycle level score 3.487 (6.75) 3.561 (4.64) 1.593 (2.07) 2.007 (1.94) Constant term -1.949-2.144-0.895-1.637 (-11.29) (-8.39) (-3.56) (-4.29) Over dispersion parameter alpha 1.561 0.801 Inflate(For zero inflated models) Bicycle level score -3.677-5.839 (-2.34) (-1.73) Constant 0.177 (0.77) -0.903 (-1.12) 36
DEVELOPING SPFs Model comparison v AIC and BIC-The lower the better v ZIP had lower AIC and BIC values for pedestrian SPF v NBRM had lower AIC and BIC values for Bicyclist SPF Information criteria(aic and BIC) for pedestrian-involved crashes Information criteria(aic and BIC) for Bicyclist-involved crashes 570 560 550 563.6564.3 556.5 550.7 548.3 545.2 700.0 680.0 660.0 677.5 662.2 540 530 520 527.8 529.7 640.0 620.0 600.0 633.4 626.7 618.3 610.5 599.2 599.9 510 580.0 500 BIC AIC 560.0 BIC AIC PRM NBRM ZIP ZINB PRM NBRM ZIP ZINB 37
DEVELOPING SPFs Model comparison v Residual probability Within sample residual probability 38
DEVELOPING SPFs Out-of-sample residual probability 39
DEVELOPING SPFs Final Models Pedestrian SPF Where Number of pedestrian crashes per five years = 1 1 ed-.ˆ ˆ.ˆƒŒ nn % ˆ.ˆ ˆŽnn % ˆ.ƒŒ ƒv^ 9^ ^9 1 + e (ˆ. -Š ƒ.œ ŽV^ 9^ ^9) v aadt /n = AADT in the major approach in thousands v aadt /"+ = AADT in the minor approach in thousands v pedlevel = Pedestrian level score 40
DEVELOPING SPFs Bicycle SPF Number of Bike crashes per five years = Where e (Dƒ.-- ˆ.ˆŠ nn % Œ.Ž -nn % Dƒ.- X" ^9^ ^9) v aadt /n =AADT in the major approach in thousands v aadt /"+ =AADT in the minor approach in thousands v bikelevel =Bicycle level score 41
CONCLUSIONS AND RECOMMENDATION v Proper sampling technique was introduced to get the representative sample of the target population(urban intersections in Michigan) v Non-motorized surrogate measure of exposure were developed from data inventory that is available at statewide level v Methodology formulated in this study can be used to develop nonmotorized SPFs at county level, census tract, census block group and at corridor level for instance at the road mid-blocks areas v Transferability of the model is possible provided that proper calibration factors are applied 42