Development of Decision Support Tools to Assess Pedestrian and Bicycle Safety: Development of Safety Performance Function

Transcription

1 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

2 INTRODUCTION 2

3 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

4 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

5 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

6 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

7 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

8 SITE SELECTION 8

9 SITE SELECTION Sampling Strategy and Preliminary Data Collection Aggarwal(1988) 9

10 SITE SELECTION Identifying target population Urban intersections with collector and arterial roads. 10

11 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 ,999 50, , ,000-more Non-motorized crashes: Pedestrians and No crash observed Bicyclists crashes( ) 1-5 crashes 6-10 crashes >10 crashes 11

12 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

13 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 , , , ,000-more , , , ,000-more

14 DATA COLLECTION 14

15 DATA COLLECTION Data that were collected; v Non-motorized crash data( ) v Demographic data v Land use data v Traffic volume data v Road Geometry data v Walk score index 15

16 DATA COLLECTION Non-motorized crash data 16

17 DATA COLLECTION Landuse data 17

18 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

19 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

20 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 Walkers Paradise Daily trips do not require a car Very Walkable Most trip can be accomplished on foot Somewhat Walkable Some trips can be accomplished on foot Car Dependent Most trips require a car 0-24 Car Dependent almost all trips require a car 20

21 DEVELOPING SURROGATE MESURE FOR NON-MOTORIZED EXPOSURE 21

22 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

23 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

24 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

25 NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model specification-pedestrian level score 25

26 NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model Estimation-Pedestrian level score Variable Standardized Coef. Std. Err. z P>z Percent using public transport Population per square mile Percent of poverty below Walking per square mile Pedestrian facility Walk score Proportion of commercial land use

27 NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model specification-bicyclist level level score 27

28 NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Model Estimation-Bicycle level score Variable Standardized Coef. Std. Err. z P>z Bike facility Poverty level below Population per square mile Speed limit major Speed limit minor Proportion of commercial land use

29 NON-MOTORIZED SURROGATE EXPOSURE MEASURE Factor analysis Factor score Pedlevel = perc VWX pop \]/"9^ cpov %&%efg h walking ]/"9^ ped mno9%p (walkscore ) pro o&// Bikelevel = bike mno"9"%p pov %&%efg (pop_sqmile ) (speedlmt_min ) (speedlmt_maj ) (pro_comm 0.146) 29

30 DEVELOPING SPFs 30

31 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

32 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

33 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

34 DEVELOPING SPFs Data Description Density Density Pedestrian crashes Bicycle crashes v Total number of intersection=240 v 85%of intersection-model estimation and 15%- Model validation 34

35 DEVELOPING SPFs Model estimation-pedestrian SPFs Variable PRM NBRM ZIP ZINB AADT major approach (3.84) (3.3) (2.14) (2.13) AADT minor approach (3.02) (2.6) (2.51) (2.49) Pedestrian level score (9.19) (7.81) (2.69) (2.59) Constant term (10.36) (-9.45) (-4.46) (-4.27) Over dispersion parameter alpha Inflate(For zero-inflated models) Pedestrian level score (-4.31) (-4.18) Constant (-1.88) (-1.73) 35

36 DEVELOPING SPFs Model estimation-bicycle SPFs Variable PRM NBRM ZIP ZINB AADT major approach (3.72) (2.69) (2.15) (2.37) AADT minor approach (6.29) (3.63) (5.15) (3.91) Bicycle level score (6.75) (4.64) (2.07) (1.94) Constant term (-11.29) (-8.39) (-3.56) (-4.29) Over dispersion parameter alpha Inflate(For zero inflated models) Bicycle level score (-2.34) (-1.73) Constant (0.77) (-1.12) 36

37 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 BIC AIC BIC AIC PRM NBRM ZIP ZINB PRM NBRM ZIP ZINB 37

38 DEVELOPING SPFs Model comparison v Residual probability Within sample residual probability 38

39 DEVELOPING SPFs Out-of-sample residual probability 39

40 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

41 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

42 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