24
Roadway Stratification Variables and Methods Ioannis (Yianni) Tsapakis Texas A&M Transportation Institute
Roadway Stratification Variables and Methods
Ioannis (Yianni) TsapakisTexas A&M Transportation Institute
2
AADT Estimation
A) Traffic Count Based
B) Non-Traffic Count Based
“Traditional” Approach and
Sampling
Non-Traditional Methods
Disaggregated Estimates at the Segment
Level
Aggregated Estimates
(e.g., County Level)
C) Travel Demand Models
B) Non-Traffic Count Based
C) Travel Demand Models
• Stratification Variables• Correlations with AADT• Decision Trees• Random Sampling
AADT Estimation
3
Number of CCSs on NFAS Roads
0
2
4
6
8
10
12
AK
AZ
DE
GA IA ID KY
LA ME
MI
MN
MO
MS
MT
NC
NE NJ
NM NV
NY
OH PA
SD TN TX VA
WV
WY
Nu
mb
er o
f CC
Ss o
n F
C6
& F
C7
4
Short-Duration Counts
State # Counts
North Carolina 24,365
Vermont 2,370
Virginia 93,937
AADT Distribution for FC 6R
Median=586
Median=1,100
Median=473
North Carolina
Vermont
Virginia
Data (>60 variables)Data Type Source Attribute/Variable
Roadway HPMS, DOTs network, FC, U/R, #lanes, pavement_type
Counts DOTs ADT, AADT, lat, long, route_name, year
CCSs (TMAS) FHWA AADT, FC, lat, long
Administrative FHWA Counties, cities
Demographic, Socioeconomic
U.S. Census Bureau, American CommunitySurvey
population, #households, #employed residents, #employees, travel_time_to_work, OD_flows, occupied_houses, household_income, household_earnings, per_cap_income, and corresponding densities…
Land UseUSGS, ESRI, DOTs, Other
farm_density, land_cover
Proximity TTIdistance_to_closest_IH, distance_to_closest_US,distance_to_closest_count_on_same_road,distance_to_closest_count_within_buffer
6R 7R 7U
Density_of_Workers_who_Work_in_a_Block 0.538 0.255 0.127
Population_Density 0.521 0.263 0.054
Housing_Unit_Density 0.506 0.233 0.056
Occupied_Housing_Unit_Density 0.501 0.255 0.051
Density_of_Workers_who_Live_in_a_Block 0.495 0.254 0.048
Vacant_Housing_Unit_Density 0.369 0.083 -0.030
Number_of_Workers_who_Work_in_a_Block 0.223 0.283 0.094
Per_Capita_Income_Last_12_Months_ACS 0.172 0.083 -0.019
Number_of_Workers_who_Live_in_a_Block 0.103 0.151 0.066
Population 0.102 0.143 0.091
VermontVariable
Correlations with AADT - VT
6R 7R 7U
Per_Capita_Income_Last_12_Months 0.229 0.086 -0.016
Density_of_Workers_who_Live_in_a_Block 0.204 0.408 0.123
Population_Density 0.202 0.404 0.126
Population 0.183 0.079 -0.006
Travel_Time_to_Work 0.174 0.098 0.019
Occupied_Housing_Unit_Density 0.171 0.402 0.132
Housing_Unit_Density 0.155 0.395 0.131
Number_of_Workers_who_Work_in_a_Block 0.155 0.117 0.074
Density_of_Workers_who_Work_in_a_Block 0.148 0.173 0.094
Occupied_Housing_Units 0.136 0.062 -0.005
VirginiaVariable
Correlations with AADT - VA
Stratification Example (Vermont)
Min Max Mean St. Dev. COV
1 206 3 6278 443 622 1.41
2 101 10 3400 415 490 1.18
3 206 10 6720 392 637 1.63
4 122 43 9766 1060 1427 1.35
5 40 10 956 265 257 0.97
6 202 30 3468 529 543 1.03
7 29 50 1051 399 255 0.64
8 103 20 3800 554 666 1.20
9 114 10 1577 441 326 0.74
10 181 10 4646 421 526 1.25
11 279 10 2768 348 381 1.10
12 228 3 3108 490 503 1.03
13 250 8 2421 379 392 1.03
14 308 10 4835 467 660 1.41
1.20
AADTCounty #
# Counts
(n)
Stratification Example (Vermont)
Min Max Mean St. Dev. COV
1 6R Low 178 20 1400 410 256 0.62
2 6R Medium 188 49 3108 662 465 0.70
3 6R High 85 203 6720 1038 937 0.90
4 7R Low 596 3 1700 175 186 1.07
5 7R Medium 599 10 3800 351 398 1.13
6 7R High 460 11 4835 609 655 1.08
7 7U Low 1 120 120 120 - 0.00
8 7U Medium 12 118 1600 651 480 0.74
9 7U High 250 3 9766 860 1177 1.37
1.05
# Counts
(n)
AADTGroup
#
FC & R/U
Code
Population
Density
Sample Size Calculation
𝑛 =
𝑍2𝐶2
𝑑2
1 +1𝑁
𝑍2𝐶2
𝑑2− 1
HPMS Field Manual, 2016
For C=1.20 n≈67
For C=1.05 n≈52
n = required sample sizeZ = value of standard normal statistic for alpha confidence levelC = coefficient of variationd = desired precision rateN = population stratum size
Counts needed for County and group based on COV
Decision Trees
Findings
• Promising Stratification Variables to use when calculating AADT:
– FC
– R/U
– Population density
– Housing unit density
– Occupied housing unit density
– Density of employees who live in a Census block
– Density of employees who work in a Census block
– Land use
13
Findings
• Calculate densities of Census data attributes
• Decision trees can improve roadway stratification
14
15
AADT Estimation
A) Traffic Count Based
B) Non-Traffic Count Based
“Traditional” Approach and
Sampling
Non-Traditional Methods
Disaggregated Estimates at the Segment
Level
Aggregated Estimates
(e.g., County Level)
C) Travel Demand Models
B) Non-Traffic Count Based
C) Travel Demand Models
AADT Estimation
• GPS/LBS data• Regression• ITE Trip Generation Method• OD data
Passively Collected Data – All Public Roads - FHWA Pool Fund Study – TPF-5(384)
Impact of AADT Estimation Errors on Data-Driven Safety Analysis
Subasish Das, Ph.D.
Texas A&M Transportation Institute
17
Objective
Determine impact of AADT on data-driven safety analysis
- Apply Empirical Bayes (EB) method that uses safety performance functions (SPFs)
- Perform sensitivity analysis
- (AADT change for segments)
- Conduct simulation
18
SPFs𝑁𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 = 𝛽0 × 𝐿𝑒𝑛𝑔𝑡ℎ𝛽1 × AADTβ2
Specific to NSAS NC
19
CURE Plots
20
Sensitivity Analysis
Steps
1. Apply EB Method within each FC
2. Rank segments
3. Determine percentile of the rank of each segment
4. Increase AADT of each segment by 10%, 50%, 100%, 250%, 500%
5. Repeat Steps 1-3 for each segment and % increase:
185,930 times = (3,110+12,386+3,097)*5*2
6. Calculate percentile rank change of each segment
21
6R: Rural Minor Collector
10% AADT Increase
50% AADT Increase
100% AADT Increase
250% AADT Increase
500% AADT Increase
Per
cen
tile
Ran
k C
han
ge
𝑁𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 = 2.432 × 𝐿𝑒𝑛𝑔𝑡ℎ0.988 × AADT0.090
SPF Dependent
Under Examination
• Repeat analysis using new SPFs:
𝑁𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 = 𝑒𝛽0 × 𝐿𝑒𝑛𝑔𝑡ℎ × AADTβ2
22
Roadway Crash Type Safety Performance FunctionsOver-dispersion
Parameter
Rural Local (7R) Total 𝑁7𝑅,𝑡𝑜𝑡 = 𝑒0.864 × 𝐿 × 𝐴𝐴𝐷𝑇0.043 0.353
Urban Local (7U) Total 𝑁7𝑈,𝑡𝑜𝑡 = 𝑒0.532 × 𝐿 × 𝐴𝐴𝐷𝑇0.095 0.944
Rural Collector (6R) Total 𝑁6𝑅,𝑡𝑜𝑡 = 𝑒0.877 × 𝐿 × 𝐴𝐴𝐷𝑇0.092 0.406
7R 7U 6U
Summary - Findings
• Developed SPFs by FC for KABCO and KABC crashes in NC
• Models validated using CURE plots
• AADT affects expected crash frequency safety risk segment ranking allocation of safety funds
• Impact of AADT on results of EB method depends on:
– SPF reliability and goodness-of-fit
– Sample size used to develop SPF
– Objective function used to estimate parameter estimates
– Model form
– Independent variables
– Overdispersion parameter
23
Thank You
Ioannis (Yianni) Tsapakis, PhD
Associate Research Scientist
Texas A&M Transportation Institute
24
Stuart Thompson
Office of Safety
Federal Highway Administration
