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Publication Number:  FHWA-HRT-16-035    Date:  June 2016
Publication Number: FHWA-HRT-16-035
Date: June 2016

 

Safety Evaluation of Intersection Conflict Warning Systems

Chapter 6. Development of Safety Performance Functions

This chapter presents the SPFs developed for each State, which are subsequently used in the EB methodology.(13) Generalized linear modeling was used to estimate model coefficients assuming a negative binomial error distribution, which was consistent with the state of research in developing these models. In specifying a negative binomial error structure, the overdispersion parameter, k, was estimated iteratively from the model and the data. For a given dataset, smaller values of k indicated relatively better models.

SPFs were calibrated separately for intersections with two-lane and multilane major routes for Minnesota, Missouri, and North Carolina using the corresponding reference sites from each State. The SPFs developed are presented by State in the following sections.

The form of the SPFs for all States is given in figure 7.

Figure 7. Equation. SPF model form for all States. Crashes per mile per year equals the product of the exponential value of a times TotalEntering to the power of b times the exponential value of the quantity characteristic times c plus each characteristic to the characteristic times t close quantity.

Figure 7. Equation. SPF model form for all States.

Where:

TotalEntering = Total entering volume (major route AADT + minor route AADT).
characteristic = Intersection characteristics included in SPF, defined by associated estimated parameters c through s.

The following definitions were used for all States for parameters with intersection characteristics:

c = Proportion of total entering volume from minor approach.
d = Presence of flashers on the minor route approaches.
e = Presence of flashers on the major route approaches.
f = Number of major route left-turn lanes.
g = Number of minor route left-turn lanes.
h = Number of major route right-turn lanes.
i = Number of minor route right-turn lanes.
j = Advance intersection warning sign on major route approaches.
l = Posted speed limit on major route.
m = Presence of lighting at intersection.
n = Advance STOP AHEAD warning sign on minor route approaches.
o = Intersection angle.
p = Presence of channelization on minor route approaches.
q = Presence of dual stop signs on the minor route approaches.
r = Median width on major route.
s = Posted speed limit on minor route.
t = Presence of a median on major route.

In addition, the following parameter was provided for each SPF:

k = Overdispersion parameter of the model.

Minnesota Safety Performance Functions

The SPFs for two-lane at two-lane intersections are provided in table 12, and the SPFs for four‑lane at two-lane intersections are provided in table 13.

Table 12. Minnesota two-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)
a b c d e f g h i j l m n k
Total
-7.913 (1.314)
0.866 (0.143)
2.976 (0.569)
-0.527 (0.195)
0.258
Fatal and injury
-5.791 (1.786)
0.557 (0.195)
2.611 (0.779)
-0.841 (0.337)
0.473 (0.266)
0.424
Right-angle
-14.557 (4.266)
0.825 (0.272)
2.010 (1.129)
-0.856 (0.412)
-0.364 (0.174)
0.620 (0.313)
0.742 (0.420)
0.115 (0.053)
0.551 (0.328)
0.433
Rear-end
-20.508 (4.817)
2.259 (0.583)
3.350 (1.709)
-0.932 (0.495)
1.024 (0.511)
-0.833 (0.391)
0.379 (0.215)
-0.837 (0.456)
0.562
Nighttime
-12.177 (3.036)
1.251 (0.335)
2.588 (1.361)
-0.769 (0.346)
0.254

— Indicates not applicable.

Table 13. Minnesota four-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)
a b c e j n o p q k
Total
-8.481 (1.581)
1.198 (0.151)
4.121 (0.839)
0.966 (0.237)
-0.337 (0.190)
-0.394 (0.144)
-0.032 (0.005)
-0.417 (0.191)
0.712 (0.192)
0.056
Fatal and injury
-5.123 (1.808)
0.772 (0.180)
2.391 (0.985)
1.144 (0.260)
-1.038 (0.300)
-0.034 (0.007)
0.787 (0.228)
0.012
Right-angle
-9.030 (2.105)
1.227 (0.203)
2.914 (1.160)
1.051 (0.276)
-0.763 (0.258)
-0.039 (0.007)
-0.505 (0.261)
0.605 (0.255)
0.070
Rear-end
-7.843 (3.385)
0.730 (0.363)
-0.717 (0.386)
1.611
Nighttime
-10.665 (2.672)
1.202 (0.262)
5.010 (1.458)
1.357 (0.408)
-0.816 (0.261)
-0.021 (0.009)
4e-7

— Indicates not applicable.

Missouri Safety Performance Functions

The SPFs for two-lane at two-lane intersections are provided in table 14, and the SPFs for four‑lane at two-lane intersections are provided in table 15.

Table 14. Missouri two-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)  
a b c e f h i j m n o p q s k  
Total
-8.314 (1.252)
0.700 (0.130)
2.912 (0.593)
0.788 (0.298)
0.187 (0.091)
0.298 (0.141)
0.601 (0.157)
0.023 (0.009)
-0.683 (0.409)
0.294
Fatal and injury
-14.938 (2.243)
1.166 (0.193)
5.192 (0.726)
0.701 (0.207)
0.044 (0.013)
0.368
Right-angle
-19.026 (2.821)
1.454 (0.241)
6.575 (0.921)
-1.531 (0.556)
0.518 (0.205)
--
0.986 (0.315)
0.372 (0.218)
0.812 (0.235)
0.045 (0.016)
-2.147 (0.655)
-1.007 (0.429)
0.032 (0.012)
0.363
Rear-end
-12.296 (2.431)
1.258 (0.300)
1.928 (0.356)
0.824 (0.324)
-0.931 (0.313)
0.916 (0.257)
0.650
Nighttime
-11.085 (2.625)
0.639 (0.246)
2.786 (1.022)
-0.321 (0.192)
1.064 (0.504)
0.841 (0.280)
0.043 (0.021)
2e-7

— Indicates not applicable.

Table 15. Missouri four-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)  
a b c d e f h j l n o p r s k
Total
-2.179 (1.355)
0.871 (0.118)
10.185 (1.824)
-0.462 (0.199)
0.455 (0.117)
0.246 (0.077)
0.925 (0.163)
-0.057 (0.011)
0.286 (0.138)
-0.034 (0.007)
0.319 (0.098)
-0.005 (0.003)
0.268
Fatal and injury
-1.058 (1.675)
0.729 (0.124)
5.733 (2.031)
0.361 (0.151)
0.890 (0.156)
-0.037 (0.010)
-0.056 (0.008)
0.288 (0.121)
-0.007 (0.003)
0.017 (0.007)
0.123
Right-angle
-3.586 (1.427)
0.502 (0.146)
13.626 (2.097)
0.804 (0.207)
1.319 (0.211)
0.429 (0.164)
-0.037 (0.008)
0.581 (0.136)
0.016 (0.006)
0.368
Rear-end
-9.471 (2.289)
1.738 (0.294)
8.643 (3.508)
-1.607 (0.428)
0.419 (0.166)
1.181 (0.321)
-0.155 (0.023)
1.064 (0.297)
0.027 (0.014)
0.549
Nighttime
-12.962 (1.738)
1.381 (0.188)
5.658 (2.807)
-0.532 (0.254)
0.727 (0.212)
-0.009 (0.004)
0.360

— Indicates not applicable.

North Carolina Safety Performance Functions

The SPFs for two-lane at two-lane intersections are provided in table 16, and the SPFs for four‑lane at two-lane intersections are provided in table 17.

Table 16. North Carolina two-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)
a b c g h i l o q s k
Total
-5.148 (0.578)
0.683 (0.054)
1.977 (0.223)
0.131 (0.074)
-0.012 (0.005)
-0.008 (0.002)
0.213
Fatal and injury
-6.098 (0.676)
0.656 (0.067)
1.725 (0.284)
0.139 (0.080)
0.211 (0.061)
-0.009 (0.005)
0.262
Right-angle
-5.567 (0.675)
0.577 (0.071)
2.233 (0.302)
0.201 (0.084)
-0.009 (0.003)
0.290 (0.066)
0.350
Rear-end
-10.130 (1.527)
1.331 (0.151)
-0.861 (0.269)
-0.039 (0.012)
-0.010 (0.005)
0.741
Nighttime
-8.312 (1.219)
0.669 (0.116)
2.379 (0.437)
-0.296 (0.112)
-0.007 (0.004)
0.028 (0.008)
0.214

— Indicates not applicable.

Table 17. North Carolina four-lane at two-lane intersection SPFs.
Crash Type Parameter Estimates (Standard Error)
a b c f h i l o p q r t k
Total
-4.414 (1.083)
0.642 (0.093)
3.742 (0.451)
-0.037 (0.012)
0.306 (0.142)
0.301 (0.124)
0.258
Fatal and injury
-5.128 (1.072)
0.472 (0.109)
3.838 (0.537)
-0.254 (0.132)
-0.158 (0.071)
0.114 (0.056)
0.345 (0.189)
0.760 (0.187)
0.291
Right-angle
-2.584 (1.232)
0.217 (0.123)
3.791 (0.625)
0.319 (0.058)
0.642 (0.168)
-0.697 (0.286)
0.495
Rear-end
-12.819 (2.966)
0.562 (0.228)
2.553 (0.946)
0.417 (0.098)
0.074 (0.040)
0.032 (0.008)
-0.014 (0.005)
1.005
Nighttime
-8.531 (1.727)
0.803 (0.173)
2.315 (0.750)
0.314 (0.209)
-0.009 (0.005)
0.399

— Indicates not applicable.

 

 

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