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 Federal Highway Administration > Publications > Research Publications > 15048 > Chapter 6. Developmentof Spfs
 Publication Number:  FHWA-HRT-15-048    Date:  June 2015
 Publication Number: FHWA-HRT-15-048 Date: June 2015

# Chapter 6. Development of SPFs

This section presents the SPFs developed for each State. The SPFs are used in the EB methodology to estimate the safety effectiveness of this strategy.(6) Generalized linear modeling was used to estimate model coefficients assuming a negative binomial error distribution, which is consistent with the state of research in developing these models. In specifying a negative binomial error structure, the dispersion parameter, k, was estimated iteratively from the model and the data. For a given dataset, smaller values of k indicate relatively better models.

SPFs were calibrated separately for Kentucky and Pennsylvania using the corresponding reference sites from each State. As discussed in the methodology section, the Missouri SPFs were developed separately for the before and after periods at the treated sites. The SPFs developed are presented by State in the following sections. The parameter estimates are presented by State with the standard error of the estimates.

Kentucky SPFs

The form of the SPFs for Kentucky, which are presented in table 12, is seen in figure 6:

Figure 6. Equation. SPF model form for Kentucky.

Where:

AADT = Average annual daily traffic volume.
reftype = 1 if a resurfacing reference site; 0 if a retrofit reference site.
a, b, c = Parameters estimated in the SPF calibration process.
k = The overdispersion parameter of the model.

Table 12. Kentucky SPFs.

Parameter Estimates (Standard Error)

Crash Type
a
b
c
k
Total
-5.8124
(0.3410)
0.6304
(0.0355)
1.1548
(0.1859)
0.8803
Injury
-6.3308
(0.3641)
0.5520
(0.0385)
1.0702
(0.1839)
0.6981
-5.0019
(0.3974)
0.3933
(0.0418)
1.1128
(0.2046)
0.9091
-9.3272
(0.6967)
0.6610
(0.0751)
0.7647
(0.2791)
0.8055
Sideswipe-Opposite-Direction
-7.0892
(0.5705)
0.4372
(0.0612)
0.8975
(0.2597)
0.8536

Missouri SPFs

As discussed in the methodology section, the analysis of the Missouri data required that SPFs be developed for both the before and after periods. The before period SPFs are shown in table 13. For the after period, the time trend is only based on total crashes because of the low numbers of other crash types. Thus, only total crashes were modeled, as indicated in n/a = not applicable.

table 14.

The form of the SPFs for Missouri is seen in figure 7:

Figure 7. Equation. SPF model form for Missouri.

Where:

AADT = Average annual daily traffic volume.
shldwid = Average shoulder width in ft.
urbrur = 1 if rural; 0 if urban.
a, b, c, d = Parameters estimated in the SPF calibration process.
k = The overdispersion parameter of the model.

Table 13. Missouri before period SPFs.

Parameter Estimates
(Standard Error)

Crash Type
a
b
c
d
k
Total
-7.8094
(0.6409)
1.0091
(0.0747)
-0.0691
(0.0144)
-0.4479
(0.1205)
0.8958
Injury
-8.7627
(0.7731)
0.9958
(0.0892)
-0.0581
(0.0166)
-0.3273
(0.1503)
0.8644
-5.3832
(0.7745)
0.6168
(0.0906)
-0.1116
(0.0179)
-0.2298
(0.1652)
0.9827
-12.5421
(1.5038)
1.1047
(0.1751)
N/A
N/A
0.8202
Sideswipe-Opposite-Direction
-11.5757
(1.3814)
1.0508
(0.1662)
-0.0553
(0.0284)
N/A
0.5565

N/A = Not applicable.

Table 14. Missouri after period SPFs.

Parameter Estimates
(Standard Error)

Crash Type
a
b
c
d
k
Total
-6.7214
(1.0431)
0.8107
(0.1193)
-0.0440
(0.0202)
-0.6187
(0.1828)
0.8154

Pennsylvania SPFs

The form of the Pennsylvania SPFs, which are provided in table 15, is seen in figure 8:

Figure 8. Equation. SPF model form for Pennsylvania.

Where,

AADT = Average annual daily traffic volume.
shldwid = Average shoulder width in ft. width = Pavement width in ft.
a, b, c, d = Parameters estimated in the SPF calibration process.
k = The overdispersion parameter of the model.

Table 15. Pennsylvania SPFs.

Parameter E cvbstimates
(Standard Error)

Crash Type
a
b
c
d
k
Total
-5.9379
(0.0402)
0.7603
(0.0050)
-0.0471
(0.0019)
N/A
0.4519
Injury
-6.7027
(0.0461)
0.7703
(0.0057)
-0.0371
(0.0021)
N/A
0.4493
-5.8811
(0.0728)
0.6254
(0.0106)
-0.0793
(0.0036)
-0.0233
(0.0016)
0.9507
-10.3415
(0.1232)
0.9024
(0.0146)
-0.0325
(0.0051)
N/A
0.7623
Sideswipe-Opposite-Direction
-10.0866
(0.1496)
0.8161
(0.0178)
-0.0452
(0.0064)
N/A
0.7521

N/A = Not applicable.