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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
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| This report is an archived publication and may contain dated technical, contact, and link information |
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| Publication Number: FHWA-HRT-17-084 Date: February 2018 |
Publication Number: FHWA-HRT-17-084 Date: February 2018 |
This chapter presents the crash prediction models. The research team used generalized linear modeling 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 modeling analysis iteratively estimated the dispersion parameter, k, from the model and the data. For a given dataset, smaller values of k indicate relatively better models.
The research team first generated a correlation matrix for all potential explanatory variables. The correlation between predictors was key to minimizing the negative effects of multicollinearity. Having two highly correlated variables in a model may result in erratic changes of the estimated coefficients and lead to biased model estimation results. The correlation matrix was used as guidance throughout the model specification and development process.
The safety performance function development began with the simplest functional form in which only traffic volumes were included. Each potential predictor was then added to the model, and the goodness of fit was evaluated. During the initial examination of data, the research team found that the cross-street AADTs at some locations appeared abnormally small for signalized intersections. Seven of the 400 candidate study locations had fewer than 100 vehicles per day on the cross streets; therefore, the research team examined locations with up to 500 and 1,000 vehicles per day, and the number of locations increased to 17 and 34, respectively. All of these intersections with abnormal AADTs were located in California. The research team conducted a thorough examination of these intersections in Google® Earth™, Google® Street View™, and HSIS, looking at 10 years of HSIS roadway data. The effort confirmed that no mistakes had been made in matching the traffic volumes. The abnormally low AADT values had originated from the HSIS data files. Visual verification suggested that these very low AADT values appeared to be improbable. Aerial images in Google® EarthTM showed long vehicle queues and large parking lots on the cross streets at a majority of these intersections. Although this was not enough for a reliable estimate of the cross-street AADT, the evidence demonstrated the inaccuracy of these very low AADT values. The research team examined the impacts of these low AADT values on the model parameters by estimating and comparing several models for total crashes as follows:
The results showed minimal differences among these five models. In the end, the research team selected Model 3, replacing the cross-street AADT values for 17 intersections with values of 500 vehicles per day. The data summary presented in table 3 for 275 intersection reflects this correction.
The data for this study represent three regions: Northern California, Southern California, and the largest city in North Carolina. It is reasonable to assume that these three regions might have inherently different characteristics that can affect the safety outcomes or at least crash counts at signalized intersections. These elements could be unknown, immeasurable, or unavailable for the analyses conducted in this study. For example, the climate and the driver population in Charlotte are probably not the same as those in California. The research team tested this assumption by estimating crash prediction models using separate subsets of data from each of the three regions and comparing the model parameters. The test results revealed little difference between Northern and Southern California in this regard, so all intersections from California were considered as one group. The tests indicated larger differences between Charlotte and California sites, but the 95-percent intervals of the model parameters still overlapped. This process and its results supported the decision to analyze all intersections together as a single dataset and use an indicator to account for the inherent differences between California and Charlotte.
The research team developed crash prediction models separately for total, fatal and injury, rear-end, sideswipe, right-angle, and right- and left-turn crashes at signalized intersections. Combinations of clearances on both approach and receiving corners were tested. The research team decided to use a corner clearance of 50 ft for all models after considering the overall model fit and the practicality of potential applications. The following sections present the crash prediction models for these crash types. The definition of variables included in the final crash prediction models are as follows:
Figure 7 presents the functional form of the crash prediction model.
Figure 7. Equation. Model for total crashes.
Table 4 presents the model parameters for total crashes.
Table 4. Model parameters for total crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Mainline AADT | β1 | 0.616 | 0.128 | <0.01 |
| Cross-street AADT | β2 | 0.295 | 0.051 | <0.01 |
| Indicator for intersection in Charlotte | β3 | 2.365 | 0.174 | <0.01 |
| 50 mph or higher posted speed | β4 | 0.497 | 0.118 | <0.01 |
| Mainline with 11-ft lane or narrower | β5 | –0.492 | 0.127 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β6 | –0.199 | 0.099 | 0.05 |
| Number of receiving corners with clearance of 50 ft or less | β7 | 0.282 | 0.084 | <0.01 |
| Intercept term | β8 | –7.442 | 1.281 | <0.01 |
| Dispersion parameter (k) | — | 0.517 | 0.058 | — |
| —Not applicable. | ||||
Figure 8 presents the functional form of the crash prediction model.
Figure 8. Equation. Model for fatal and injury crashes.
Table 5 presents the model parameters for fatal and injury crashes.
Table 5. Model parameters for fatal and injury crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Mainline AADT | β1 | 0.685 | 0.134 | <0.01 |
| Cross-street AADT | β2 | 0.257 | 0.054 | <0.01 |
| Indicator for intersection in Charlotte | β3 | 1.978 | 0.173 | <0.01 |
| 50 mph or higher posted speed | β4 | 0.331 | 0.124 | <0.01 |
| Mainline with 11-ft lane or narrower | β5 | –0.349 | 0.125 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β6 | –0.238 | 0.104 | 0.02 |
| Number of receiving corners with clearance of 50 ft or less | β7 | 0.258 | 0.085 | <0.01 |
| Intercept term | β8 | –8.464 | 1.344 | <0.01 |
| Dispersion parameter (k) | — | 0.431 | 0.063 | — |
| —Not applicable. | ||||
Figure 9 presents the functional form of the crash prediction model.
Figure 9. Equation. Model for rear-end crashes.
Table 6 presents the model parameters for rear-end crashes. In table 6, driveway density has a negative coefficient estimate. This indicates that an increase in driveway density is statistically associated with a reduction in rear-end crashes. It is important to emphasize that the driveway density in this context represents the longer roadway segment on that corridor. The driveway density in this model does not suggest that having more driveways near an intersection reduces rear-end crashes.
Table 6. Model parameters for rear-end crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Mainline AADT | β1 | 0.827 | 0.155 | <0.01 |
| Cross-street AADT | β2 | 0.263 | 0.060 | <0.01 |
| Indicator for intersection in Charlotte | β3 | 1.910 | 0.204 | <0.01 |
| 50 mph or higher posted speed | β4 | 0.332 | 0.153 | 0.03 |
| Mainline with 11-ft lane or narrower | β5 | –0.461 | 0.159 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β6 | –0.234 | 0.119 | 0.05 |
| Number of receiving corners with clearance of 50 ft or less | β7 | 0.311 | 0.101 | <0.01 |
| Driveway density | β8 | –0.006 | 0.003 | 0.05 |
| Intercept term | β9 | –9.529 | 1.542 | <0.01 |
| Dispersion parameter (k) | — | 0.670 | 0.080 | — |
| —Not applicable. | ||||
Figure 10 presents the functional form of the crash prediction model.
Figure 10. Equation. Model for sideswipe crashes.
Table 7 presents the model parameters for sideswipe crashes.
Table 7. Model parameters for sideswipe crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Mainline AADT | β1 | 0.663 | 0.178 | <0.01 |
| Cross-street AADT | β2 | 0.388 | 0.076 | <0.01 |
| Indicator for intersection in Charlotte | β3 | 1.968 | 0.222 | <0.01 |
| 50 mph or higher posted speed | β4 | 0.618 | 0.172 | <0.01 |
| Mainline with 11-ft lane or narrower | β5 | –0.346 | 0.166 | 0.04 |
| Number of approach corners with clearance of 50 ft or less | β6 | –0.186 | 0.139 | 0.18 |
| Number of receiving corners with clearance of 50 ft or less | β7 | 0.269 | 0.109 | 0.01 |
| Indicator for residential area | β8 | –0.601 | 0.212 | <0.01 |
| Intercept term | β9 | –10.560 | 1.825 | <0.01 |
| Dispersion parameter (k) | — | 0.466 | 0.096 | — |
| —Not applicable. | ||||
Figure 11 presents the functional form of the crash prediction model.
Figure 11. Equation. Model for right-angle crashes.
Table 8 presents the model parameters for right-angle crashes.
Table 8. Model parameters for right-angle crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Intersection AADT | β1 | 0.641 | 0.196 | <0.01 |
| Indicator for intersection in Charlotte | β2 | 3.260 | 0.270 | <0.01 |
| 50 mph or higher posted speed | β3 | 0.732 | 0.196 | <0.01 |
| Mainline with 11-ft lane or narrower | Β4 | –0.822 | 0.211 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β5 | 0.031 | 0.158 | 0.84 |
| Number of receiving corners with clearance of 50 ft or less | β6 | 0.352 | 0.137 | 0.01 |
| Intercept term | β7 | –7.014 | 2.079 | <0.01 |
| Dispersion parameter (k) | — | 1.096 | 0.182 | — |
| —Not applicable. | ||||
Figure 12 presents the functional form of the crash prediction model.
Figure 12. Equation. Model for turning crashes.
Table 9 presents the model parameters for turning (right- or left-turn) crashes.
Table 9. Model parameters for turning crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Intersection AADT | β1 | 0.923 | 0.189 | <0.01 |
| Indicator for intersection in Charlotte | β2 | 2.560 | 0.236 | <0.01 |
| 50 mph or higher posted speed | β3 | 0.574 | 0.186 | <0.01 |
| Mainline with 11-ft lane or narrower | β4 | –0.537 | 0.181 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β5 | 0.004 | 0.147 | 0.98 |
| Number of receiving corners with clearance of 50 ft or less | β6 | 0.199 | 0.120 | 0.10 |
| Intercept term | β7 | –10.270 | 2.018 | <0.01 |
| Dispersion parameter (k) | — | 0.639 | 0.124 | — |
| —Not applicable. | ||||
Figure 13 presents the functional form of the crash prediction model.
Figure 13. Equation. Model for nighttime crashes.
Table 10 presents the model parameters for nighttime crashes.
Table 10. Model parameters for nighttime crashes.
| Variable | Coefficient | Estimated Value | SE | P-Value |
|---|---|---|---|---|
| Mainline AADT | β1 | 0.986 | 0.164 | <0.01 |
| Cross-street AADT | β2 | 0.282 | 0.069 | <0.01 |
| Indicator for intersection in Charlotte | β3 | 2.675 | 0.217 | <0.01 |
| 50 mph or higher posted speed | β4 | 0.501 | 0.160 | <0.01 |
| Mainline with 11-ft lane or narrower | β5 | –0.463 | 0.154 | <0.01 |
| Number of approach corners with clearance of 50 ft or less | β6 | –0.067 | 0.129 | 0.60 |
| Number of receiving corners with clearance of 50 ft or less | β7 | 0.257 | 0.103 | 0.01 |
| Intercept term | β8 | –12.720 | 1.669 | <0.01 |
| Dispersion parameter (k) | — | 0.545 | 0.089 | — |
| —Not applicable. | ||||
