Safety Evaluation of Red-Light Indicator Lights (RLILs) At Intersections

Chapter 6. Development of SPFs

This section presents the SPFs developed for each crash type. The SPFs support the use of the EB methodology to estimate the safety effectiveness of the strategy.⁽⁵⁾ The research team used generalized linear modeling 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 dispersion parameter, k, was estimated iteratively from the model and the data. For a given dataset, smaller values of k indicate relatively better models (i.e., less dispersion).

SPFs for Spillover and Migration Effects

Before developing SPFs, the research team analyzed separate reference groups to identify potential crash migration and spillover effects. The project team used data from both reference groups to develop yearly multipliers for each group. Figure 7 provides the form of the SPF. Table 7 presents the estimated coefficients, as well as the value of k, the overdispersion parameter of the model.

Where:

TotalEnter = Total entering volume.
PropAADTMin = Proportion of entering volume from minor route.
ShldT1 = Indicator for paved shoulder.
a, b, c, d = Parameters estimated in the SPF calibration process.

Table 8 presents the observed crashes versus predicted crashes for each of the two reference groups. In the table, group 1 is the non-spillover/migration reference group, and group 2 is the potential spillover/migration reference group. Yearly factors are the ratio of observed crashes to predicted crashes for the given group within the given year. Because the base model was independent of year, yearly fluctuations were not a consideration in predicted crashes. Crash spillover was evident when the ratio for the spillover group became smaller with increasing time (because treatments were in use from 2004 to 2010). Crash migration occurred when the ratio increased with time. However, table 8 and figure 8 illustrate that there was no noticeable trend for the potential spillover/migration group. The ratios for groups 1 and 2 follow a consistent trend, indicating that neither crash spillover nor crash migration was observable. However, there was a slight underprediction for the non-spillover/migration group and a slight overprediction for the potential spillover/migration group. In addition, there was no apparent increasing or decreasing trend for either group, indicating that there was no observed districtwide crash migration or spillover effects.

Note: Group 1 is non-spillover/migration, and group 2 is potential spillover/migration.

While the results shown in table 8 and figure 8 provided evidence that crash migration and spillover were not of concern, they were insufficient to definitively conclude that the analysis could combine the two groups into a single reference group. Therefore, the research team conducted a supplementary analysis to estimate a second SPF, including an indicator for group 2 (the potential spillover/migration group) after the application of the nearby treatments. Table 9 presents the SPF results. The model includes yearly indicators to account for annual fluctuation that other predictor variables do not capture.

SE = Standard error.
N/A = Not applicable.

The resulting SPF showed no statistical difference for group 2 compared with group 1. Post-treatment application in that the indicator variable was insignificant, with the direction of effect being negative. This indicates that no crash migration or spillover effects occurred in group 2 after the application of the treatment at nearby sites. In addition, the research team included an indicator to account for systematic differences between the potential spillover/migration group and non-spillover/migration group (see table 8 ). Because the potential spillover/migration group consistently overpredicted crashes, the indicator should have been negative (meaning that fewer crashes would be predicted at potential spillover/migration sites compared to non-spillover/ migration sites). This was found to be the case; however, the indicator was not statistically significant even at the 90-percent confidence level (P > 0.10). This study found similar results for the other crash types considered.

Table 10 presents SPF model results (similar to the SPF results in table 9 ) for the nearby treatment indicator for all crash types without providing the estimates for other variables. This shows that spillover/migration did not occur for any crash types. Overall, the research team concluded that the two potential reference groups could be combined to estimate the SPFs for the EB analysis.

SPFs for Combined Reference Data

The form of the SPF for total crashes for combined reference groups is given by figure 9 , and the results are presented in table 11 , where k is also provided for each SPF.

Where:

Curve = Indicator for intersection being on a horizontal curve.

Note: The letters for parameters in table 11 correspond with those in figure 9 .
N/A = Not applicable.

In addition, the research team considered crash sample size for reference sites in the development of SPFs. Because total crashes ranged from a minimum of 110 crashes in 2008 to a maximum of 162 in 2004, the research team developed an SPF for total crashes. For all other crash types, there were too few crashes per year to develop separate reliable SPFs. Therefore, the research team used the total crashes SPF for other crash types, along with a proportion factor relating the crash type in question with total crashes. The research team multiplied the prediction from the SPF by the proportion factor to determine the number of predicted crashes of each specific crash type. The following crash type proportions were used:

• Fatal and injury crashes = 0.570.
• Right-angle crashes = 0.152.
• Left-turn crashes = 0.132.
• Rear-end crashes = 0.391.
• Disobey signal crashes = 0.048.
• Nighttime crashes = 0.305.

Table 12 provides annual factors (i.e., multipliers) estimated from the total crashes SPF. For multipliers greater than 1.00, more crashes were predicted for that year than the base year. For multipliers less than 1.00, fewer crashes were predicted for that year than the base year. The base year for multipliers was 2003. All crash types used the annual factors from the total crashes SPF.

Based on the large difference in crash rates between the treatment and reference sites (see table 6 ), the team decided to calibrate the SPF to the treatment site data just before treatment. The difference in crash rates was too large to be explained by RTM bias. Therefore, the research team used the treatment sites to account for the underprediction, using only the final year of crash data before treatment installation to calibrate the SPF. This was consistent with the approach used by Srinivasan et al.⁽¹³⁾

In the study by Srinivasan et al., the authors calibrated SPFs to be more representative of the treatment group using before-period data.⁽¹³⁾ The authors plotted 6 consecutive years of crash data for treatment sites to look for evidence of randomly high crashes during the before period. The plot showed that the counts for 2, 3, and 4 years before treatment were higher than for 1, 5, and 6 years before treatment. The authors selected 5 or more years before treatment to calibrate the SPF.

Figure 10 provides a plot of the before-period crashes at the treatment sites for the current study. Figure 10 is based on 40 of 108 sites for which 4 years of before data were available. (Crash data were not available for 4 years before treatment for the other 68 sites.) The plot indicates that the year before installation was the least prone to randomly high crash counts, as was also the case for the Srinivasan et al. data.⁽¹³⁾ This result is intuitive for two reasons. First, the timeframe to identify and treat the intersections generally ranged from 6 months to 1 year. Second, there was a lag between the end of a calendar year and the availability of crash data for that year. As such, it was unlikely that crash data were available for inclusion in the site-selection process for the year prior to RLIL installation. The large difference between predicted and observed crashes at treatment sites was similar in magnitude to the difference found by Srinivasan et al.⁽¹³⁾

The research team developed calibration factors by dividing the observed number of crashes for the year prior to treatment by the predicted number of crashes in the same year. This involved 2003 to 2009 data because installations occurred from 2004 to 2010. The research team developed calibration factors separately by crash type, which was consistent with Srinivasan et al.⁽¹³⁾ The following calibration factors by crash type were used:

• Total crashes = 1.638.
• Fatal and injury crashes = 1.546.
• Right-angle crashes = 2.034.
• Left-turn crashes = 1.146.
• Rear-end crashes = 1.782.
• Disobey signal crashes = 3.083.
• Nighttime crashes = 1.639.