Safety Evaluation of Continuous Green T Intersections

CHAPTER 7. CMF ESTIMATION

Due to the small sample sizes of the two datasets, the data from both States were combined to estimate CMFs for CGT intersections. The resulting CMFs indicated the average safety effect of the CGT intersections between the two states. CMFs for total, fatal and injury, and target crashes (rear-end, angle, and sideswipe) are described in the following subsections.

Variable selection and model specification were based on the crash prediction model forms found in the HSM.⁽³¹⁾ In addition, matching was used to remove the correlation between the treatment (CGT) and other variables in the model. The potential outcomes models considered these same variable forms, as well as the standardized bias, to further minimize the correlation between the treatment and other variables in the model. If the K-S test found that the difference was statistically significant, the variable was included in the regression model to adjust for the remaining correlation between it and the treatment (for both matching methods and the unmatched data). Failing to account for this correlation produces biased treatment effect estimates.^(15,35) The decision to use indicator variables for the posted speed limit on the continuous flow lane was made to fully account for the correlation in the full distribution of posted speed limits between the CGT and comparison group. If the posted speeds were grouped into ranges (e.g., lower than 50 mi/h and greater than or equal to 50 mi/h), the aggregation led to bias resulting from correlation between the posted speed indicator variables and the treatment.

As discussed in the Methods section, mixed effects negative binomial or Poisson regression was used to estimate the CMFs whenever possible. The optimal weights found using the genetic matching could not be accommodated using mixed effects regression, so weighted standard negative binomial regression with robust standard errors was used with the genetic matching results. The regression models for estimating the CMFs, along with the CMFs and 95-percent CIs, are shown in table 13 and table 14 for the genetic and Mahalanobis matching, respectively. For table 13, there were 297 observations used in the analysis. A weighted standard negative binomial regression model, with robust standard errors, was used to estimate the CMFs. The log-likelihood for the total, fatal and injury, and target crashes was -717.62695, -491.9991, and -599.30626, respectively. For table 14, there were 434 observations and 73 group (i.e., intersections) used in the analysis. A mixed-effects negative binomial regression model was used to estimate the CMF for total crashes, which had a log-likelihood of -938.44178. A mixed-effects Poisson regression model was used to estimate the CMF for fatal and injury crashes, which had a log-likelihood of -805.2616. Finally, a mixed-effects negative binomial regression model was used to estimate the CMF for target crashes, which had a log-likelihood of -665.20078.The statistical modeling output for the potential outcomes models for each crash type shown in table 13 and table 14 is provided in appendix A.

The weighted negative binomial model was used for total crashes, fatal and injury crashes, and target crashes (rear-end, angle, and sideswipe) using the genetic matched data. The models shown in table 13 included all independent variables that, theoretically, correlated with total, fatal and injury, or target crashes (based on the K-S tests in table 12). Variables that were not statistically significant in the negative binomial models were included in the model because Mannering and Bhat pointed out that parsimonious models are biased, are fundamentally flawed, and have little practical value.⁽³⁶⁾ Thus, the statistical models estimated in this evaluation were not specified based on statistical significance at the 95-percent confidence level.

The coefficients for all of the models were consistent with engineering intuition. The purpose of CGT intersections is to improve traffic operations. The results indicate that there were no statistically significant differences (at the 95-percent confidence level) between signalized T intersections without continuous flow lanes and CGT intersections in terms of total, fatal and injury, or target crashes (rear-end, angle, and sideswipe). It is worth noting, however, that the point estimates of the CMFs for total, fatal and injury, and target crashes were all less than 1, suggesting that there is a potential reduction in crash frequency associated with the CGT intersection relative to the conventional signalized-T intersection and that the lack of statistical significance is likely due to the small sample size rather than the lack of an effect. Thus, it is concluded that CGT intersections can have a beneficial effect on crash frequency. The CGT CMFs for each crash type and severity, with the associated 95-percent CIs, are shown in table13.

The signs and magnitudes of the coefficients for traffic volumes are consistent with the major and minor road coefficients for at-grade intersections found in the HSM.⁽³¹⁾ For the through street posted speed limit, the baseline condition was a posted speed limit of 35 mi/h. For the intersecting street posted speed limit, the baseline condition was a posted speed limit of 20mi/h. A positive coefficient indicates that the expected number of crashes is higher for the speed limit shown relative to the baseline condition. The posted speed limit indicator variables, while mostly insignificant, were retained in the model to minimize bias associated with the covariates in the matched data used to estimate the potential outcomes model that were not balanced after matching. The indicator variable for Florida indicated that there were fewer crashes in Florida than in South Carolina, which matches the descriptive statistics. The indicator variable for five or more through lanes was used because using individual indicator variables for the individual number of through lanes resulted in estimates that were nearly identical for any indicator variables for five or more lanes. The negative signs that indicate whether there were shoulders on the through and intersecting roads are logical because shoulders provide a recovery area for vehicles that leave the travel lanes. The variable Thru5UpShoulder is an interaction variable between five or more through lanes and the existence of a shoulder. The positive value indicates that intersections with five or more through lanes and shoulders on the through street did not receive the same safety benefits from the shoulders as intersections with fewer than five lanes on the through street. Finally, the presence of a fourth leg at the intersection that only allowed right-in and right-out movements correlated with lower crash frequencies. This was likely due to the fourth leg only being allowed on intersections with specific characteristics that were not collected as a part of this study but that are associated with lower crash frequencies.

Since traffic volume data were missing for several of the Florida intersections, a sensitivity analysis was performed by varying the traffic volumes for the missing locations. Traffic volumes of 500, 1,000, and 3,000 vehicles per day were tested. (As mentioned in the Data Collection section, a local jurisdiction performed a traffic count for one of the missing locations and found the AADT to be 500 vehicles per day; most missing minor street approaches had similar land use characteristics.) The difference in results was minimal when using 500, 1,000, and 3,000 vehicles per day for the missing minor street approach traffic volumes. Thus, only the results with the missing traffic volumes set at 500 vehicles per day are provided in this report.

The mixed effects negative binomial model was used for total crashes and target crashes (rear-end, angle, and sideswipe) using the Mahalanobis matched data. For fatal and injury crashes, the overdispersion parameter was not statistically significant when the mixed effects negative binomial was used, so the mixed effects Poisson was used for the final model. The random intercept was statistically significant in all of the models.

The results of the models in table 14 indicate that there were no statistically significant differences (at the 95-percent confidence level) between signalized T intersections without continuous flow lanes and CGT intersections in terms of total, fatal and injury, or target crashes (rear-end, angle, and sideswipe). As with the results from the genetic matching, the point estimates of the CMFs for total, fatal and injury, and target crashes are all less than 1.0, suggesting that there is a potential reduction in crash frequency associated with the CGT intersection relative to the conventional signalized T intersection. The lack of statistical significance is likely due to the small sample size rather than the lack of an effect. The CGT CMFs for each crash type and severity, with the associated 95-percent confidence level, are shown in table 14.

The signs and magnitudes of the coefficients for traffic volumes are consistent with the major and minor road coefficients for at-grade intersections found in the HSM.⁽³¹⁾ For the posted speed limit, the baseline condition is a posted speed limit of 35 mi/h. A positive coefficient indicates that the expected number of crashes is higher for the speed limit shown relative to the baseline condition. The posted speed limit indicator variables, while mostly insignificant, were retained in the model to minimize bias associated with the covariates from the Mahalanobis matched data that were significantly different (based on the K-S tests in table 12).

The sensitivity analysis for the missing traffic volumes that was used with the genetic matching CMF models was also performed with the Mahalanobis CMF models. The results were the same, and the missing traffic volumes were set to 500 vehicles per day.

The models in table 14 also indicate that crash frequency increased as intersection skew angle increased. This is consistent with the HSM.⁽³¹⁾ The finding that the expected crash frequency in Florida was lower than in South Carolina was consistent with the descriptive statistics.

As noted earlier, the propensity scores-potential outcomes framework reduced the overall sample size from the original data due to matching (i.e., some intersections are dropped). As such, cross-sectional models using the unmatched data were also estimated for comparison. The CMFs estimated using the full, unmatched database were provided to show the magnitude of bias that the CMFs would have had if matching was not used. The regression models and CMFs for total, fatal and injury, and the target crashes using the full dataset (i.e., no matching) are shown in table 13. The statistical modeling outputs for the models shown in table 13 and table 14 are provided in appendix A. The statistical modeling outputs for the models shown in table 15 are provided in appendix B. For table 15, there were 516 observations and 104 groups (i.e., intersections) used in the analysis. A mixed-effects negative binomial regression model was used to estimate the CMF for total crashes, which had a log-likelihood of -1134.5724. A mixed-effects Poisson regression model was used to estimate the CMF for fatal and injury crashes, which had a log-likelihood of -795.8822. Finally, a mixed-effects negative binomial regression model was used to estimate the CMF for target crashes, which had a log-likelihood of -960.89489.

The CMFs estimated using the unmatched data are more likely to be biased than the estimates using the matched data, so the CMFs from the latter should be regarded as more robust. It is encouraging that the CMFs estimated using the unmatched data are similar to the CMFs from the matched data, although the safety benefit estimated with both sets of models is statistically insignificant. Based on the K-S test results, the genetic matching resulted in the best covariate balance. Thus, the CMFs estimated from the genetic matching are preferred over the other