Assessing the safety effect of red-light camera deactivation: a geographically weighted negative binomial regression approach

Municipalities across the country have debated the safety effect of automatic red-light cameras (RLC) and their political and financial implications. Most empirical studies have used the Empirical Bayesian (EB) approach to assess the safe effects to facilitate policy debates. While popular, the EB method has several limitations in data requirement, reference site selection, and control of confounding factors. Moreover, empirical studies of the RLC deactivation effects are limited. This study fills these gaps using the Moran’s I statistic and the Geographically Weighted Negative Binomial Regression (GWNBR) approach for data in the City of Arlington, Texas. The results indicate that the total, injury, and angle crashes in Arlington are on the rise over the study period and that crashes are higher at RLC deactivation intersections than those at other intersections. The direct safety effect of removing RLCs is statistically significant. The spillover effect is observed but statistically insignificant. Speed limit plays an important role in road safety. The findings have significant implications for safety research and practices.


Introduction
Automatic red-light cameras (RLC) have been used as a safety enforcement tool to reduce intersection crashes caused by drivers running red lights, also known as red light running (Ko et al., 2017). In addition to safety benefits, RLCs are expected to increase operational efficiency and reduce the cost of law enforcement (Baratian-Ghorghi et al., 2017). Despite these convictions, there are some concerns about the negative implications for privacy and municipal financial burdens (City of Arlington, 2015;Yang et al., 2013). Questions remain regarding the purpose and tradeoffs of RLC benefits (Burkey and Ko_ Obeng, 2004;Wong, 2014;Llau et al., 2015).
The controversies have led to the termination of RLCs in some communities (Donaldson, 2017). The debates about RLCs require more empirical evidence especially those in cities where RLCs have been deactivated, since empirical research on the RLC deactivation effect is limited in scope and the RLC effects in general may vary by location (Pulugurtha & Otturu, 2014;Yang et al., 2013). Moreover, there exist some limitations in data requirements, reference site selection, and control of confounding factors in the commonly used Empirical Bayesian (EB) approach for RLC effect research (Claros et al., 2017;Lord & Kuo, 2012;Washington and Shin, 2005;Wang et al., 2015). Some studies have used the Poisson approach to overcome the limitations EB (see e.g. Hallmark et al., 2010;Wong, 2014). Nevertheless, Poisson regression is not suitable for data with overdispersion (Hilbe, 2014;Da Silva & Rodrigues, 2014). Empirical results with novel tools can inform municipal policy decisions on automatic
Using data on traffic incidents and other data between 2013 and 2016 in the City of Arlington, Texas, and a combination of methods for temporal, spatial, and statistical analyses, this study investigates the direct and spillover effects of red-light camera deactivation on traffic crashes. 1 The research attempts to answer two key questions: (1) is there any difference in the number of crashes among different intersections with or without red light camera treatment? (2) Does the deactivation of red-light cameras affect the number of crashes in intersections?
This study contributes to the scholarly and policy debates by taking the advantage of various analytical techniques including trend analysis, the Moran's I statistics and the Geographically Weighted Negative Binomial Regression (GWNBR) approach to analyze the temporal and spatial patterns of crashes and to model the relationship between the deactivation of automatic red-light cameras and safety while controlling for spatial autocorrelation and endogeneity. In addition, the study adopts the approach proposed by Da Silva and Rodrigues (2014) to search an optimum bandwidth for distance-band spatial weight estimates in order to improve the efficiency of GWNBR. It adds to the existing scholarship by introducing analytical applications that are more powerful and efficient to address the complex correlations among factors contributing to safety in this line of research. Specifically, the Moran's I statistics measure the autocorrelation of incidences based on location and extent. The GWNBR approach addresses the shortcomings of the EB and the Poisson approaches that are commonly used in the existing literature. Compared to the Negative Binomial Regression (NBR), the GWNBR approach takes spatial autocorrelation factor into account and can support empirical studies using readily available yet critical data to control for confounding factors related to safety. This study also provides new empirical evidence about the safety effect of automatic red light camera deactivation for policy debate from a previously unstudied location. It is one of the very few studies that focus on the impacts of removing automatic red-light cameras.
In the following sections, a brief assessment of the research on the safety effect of automatic red-light cameras is provided, followed by a description of the research design. The analysis results are presented in the fourth section. The final section summarizes the findings and discusses implications for future studies and policies.

Research in safety effects of automatic red-light cameras
Automatic red-light cameras combine sensing, automation, and photographic technologies. They have the ability to detect incidents when a vehicle enters an intersection after the traffic light signal turns red, automatically activate cameras to take pictures, and record a series of photographs and/or video images of the vehicle movement, date and time durations of the incidents (Retting et. al., 1999;TTI, 2012). The pictures and videos can be used as evidence of traffic violations. It is expected that drivers are more likely to stop at intersections where automatic red-light cameras are implemented in order to avoid traffic citations, therefore reducing crashes. Automatic red-light cameras are also expected to reduce the manpower for safety enforcement and increase the operational efficiency for municipalities because the technologies are able to record red light running behavior without requiring policemen on the streets ( Baratian-Ghorghi et al., 2017). In recent years, the safety effects of automatic redlight cameras have been studied using several techniques. A common method is the EB approach, which has a major advantage of accounting for the potential regression to the mean (RTM) bias -a fallacy due to unusual events and/or repeated measure errors. The RTM bias often leads to an inaccurate conclusion regarding the effect of an intervention or treatment, which in this case is the activation or deactivation of red-light cameras (Barnett et al., 2005;Hauer, 1997). Nevertheless, the method has its limitations. First, the EB method requires a large amount of data including the data in both the study and reference sites, which restrains the application of this method in studies without reference data (Wang et al., 2015). Second, there is no consistent measure or methodological procedure for selecting reference sites (Claros et al., 2017). While some studies only based on the average annual daily traffic (AADT) and roadway geometric characteristics to determine the best candidate locations for reference sites (see, e.g., Lee et al., 2014;Ahmed & Abdel-Aty, 2015), others considered additional factors such as speed limit, signal control operation, and other features (see, e.g., Pulugurtha & Otturu, 2014;Claros et al., 2017). The variation in criteria for reference site selection could induce subjectivity in data selection, and therefore affect results (Lord & Kuo, 2012). Third, many existing studies using the EB method have not directly controlled for land use or other macro elements that could potentially be relevant to crashes beyond intersection geometric characteristics. Moreover, the potential spillover effects of RLC on crashes "can make the Li and da Silva Computational Urban Science (2022) 2:15 selection of comparison sites difficult" (Washington and Shin, 2005).
Recognizing some of the challenges of safety research and limitations of the EB method, researchers and practitioners have called for exploring alternative techniques to deal with the unobserved heterogeneity and data quality, and "to advance the art of drawing cause and conclusions from cross-section and before-after comparisons" (Bonneson & Ivan, 2013). While some studies have used the Logit model or the regression tree model for this line of study (Porter et al., 2013;Shaaban & Pande, 2018), others have adopted the generalized linear model (GLM)-Poisson regression modeling approach to fill the aforesaid gaps of the EB approach (see, e.g. Retting and Kyrychenko, 2002;Burkey and Obeng, 2004;Wong, 2014). However, the application of GLM-Poisson regression models is limited in number and scope. In addition, there exists overdispersion in count data, which is a violation of a key assumption in the Poisson regression (Hilbe, 2014;Da Silva and Rodrigues, 2014). This study joins the scholars in exploring novel techniques for this line of research. It adds to the limited studies on the safety effect of RLC removal and provides new empirical evidence for policy debate from a previously unstudied location.

Research design
Using data on traffic incidents and other data between 2013 and 2016 in the City of Arlington, Texas, and the spatial statistical techniques, this study investigates the direct and spillover effects of RLC deactivation on traffic crashes. The following sections explain the research design in detail.

Study area
The City of Arlington is located in the middle of the Dallas/Fort Worth Metroplex, an area that has experienced rapid population growth in the last several years. In addition, the city is known to be the largest city without public transportation in the nation (Harrington, 2018). Despite the introduction of On-Demand Rideshare service, also known as flex transit or demand-responsive transit (DRT) a few years ago, private vehicles have been the main means of travel/main travel means. A case study of Arlington offers insights into the safety impact of RLCs in cities unique in their locations and means of travel.
The City of Arlington started the RLC program in seven locations in 2007. Over the next eight years, it added RLCs in various intersections with the highest number of RLC enforcements (23 intersections) in 2013 and 2014. However, RLCs were removed in May 2015 after the city residents approved a referendum to ban RLC enforcement in its May election (Ballotpedia, 2015). To date, the safety effect of RLC enforcement and termination in the city has not been studied.

Hypotheses, measurements, and data
This study is based on two premises: (1) RLCs reduce motorists' tendency to run red light at intersections and decrease potential crashes (Baratian-Ghorghi et al., 2017), and (2) RLCs also reduce crashes in the non-RLC intersections within close proximity to the RLCs (Ahmed & Abdel-Aty, 2015;Ko et al., 2017;Persaud, et al., 2005). Based on these two premises established by the existing literature, it is hypothesized that, all else being equal, one would expect a greater increase in the number of crashes at RLC intersections than in non-RLC intersections after camera deactivation because of the constraints by RLCs prior to their termination. In other words, it is believed that the number of crashes at RLC intersections is constrained by the RLC enforcement; once the constraint is removed, one would expect a larger increase in the number of crashes at these sites than at those without the enforcement before, all else being equal (Baratian-Ghorghi et al., 2017). Similarly, it is expected that after camera deactivation, those "near" intersections would experience a greater increase in crashes than other intersections far from the RLC intersections. In addition, it is expected that crashes are spatially clustered, known as the spillover effect "caused by jurisdiction-wide publicity and the general public's lack of knowledge of where RLCs are installed, " according to Persaud, et al. (2005). Table 1 displays the data used for the study, the expected relationships between the dependent variables and the independent variables according to the existing literature, and the data sources. The dependent variables include the counts of total, injury, and angle crashes at intersections with traffic lights. Injury counts include those crashes noted as incapacitating injury, non-incapacitating injury, and possible injury. Angle crashes include all right-angle, left-turn, and other types of angle crashes. This study focuses on angle and injury crashes because the numbers of rear-end and fatal crashes are very limited. The study uses crashes that occurred between September 2013 and December 2016 (20 months before and 20 months after automatic redlight cameras were deactivated) for the analysis.
The key predictors of interest are Deactivation and Type of Intersections. The variable "deactivation" is a measure of RLC implementation status in which the 20 months before the RLC deactivation is coded as 0 and the 20 months after that is coded as 1. There are three types of intersections, namely "RLC, " "Near, " and "None. " The intersections where automatic red-light cameras were installed and removed are defined as the "RLC" intersections. Those intersections that had no RLC treatment but were located within a quarter mile radius from the automatic red light camera intersections are defined as the "Near" intersections. The rest of the intersections are termed as "None" intersections. In addition, this study includes the control variables of average speed limit, land use, traffic counts, and driving age population. These control variables measure different aspects of safety and traffic-related factors. For example, speed limit regulates driving speeds that could potentially cause collisions. Higher speed limits require a longer distance between vehicles and a quicker response from drivers to maintain safety, which is often ignored. The land use variable is a factor that could potentially attract more traffic from elsewhere to an area around an intersection. Traffic counts measure the real traffic volume. The driving age population is a variable measuring the potential traffic generated from an area near individual intersections. It is hypothesized that the increase in any of the aforementioned variables would increase the risk and likelihood of collisions (Garder, 2004;Ewing & Dumbaugh, 2009;Pulugurtha & Otturu, 2014;Litman & Fitzroy, 2005;Lovegrove & Sayed, 2006;Kim et al., 2006;Lee et al., 2015). In addition to these variables, this study includes the interaction term of the Deactivation and Type variables, as well as spatial lag variables depending on the results of autocorrelation analysis. The interaction variable is used to investigate if the effect of deactivation on crashes is contingent upon the effect of the type of intersections. The spatial lag variables control for the spillover effects.
The unit of analysis in this study is intersection, defined as the area within a 200-foot radius from the center point of each intersection as suggested by the existing literature. According to StPeteCameras (2011), this definition is adopted in order to capture the rear-end crashes associated with the intersection). 2 Only intersections with traffic lights are included in the analysis, which include 23 "RLC" intersections, 35 "Near" intersections, and 295 "None" intersections.
Individual crashes are geocoded, then aggregated to the intersection level based on the locations and time of crashes. The total number of crashes within the defined area of intersections are the count of crashes at intersections. The average speed limit (miles/hour) is calculated by taking the mean of the speed limits posted in all directions at intersections. The public land use variable includes lands that are used for retail, commercial, or other purposes that generate activities and traffic around intersections. The data is obtained by overlaying land use and intersection layers and calculated as the percentage of public land use over the total land area. Similarly, the average daily traffic counts refer to the average of those observed or close to the defined area of intersections. Specifically, because traffic counts were observed in limited locations rotated by years in the roadway network of the city, traffic counts from 2013 and 2014 were combined and used as the data for the "before" period, and data from 2015 and 2016 were combined and used as the data for the "after" period. Traffic counts were assigned to the intersections based on the nearest location -a function provided by ArcGIS. Figure 1 displays the locations of traffic counts being conducted and intersections being studied in the City of Arlington.
Population with driving age (18 years old and over) are those in census block groups around the intersections in 2014 and 2016. All data are combined using the spatial join with the closest match option offered by ArcGIS. Table 2 displays the descriptive statistics of the main variables.

Model specification and analysis approach
This study uses the Negative Binomial Regression (NBR) modeling approach in conjunction with the consideration  Silva and Rodrigues, 2014). The NBR is a special type of GLM for count data (Molenberghs et al., 2010). The NBR approach has been used in evaluating the effects of drug treatment or other interventions (e.g. see Molenberghs et al., 2010;Marotta & McCullagh, 2018). The NBR model is preferred over the Poisson regression model because it can not only control for as many confounding factors as possible, but also has fewer restrictive  assumptions than the Poisson regression model, and therefore greater generality or applicability. Like the Poisson regression model that has been used in the current safety literature, the NBR is specific for count data and can address the autoregressive (first order) covariance structure due to repeated measures. In addition, if used properly, the NBR model can control for endogeneity or heterogeneity due to covariance between variables or fail to include observed or unobserved factors in the statistical analysis. Moreover, it can handle overdispersion, a common feature of count data and a violation of the principal assumption of the Poisson regression model (Cameron & Trivedi, 2009;Hilbe, 2014). In short, the NBR model has more statistical power and is more practical as it can overcome the aforesaid limitations of the EB approach and the Poisson models (Burkey and Obeng, 2004;Molenberghs et al., 2010). The GWNBR approach improves NBR by taking spatial effects into account and addressing the spatial dependency problem in data (Da Silva and Rodrigues, 2014). The NBR and GWNBR for modeling data with overdispersion, according to Da Silva and Rodrigues (2014), are specified as the following, respectively: where yj is the dependent variable for j = 1, 2, . . . n ; t j is an offset variable; (u j , v j ) are coordinates of data points j, for j = 1, 2, … n; Xjk is the independent variable fork = 1, 2, . . . p ; β k and ɑ are parameters related to the independent variable Xk and overdispersion, respectively (Da Silva and Rodrigues, 2014).
Da Silva and Rodrigues (2014) also recommended to identify the optimum bandwidth based on the corrected Akaike's Information Criterion (AICc) or the cross-validation (CV) criterion approach. The detailed explanation and discussion of the AICc and CV can be found in Da Silva and Rodrigues (2014). Using the SAS macro developed by Da Silva and Rodrigues (2016), we estimate the optimum bandwidth for our data and apply it as the threshold for the estimation of distance-band spatial weights. The spatial lag variables are created following the calculations of the distance-band spatial weights. More precisely, w ij = 1 when d ij ≤ δ , and w ij = 0 , for i, j = 1, . . . , n and where δ is preset critical distance cutoff (Anselin, 2020). In this case, δ was the optimum bandwidth found to minimize AICCc or CV in GWNBR model. After creating this matrix with zeros and ones, it is row-standardized, and finally, the spatial lag variables are created by the multiplication of this row-standardized matrix by the original variable, as: (2) yj ∼ NB[tj exp k βk µj, νj Xjk , α µj, νj ] Figure 2 illustrates how to use the optimum bandwidth found in GWNBR to create the matrix of weights discussed above. The distance-band weights and spatial lag variables are created using Geoda (Anselin, et al., 2006).
To inspect the multi-collinearity among the variables and the spatial autocorrelation patterns of the variables, a descriptive analysis of the data is performed, followed by the spatial analysis using the Moran's I statistic. The results of the spatial autocorrelation analysis determinate the necessity of the geographically weighted models. The effect of RLC deactivation is examined using the NBR technique with and without spatial lag factors. The results are compared with the respective results of Poisson Regression (PR) models to inspect the model efficiency. Table 3 displays the average crashes and standard deviation by type of intersections and the RLC implementation status for total, injury, and angle crashes. A number of observations can be drawn from the results. First, the average number of crashes has increased over the study period. For example, the average total crashes in all intersections are 7.32 in the period of RLC deactivation, compared to 5.79 when RLCs were enforced. The patterns for injury and angle crashes are the same (e.g. 3.69 and 3.06 for injury crashes and 1.84 and 1.25 for angle crashes). Second, this pattern remains the same for each type of intersections. For all the "None" intersection, the average number of total crashes is 6.17 in the RLC deactivation period, compared to 4.79 in the "before" period. A similar pattern is seen for the "RLC" and "Near" intersections respectively. Third, RLC intersections on average have a higher number of crashes than the "Near" and "None" intersections, as the number for total crashes in RLC intersections is 18.57 after RLC deactivation, compared to 9.63 and 6.17 for the "Near" and "None" intersections. Fourth, the trends and patterns for injury and angle crashes are the same as the ones for the total crashes, as illustrated in columns 4 and 5 of Table 3. The ANOVA tests indicate that all the differences are statistically significant at the 0.001 level.

Trends and patterns of crashes in Arlington
The last column in Table 3 also reveals that while the total traffic counts had increased significantly citywide, the average daily traffic counts at each type of intersections were generally lower after RLC deactivation. This may be due to the fact that traffic counts were conducted at limited locations rotated by year and the way how traffic counts were linked to intersections as described in Sect. 2.
(3) SpatialLagVariable = W × Variable  Moreover, the results in Table 3 indicate that the variable "Crashes" is over-dispersed as the variance, the square of standard division, is greater than the mean for each type of intersection, which is an indication of overdispersion and supports the use of NBR over PR (Hilbe, 2014). While the Moran's I statistics of total, angle, and injury crashes are positive and signify spatial clusters, the patterns are insignificant at the 0.05 level.
While the trend analyses demonstrate a significant difference between RLC enforcement and deactivation, the results also show that the trend is the same for all types of intersections and all types of crashes, which suggests that the automatic red-light camera treatment may not be the only contributor to safety in intersections. To demonstrate the detrimental safety effect of RLC deactivation, further analysis with the control of confounding factors is required. The descriptive statistics in Table 3 also suggest that the NBR model technique is more suitable than the PR model for the research since the crash count data are over dispersed (UCLA, 2019).

Multi-collinearity, spatial autocorrelation, and estimates of optimum bandwidth
The results of Pearson correlation analysis reveal no multi-collinearity among the predictors (Table 4). Further analysis of the independent variables indicates that there exists evidence of cluster patterns in average speed limit, traffic counts, percent public land use, and population aged 18 and over, as the Moran's I statistics for these variables are positive (0.19, 0.25, 0.47, and 0.23, respectively) and statistically significant at the 0.05 level or better. The results suggest the necessity to incorporate spatial lag variables in the modeling process. Table 5 illustrates the results of bandwidth search using a combination of fixed or adaptive kernel distance methods and the Akaike Information Criterion (AICc) or the cross-validation (CV) function. The results indicate that the bandwidth estimated by the fixed kernel distance with the CV function is the optimum bandwidth as the corrected AIC (AICc) is the smallest among all.

The safety effects of automatic red-light cameras
The model goodness-of-fit statistics of PR and NBR, with and without spatial lag variables, are presented in Table 6 for the numbers of total, angle, and injury crashes. The Wald χ 2 statistics suggest that all models are significant at the 0.001 level. However, the results show that the PR is the most inefficient model as expected. While the model of PR with the spatial lag variables (created from the optimum bandwidth of GWPR and here named as GWPR) improves the performance of PR, the goodness-of-fit statistics indicate it is not efficient. The results reinforce the notion that the Poisson approach is not appropriate for data with overdispersion. The Akaike's Information Criterion (AIC) statistics indicate that the model of NBR with spatial lag variables (created from the optimum bandwidth of GWNBR and here named as GWNBR) is the most efficient among all the models for each type  of crash. The Deviance results are consistent with AIC statistis. Hence, the results of the GWNBR models are the focus of the discussion below. Table 7 displays the results of the GWNBR model for the total, angle, and injury crashes, respectively. The results for total crashes show that the incidence-rate ratio (IRR) of the variable "deactivation" is about 1.40, indicating that the incident rate for the "deactivation" (After) is about 1.40 times of the incident rate for the reference group (Before). In other words, the total crash rate in the period after RLC deactivation is about 40% higher compared to the rate in the period prior to the RLC deactivation, holding other variables constant. Such a difference is significant at the 0.001 level.
Similarly, the total crash rate is about 1.32 times higher in the RLC intersections and about 72% higher in the "Near" intersections than that in the non-RLC intersections, all else being equal. These results are significant at the 0.001 and 0.05 levels respectively. The IRR for the "RLC*Deactivation" variable (about 0.90) and the IRR for the "Near*Deactivation" variable (about 0.89) are not significant at the 0.05 level. The insignificant results indicate that the effect of RLC deactivation does not vary significantly across different types of intersections. To put it differently, the effect of deactivation on crashes is uniform across all types of intersections.
Besides the key variables of interest, the model for total crashes also indicates that the total crash rate increases about 12% for every mile per hour increase in average speed limit. Moreover, results also indicate that the incidence-rate ratio (IRR) of the spatial lag of the average speed limit variable is about 1.039 and significant at the 0.05 level. The result signifies a positive effect of 4% on total crash rate, all else being equal. Similarly, traffic counts and the spatial distribution have a positive impact on total crash rate at the 0.05 level, though the extents are much smaller than the speed limit factor. The spatial pattern of public land use also shows a positive but limited effect on total crash rate. These variables are statistically significant at the 0.05 level or better. The effects of other predictors are not significant at the 0.05 level.
The model results for injury crashes are by and large the same as the results for the total crashes, except for the spatial lags of speed limit and public land use variables. The model results for angle crashes are also generally consistent with those for total crashes in terms of signs. However, there is no significant difference in angle crashes among the types of intersections as the variables ("RLC" and "Near") are not significant at the 0.05 level. Unlike the results for total crashes, the variables of traffic counts, spatial lags of speed limits and traffic counts are also insignificant at the 0.05 level. Nevertheless, the effect of RLC deactivation on the incident-rate ratio of angel crashes is the highest, about 1.56 compared to about 1.38 for injury crashes and about 1.40 for total crashes.

Summary and discussion
The safety effects of RLCs are important for decisionmaking by municipals. However, the number of crashes is affected not only by RLC implementation status, but also the environment characteristics around intersections. This study investigates the effect of RLC deactivation on the number of total, injury, and angle crashes in the city of Arlington, Texas. The crash data, along with traffic, land use, and demographic data, are analyzed using the Geographically Weighted Negative Binomial Regression Modeling approach. The study contributes to the state of knowledge and the debate about the safety effects of RLCs with new empirical evidence. The GWNBR is a powerful statistical tool that offers the capacity to analyze the effect with control of RTM bias and other confounding factors without requiring a large amount of data from reference sites. The Moran's I statistic can detect the spatial autocorrelation of dependent and independent variables with statistical confidence and offers a data-driven, evident-based rationale for investigating the spillover effect that has been hypothesized in prior studies. The approach for optimum bandwidth estimation by Da Silva and Rodrigues (2014) further aids the application of GWNBR.
The results of this study suggest that overall, crashes at intersections with traffic lights in Arlington have been on the rise over the years and crashes on average are higher at intersections with RLCs than those without. In addition, the study reveals that spatial cluster patterns of population aged 18 and over, speed limits, traffic counts, and public land use. While the Moran's I statistics for crashes are positive, no significant spatial cluster is detected with statistical confidence. The spillover effect of crashes cannot be inspected.
The model results indicate that the type of intersections, RLC implementation status, speed limit at intersections, traffic counts, and the spatial lags of the speed limits, traffic counts, and percent of public land use variables are factors statistically significant to the number of total crashes at the 0.05 level or better. On the other hand, the effects of driving age population, regardless its spatial pattern, and the percent of land for public uses are not significant at the 0.05 level.
The model results for injury crashes are by and large consistent with the model results for the total crashes, though the magnitudes of individual variables vary. Specifically, the IRRs of the independent variables for injury crashes are generally smaller than the ones for total crashes. The spatial lags of average speed limit and percent public land use are statistically insignificant despite consistent signs. The effect of RLC deactivation is the highest on angle crashes. While the results for angle crashes are generally in agreement with those of total and injury crashes in terms of signs, many are not significant at the 0.05 level. These findings lend support for previous studies that call for attention to the tradeoff in safety effects of RLCs on different types of crashes and the cost/ benefit analysis of RLCs. Furthermore, the "none moderation" effect, as revealed by the insignificance effect of the interaction term between type of intersection and RLC implementation status, suggests that the effect of RLC is independent from the effect of time, and that RLC deactivation does have a detrimental effect on safety. These findings support the professional judgment about the intersections with significant safety concerns of the city staff and reinforce the necessity and rationale for placing RLCs at certain high-risky intersections (Gallagher & Fisher, 2017;Shin & Washington, 2007).
The model results consistently confirm that higher speed limits at intersections are likely to associate with higher numbers of total, injury, and angle crashes, holding other factors constant. The finding is consistent with studies by Council et al. (2005), Kitali et al. (2021) to name a few. This could be a result that drivers travel at a faster speed with close distance from each other. The findings suggest that focusing on intersections known to have safety concerns is necessary. Regulating the speed limit at these intersections might be helpful. The safety effect of the speed limit could be enhanced by placing warning or speed limit signs at distant places approaching these intersections.
This study is not without limitations. First, the empirical results are limited to the City of Arlington since they are based on data from that city. Second, the data is limited to 20 months before and after RLC deactivation respectively. Although the study captures the time when RLC enforcement was the highest and the same length of time when RLCs were removed, data with a longer time may reveal different results. Third, while this study controls for several confounding factors, it may not capture other significant factors, such as the safety signs and locations as such data are not available to the researchers. In addition, traffic counts at intersections may not reflect the true traffic volume due to the practice how traffic counts were conducted. Research with fine-tuned model specifications and improved measurements and data would offer more insight into the effects of RLCs and other safety policies and practices. In addition, the benefit-cost analysis would provide additional information to inform policy decisions, since automatic red light camera enforcement and deactivation may result in an increase or decrease in different types of crashes, and some types of crashes are more detrimental than others as suggested by many previous studies (see, e.g., Council et al., 2005;Persaud et al., 2005;Claros et al., 2017). Nevertheless, this research offers insights into a more powerful and efficient method for studying safety effects with limited data and empirical evidence of RLC deactivation for a previously unstudied area.