1 Understanding speed selection behavior of drivers following speed limits increases is critically 2 important. To date, the literature has largely focused on freeways and the effects of speed limit 3 changes on two -lane highways remains under researched. Prior research has generally focused on 4 changes to mean speeds, though the speeds of both the highest and lowest drivers are also of great 5 interest. This study investigates trends in free -flow travel speeds following 2017 legislation that 6 increased the posted speed limit from 55 to 65 mph on 943 miles of rural highways in Michigan. 7 Speed data were collected for over 46,000 drivers at 67 increase segments where speed limit 8 increased and 28 control segments, where speed limits remained unchanged, before and during 9 each of the two successive years following the speed limit increases. Site -specific traffic, 10 geometric, and cross -sectional information was also collected. I mpacts of the speed limit increases 11 on the 15th, 50th, and 85th percentile speeds were evaluated using quantile regression. Separate 12 analyses were conducted for passenger cars and heavy vehicles. Locations where the speed limits 13 were raised experienced increases in travel speeds ranging from 3.8 to 5.1 mph. The control sites 14 experienced marginal changes in speeds, which suggests any spillover effects of the higher speed 15 limits have been limited. Significant differences were observed across the quantiles with respect 16 to the effects of the speed limit inc reases, as well as numerous site -specific variables of interest. 17 The results provide important insights as to the nature of driver speed selection and the impacts of 18 speed limit increases. 19 20 Keywords: speed limit increase , non -freeways, rural highway s, quan tile regression 21 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 3 INTRODUCTION AND BACKGROUND 1 The impact s of speed limits on traffic operations and safety have been long -standing areas of 2 interest to transportation policy and research . Maximum statutory speed limits are posted to inform 3 driver s of the highest speed that is considered safe and reasonable under ideal traffic, road, and 4 weather conditions (1). Speed limits also provide a basis for the enforceme nt of unreasonably high 5 travel speeds. 6 Speed limits are generally applicable for a particular class of highways with specifi c 7 design, functional, jurisdictional , or location characteristics (2). These limits are typically 8 established in consideration of the design speed of the road, which influences various geometric 9 design features such as minimum stopping sight distance, minimum horizontal curve radius, and 10 maximum grade (3). The American Association of State Highway and Transportation Officials 11 (AASHTO) recommends using above -minimum criteria where practical (3) and, ideally, the 12 statutory speed limit should be set at or below the highway’s prevailing design speed . 13 Speed limit policies in the United States have changed considerably over time , starting 14 with the implementation of the National Maximum Speed Law (NMS L) of 55 mph in 1974 . In 15 1987, the Surface Transportation and Uniform Relocation Assistance Act allowed for increases 16 of up to 65 mph on rural interstates (4) and the NMSL was fully repeal ed in 1995 , restor ing the 17 autonomy of establishing speed limits to the individual states (5). Subsequent to the enactment of 18 these laws, speed limits were predominantly increased on limited -access rural freeways , which are 19 the types of roads with the highest speed limits and are also the safest when considerin g crash risks 20 per distance traveled (6) given their higher design standards. The research literature shows that 21 fatalities on rural interstates are consistently higher among those states with higher maximum 22 statutory spee d limits (7). Despite this fact, at least 25 states have increased or proposed to increase 23 maximum speed limit s since 2011 (5, 8–10). 24 In general, the research literature has focused predominantly on limited access freeways. 25 Some early studies following the 1987 NMSL relaxation found average speeds to increase by 2 to 26 7 mph following the spe ed limit increase to 65 mph (11–14). Subsequent studies have shown 27 increases on the or der of 2 to 3 mph, in general, for 5 -mph increase s in the posted limit (15, 16). 28 Although speed limit increases generally increase operating speeds, the exact relationship is not 29 straight -forward and several studies demonstrate considerable variability in the magnitude of speed 30 increases after speed limits are changed (16, 17). Earlier research has shown drivers’ speed 31 selection to be impacted by not only the posted speed limit, but also by roadway and roadside 32 characteristics, as well as traffic volumes (18–22). Design speed , pavement conditions, and 33 weather are some of the other factors that directly impact drivers’ speed selection while differences 34 are also observed acr oss vehicle types and among driver with different socio -economic 35 characteristics (22, 23). 36 In contrast, research on the effects of speed limit changes on two -lane highways has been 37 more limited. This is due, in part, to the significant variability in the design characteristics of such 38 highways, where speeds can range from 25 to 75 mph. This makes it difficult to assess the 39 magnitude of large -scale speed limit increases across states as has been done frequently in the case 40 of freeways (7). A National Cooperative Highway Re search Program (NCHRP) project (15) found 41 that increasing speeds from 55 mph to 65 mph resulted in increases i n average speed of 3.4 mph 42 from a before -after analysis. Additional studies have investigated the relationship between 43 roadway geometry and operating speeds, particularly on horizontal curves . The majority of these 44 studies have also focused on freeways ( 16-20), though a few recent studies have examined speeds 45 on rural two -lane highways ( 21, 22 ). The research literature shows that increases in speed lim its 46 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 4 significantly affect speeds on two -lane roads, but the results are highly dependent on contextual 1 factors (24). 2 At least 27 US states have maximum speed limits that are lower on two -lane highways as 3 compared to freeways, while the remaining states provide the same maximum speed limit for both 4 roadway types (25). However, various states have also recently increased the speed limits on these 5 roadways, as well. The safety literature generally suggests that increasing speed limits on non - 6 freeways will result in an increase in the overall crash rate and will also result in a higher proportion 7 of more severe crashes due to the increase in the energy dissipated during crashes due to vehicles 8 traveling at higher speeds (15). However, further research in this area is warranted given 9 continuing consideration of speed limit increases in both the US and abroad . 10 Related to this issue, the State of Michigan passed Public Acts 445 and 447 in 2016 , which 11 increased the state’s maximum statutory speed limits from 55 to 65 mph on more th an 900 miles 12 of state -maintained two -lane highways . Moreover, the speed limit for heavy vehicles, including 13 trucks and buses, als o increased to 65 mph on these same highways (26, 27). Implementation of 14 the speed limit increases began in June of 2017 and concluded later that year. Consequently, this 15 provides an appropria te setting to obtain important insights as to the immediate and longer term 16 impacts on driver speed selection . To that end , this paper presents the results of a longitudinal 17 case-control evaluation that was performed to quantify changes in driver speed sel ection as a 18 function of speed limit, vehicle type, and various site characteristics . 19 In addition, this study addresses another gap in the research literature by examining the full 20 speed distribution of vehicles under free-flow conditions . Much of the prior research has 21 investigated impacts on mean speeds, often examining aggregate trends that include trailing 22 vehicles where the driver was not free to select their preferred speed (9, 12, 14, 15, 16). Such 23 methods are unable to fully exploit the rich information available in the speed data distributions . 24 For example, the aforementioned NCHRP project (15) utilized daily aggregated average speed 25 measures from permanent traffic recorders as a part of a before -after st udy, as well as cross - 26 sectional data that did not include any data from the period before the speed limit increases 27 occurred. 28 The speeds at either extreme of the speed distribution are of particular interest as crash 29 risks are significantly increased when there is substantive variability in speeds. To address these 30 concerns, this study involves the estimation of a series of quantile regression models to assess 31 changes in the 15th, 50th, and 85th percentile speeds following the speed limit increases. The re sults 32 help to advance our understanding of how speed limit increases affect the driving population and 33 how these underlying behavioral changes may help to explain related increases that are observed 34 with respect to crash risks. 35 36 DATA COLLECTION AND SUMMARY 37 This study evaluat es change s in travel speeds along rural two-lane highways maintained by the 38 Michigan Department of Transportation (MDOT). The primary objective is to discern impacts 39 associated with the 2017 statewide speed limit increase s. As a p art of this effort, a case -control 40 analysis is conducted to compare speeds before and after this increase went into effect. The control 41 locations include highway segments where the 55 -mph maximum limit was maintained and allow 42 for a determination of whethe r any spillover effects are observed where speeds increase at other 43 locations due, in part, to increases occurring elsewhere in the system. In addition, the speed data 44 from all locations are integrated with robust information detailing the roadway and road side 45 environment, as well as prevailing traffic conditions. This is important as AASHTO notes that 46 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 5 driving speeds are affected by four general factors, including physical characteristics of the road 1 and roadside interference, weather, other vehicles, and t he speed limit (3). This section provides 2 details of the site selection and data collection procedures employed as a part of this study. 3 4 Site Selection 5 Prior to the speed limit increases in mid -2017, the research team identif ied locations on the MDOT 6 rural two-lane highway network where periodic spot-speed data collection would be performed 7 before and after implementation of the increased speed limit . This included a sample of locations 8 where the speed limit was set to be increased to 65 mph, along with a comparison sample of similar 9 highways where the 55 mph limit would be retained. As the speed limit increase s mostly occurred 10 in MDOT’s most rural Superior and North regions, the majority of both the speed limit increase 11 and control sites were selected from those areas. Additional control sites were selected from central 12 and southern Michigan to provide representation among other regions where the 55 mph speed 13 limit was retained. 14 The data collection setup at most locations occurred along straight , flat (i.e., grades less 15 than 2 percent) sections of highwa y. However, a select group of horizontal curves with advisory 16 speeds below 55 mph were also included as such locations have been shown to exhibit 17 disproportionately high numbers of sp eed-related crashes . Generally speaking, no more than one 18 site was selected per county along a specific highway route. Figure 1 provides a map of the routes 19 where speed limits were increased to 65 mph, in addition to identifying locations where data were 20 collected for both the speed limit increase and control sites . 21 Data were collected from a total of 95 sites . At each location, spot speed data were obtained 22 from covert roadside locations using either elevated high -definition video cameras or handheld 23 Light Detection and Ranging ( LiDAR ) speed guns . The sites include 67 locations (30 camera sites 24 and 37 LIDAR sites) at which the speed limits were increased, as well as 28 control sites (18 25 camera sites and 10 LIDAR sites) where the 55 -mph limit remained in place . Supplementary site - 26 specific information was also collected using aerial photography, including details such as lane 27 width, shoulder widths, horizontal curvature, and the presence of no -passing zones or passing relief 28 lanes . 29 30 Speed Data Collection 31 Three waves of speed data collection were performed as a part of this study. The initial wave 32 occurred during the late spring and s ummer of 2017 prior to the speed limit increases. Data for the 33 periods after the speed limit increase s were c ollec ted during late spring and summer of 2018 and 34 2019. Data were collected between the hours of 8:30 am and 6:30 pm on weekdays under clear 35 weather and dry pavement conditions . 36 For the L iDAR data collection , measurements were obtained from an unmarked vehicl e 37 parked on a side street, driveway, or parking area that was not readily visible to motorists on the 38 subject highway segment . Specific attention was given to being covert so as not to impact the 39 speed of approaching drivers. At each site, the targets were to collect 100 speed measurements for 40 passenger vehicles and at least 10 for heavy vehicles in each direction of travel . During data 41 collection, only vehic les with a headway of at least 4 .0 seconds were considered in order to reduce 42 potential impacts of platooning . Due to the rural nature of these highways, free flow conditions 43 were typically present during the data collection. 44 For the data collection with high definition video cameras , the cameras were temporarily 45 installed on a telescoping pole at covert roadside locations . After completion of the field video 46 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 6 recordings , a team of trained reviewers manually performed a frame -by-frame review of the videos 1 to assess the time required for each vehicle to traverse a fixed distance between known reference 2 markers. Vehicle classification , headway, and hourly volume in the direction of speed data 3 collection during each study period were also recorded. Vehicles were classified as passenger 4 vehicles , passenger vehicles with trailer s, truck, single un it, tractor -trailer, motorcycle, farm 5 equipment, or all -terrain vehicle. As the camera dataset included all the vehicles during the 6 observation time, the dataset was filtered to include only vehicle observations with a minimum 7 headway of 4.0 seconds. 8 9 FIGURE 1 Location of Speed Limit Increase and Control Sites for Speed Data Collection . 10 11 The collected and calculated data were tabulated and coded into a single data file for 12 subsequent analyses . The initial data se t included complete records for 62,939 vehicle observations 13 collected across the three data collection periods from the 95 sites. Prior to the analyses, the dataset 14 was filtered to exclude motorcycles, all -terrain vehicle s, farm equipment , passenger vehicles with 15 trailer s, and any other observations where free -flow condition could have been compromised ( e.g., 16 bicyclist or pedestrian on the shoulder, turning vehicles , passing vehicles , vehicles with brake 17 lights on). Table 1 presents the desc riptive statistics for each variable included in the final dataset, 18 which included 46,162 free-flowing vehicle s. Site types (increase or control) and data collection 19 period (before or after the speed limit increase) were combined and categorized in four gr oups t o 20 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 7 test the impact of speed limit change on increase and control segments. Observed vehicles were 1 categorized into passenger cars and heavy vehicles allow ing separate analysis for each vehicle 2 types. Sites were also categorized based on the passing pe rmission or presence of passing relief 3 lane on both directions. Roadway geome tric characteristics such as lane width and degree of 4 curvature were also used to categorize the collected data. Furthermore, location of the data 5 collection sites in different MDOT region s were also used to categorize collected data. 6 TABLE 1 Descriptive s tatistics for study sites (n = 46,162) 7 Parameters Mean Std. Dev. Traffic v olume (veh/hr) 280.00 247.84 Before -control sites (1 if yes; 0 if no) 0.13 0.33 Before -increase sites (1 if yes; 0 if no) 0.21 0.41 After -control sites (1 if yes; 0 if no) 0.24 0.43 After -increase sites (1 if yes; 0 if no) 0.42 0.49 Passenger vehicle (1 if yes; 0 if no) 0.89 0.31 Heavy vehicle (1 if yes; 0 if no) 0.11 0.31 Normal section or one -way passing lane (1 if yes; 0 if no) 0.90 0.31 Two-way passing lanes (1 if yes; 0 if no) 0.10 0.31 Passing permitted (1 if yes; 0 if no) 0.81 0.40 Passing restricted (1 if yes; 0 if no) 0.20 0.40 Lane width = 12 feet (1 if yes; 0 if no) 0.74 0.44 Lane w idth =11 feet (1 if yes; 0 if no) 0.26 0.44 Degree of curvature =0 (1 if yes; 0 if no) 0.86 0.35 Degree of curvature <5 (1 if yes; 0 if no) 0.08 0.27 Degree of curvature =5 -10 (1 if yes; 0 if no) 0.04 0.20 Degree of curvature >10 (1 if yes; 0 if no) 0.02 0.14 MDOT region = Superior (1 if yes; 0 if no) 0.43 0.50 MDOT region = Bay (1 if yes; 0 if no) 0.06 0.24 MDOT r egion =North (1 if yes; 0 if no) 0.46 0.50 MDOT region = Grand (1 if yes; 0 if no) 0.04 0.19 MDOT region = University (1 if yes; 0 if no) 0.01 0.11 8 STATISTICAL METHODS 9 Using the data described previously, a series of regression models were estimated in order to 10 discern the impacts of the speed limit increases while controlling for the effects of other pertinent 11 factors , including lane width, horizontal curvature, and the presence of passing restrictions and 12 passing relief lanes. Most of the prior studies evaluating impact of speed limit increase utilize d 13 aggregate d data and compare d before -after speed metrics using ordinary least squares ( OLS ) 14 regression techniques (16, 19, 28 -30), ANOVA , and t -tests ( 31-33). These methods while were 15 successful proving significant change in speed following the speed limit increase s, lacked to 16 provid e further details on driver speed selection behavior. While ordinary least squares (OLS) has 17 been the most widely applied method for the analysis of speed data in a regression setting, there 18 are several important limitations to OLS considering the study co ntext. First, speed data tend to be 19 skewed and, as such, the estimates for the conditional mean are not necessarily reflective of the 20 entire speed distribution. Secondly, there is particular interest in the higher and lower quartiles. 21 For example, the 85th percentile is still widely used as a metric for establishing speed limits and, 22 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 8 as such, changes in this metric are of particular interest. There is also a potential concern as to 1 drivers who are uncomfortable traveling at the highest speeds, which may res ult in platooning and 2 high-risk passing by other motorists. Quantile regression is an appealing alternative to OLS as this 3 allows for estimation of the entire conditional distribution rather than just the conditional mean. A 4 few pr ior studies have successfully utilized quantile regression approach to analyze speed data (34, 5 35). To the best of our knowle dge, this is the first study using this technique to evaluate impact of 6 speed limit policy change. For the purposes of this study, the analysis foc uses on the 15th, 50th, and 7 85th percentile speeds. In addition, separate models are estimated for passenger cars and heavy 8 vehicles to determine how speed selection within both groups were impacted by the speed limit 9 increase . Quantile models are similar to OLS linear regression models as they also assume an 10 additive relationship between the dependent variable and the independent variable s. However, 11 unlike OLS , quantile regression does not make any assumption s about the distribution of the 12 dependent variab le and is more resilient to the influence of outliers (36). 13 The general form of the quantile regression model is similar to that of a linear regression 14 model. Quantile level s are denoted by 𝜏, which represents the value of the dependent variable 15 below which the proportion of the conditional response population is 𝜏. Within the context of this 16 study, the quantile regressio n model takes the form shown in Equation 1: 17 18 𝑄𝜏(𝑦𝑖)= 𝛽0(𝜏)+ 𝛽1(𝜏)𝑥𝑖1+ 𝛽2(𝜏)𝑥𝑖2+⋯+𝛽𝑝(𝜏)𝑥𝑖𝑝+ 𝜀𝑖 (1) 19 where 𝑄𝜏(𝑦𝑖) is the 𝜏th quantile of the speed distribution, 𝑥𝑖𝑗 are observed independent variables 20 associated with observation i, and 𝜀𝑖 is a random erro r term with mean equal to zero. The beta 21 coefficients 𝛽𝑗(𝜏) are now the functions of quantile level 𝜏. The 𝛽𝑗(𝜏) parameters are estimated by 22 solving the minimization problem: 23 min 𝛽0(𝜏),⋯,𝛽𝑘(𝜏) ∑ 𝜌𝜏𝑛 𝑖=1 (𝑦𝑖−𝛽0(𝜏)−∑ 𝑥𝑖𝑗𝛽𝑗(𝜏)𝑝 𝑗=1) (2) 24 25 where 𝜌𝜏(𝑟)=𝜏max (𝑟,0)+(1−𝜏)max (−𝑟,0). The function 𝜌𝜏(𝑟) is referred to as the check 26 loss which gives asymmetric weights to each of the individual error 𝑟 for each data point, 27 depending on the quantile and the sign of the error. The function max () returns the maximum 28 value in the parenthe sis. Thus, for positive errors, the check f unction multiplies the error by 𝜏, and 29 by (1−𝜏) if the error is negative. Minimizing equation (2) results in minimum median absolute 30 deviation for the quantile model. For each quantile level 𝜏, the solution to this minimization 31 problem yields a distinct set of regression coefficients (37). The quantil e regression was conducted 32 using R -Studio in order to estimate a model for the 15th, 50th, and 85th percentile speeds. 33 The same set of predictor variables were included in each model. This included binary 34 indicator variables for the study period (before vs. after) and site type ( increase vs. control), hourly 35 volume during the observation period , lane width, degree of curve, MDOT region, and presence 36 of passing lanes or passing restrictions . Although t he dataset included several other variables , 37 including shoulder width and type, t errain, pavement type, and time-of-day, these variables were 38 not found to be statistically significant. 39 40 RESULTS AND DISCUSSION 41 Figure 2 provides an aggregate -level summary of changes in the average speed, 85th percentile 42 speed, and speed s tandard deviation for both passenger cars and heavy vehicles at locations where 43 the speed limit increases occurred. This figure provides details for the periods immediately before, 44 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 9 one year after, and two years after the speed limit increases went into effect and only for the tangent 1 segments (as speeds were significantly different during all periods at the horizontal curve 2 locations). 3 These preliminary results show the average speed s of passenger cars were 3.8 mph higher 4 after one year and 4. 1 mph higher after two years compared to the pre-increase period . For heavy 5 vehicles , these increase s were 4.1 mph and 4. 5 mph, respectively . The 85th percentile speed s 6 increased by 4.0 mph after one year and 5.0 mph after two years for bo th vehicle types. 7 Importantly, the speed standard deviation (averaged across all sites) also increased following the 8 speed limit increase. This suggests there was significant variability in the magnitude of increases 9 across the distribution of drivers. 10 It is important to note tha t these data provide results at an aggregate level and do not 11 consider the effects of traffic volume and geometric characteristics . These factors were considered 12 in the subsequent regression analysis , along with similar data for the control locations. 13 14 (a) Passenger cars 15 16 (b) Heavy veh icles 17 FIGURE 2 Trends in Mean , 85th Percentile , and Standard Deviation of Speeds on Tangent 18 Segments where Speed Limit Increases Occurred 19 20 As noted previously, s eparate quantile regression models were estima ted for passenger cars 21 and heavy vehicle s at the 15th, 50th, and 85th percentiles (quantile s, τ = 0.15, 0.50 , and 0.85 ). Results 22 of these models are provided in Table 2 and Table 3 for passenger vehicles and heavy vehicles, 23 respectively. For each quantile model, parameter estimates are provided, along with standard errors 24 and the p -value that corresponds to the t -statistic used to ev aluate whether each of these parameters 25 was significantly different than zero. For each quantile, a separate model and the model equation 26 can be written using the parameter estimates showed in Table 2. The parameters can be interpreted 27 at different quantil e level s separately. F or example, at τ = 0.15 (15th percentile ) if Period and Site 28 Type are set to “After -increase sites”, the speed will be 3.78 mph higher than the “Before -control sties”. 29 The same will be higher by 5.01 and 4.91 mph at τ = 0.50 and τ = 0.85 , respectively. 30 For comparison purposes, Figure 3 and Figure 4 provide graphical comparisons of the 31 parameter estimates for each quantile, along with the same estimates for an OLS model of mean 32 speeds for both vehicle types. When examining these plots, the OLS parameter estimates are 33 reflected by a horizontal line, along with the associated 95 per cent confidence intervals for each 34 of the OLS parameters. If the quantile regression parameters fall outside of these bounds, it is 35 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 10 reflective of differences that are statistically significant at this same confidence level. It is clear 1 from these respectiv e tables and figures that quantile regression is able to identify relationships in 2 the data that would not be possible under the more typical OLS framework. The remainder of this 3 section details the results of these analyses and provides accompanying discu ssion of the practical 4 implications of these results. 5 6 TABLE 2 Linear Quantile Regression Model for Passenger Vehicle Speeds 7 Dependent Variable= Speed of PC ( n = 41,223) ` τ = 0.15 τ = 0.50 τ = 0.85 Parameters Estimate (Std. Error) P- value Estimate (Std. Error) P- value Estimate (Std. Error) P- value Intercept 57.72 (0.52) <0.01 63.36 (0.35) <0.01 69.57 (0.51) <0.01 Ln(Hourly Total V olume) -0.84 (0.08) <0.01 -0.84 (0.05) <0.01 -1.03 (0.08) <0.01 Period and Site Type Before -control sites Base Condition Before -increase sites 1.51 (0.17) <0.01 0.85 (0.12) <0.01 0.27 (0.17) 0.12 After -control sites -0.78 (0.15) <0.01 -0.35 (0.10) <0.01 -0.25 (0.15) 0.09 After -increase sites 3.78 (0.16) <0.01 5.05 (0.11) <0.01 4.91 (0.16) <0.01 Cross -section Normal/one -way passing Base Condition Two-way passing -0.06 (0.17) 0.72 0.23 (0.12) 0.04 1.34 (0.16) <0.01 Lane W idth 12 feet Base Condition 11 feet -0.07 (0.12) 0.55 -0.28 (0.08) <0.01 -0.21 (0.12) 0.07 Passing Restricted Base Condition Permitted 2.05 (0.15) <0.01 1.12 (0.10) <0.01 0.80 (0.15) <0.01 Degree of C urvature 0 Base Condition <5 -5.28 (0.20) <0.01 -2.46 (0.14) <0.01 -0.77 (0.20) <0.01 5-10 -11.50 (0.24) <0.01 -10.69 (0.16) <0.01 -8.07 (0.23) <0.01 >10 -25.64 (0.34) <0.01 -27.34 (0.23) <0.01 -15.60 (0.34) <0.01 MDOT Region Superior Base Condition Bay -4.52 (0.21) <0.01 -3.51 (0.14) <0.01 -3.24 (0.20) <0.01 North -0.62 (0.11) <0.01 -0.85 (0.07) <0.01 -0.77 (0.10) <0.01 Grand 0.61 (0.23) <0.01 0.75 (0.16) <0.01 1.32 (0.23) <0.01 University -3.24 (0.40) <0.01 -2.12 (0.27) <0.01 -1.80 (0.40) <0.01 8 Effect s of Speed Limit Increase 9 First, it should be noted that the sites where the speed limits were increased tended to have higher 10 speeds than the control sections. While the control sites were matched by traffic volume, geometric 11 characteristics, and proximity to the sites where limit s were increased, these results were expected, 12 as the prior operating speeds were one of the factors considered in the selection of the segments 13 where speed limits were changed (38). The 15th, 50th, and 85th percentile speeds were 57.7 mph, 14 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 11 63.4 mph, and 69.6 mph, respectively when the 55 mph limit was in place (with other parameters 1 set to zero). Prior to the speed limit change, speeds ranged from 0.3 to 1.5 mph higher among 2 passenger cars and 0.16 to 1.45 mph higher among heavy vehicles at the sites where the increases 3 would subsequently occur. 4 It is interesting to note that these differences were largest for the lowest quartile and 5 smallest for the highest quartile. This suggests that the drivers who tend to travel the fastest also 6 tend to maintain these higher speeds irrespective of other roadway conditions when the speed limit 7 is the same. In contrast, the drivers who travel at lower speeds tend to increase their speeds when 8 conditions are more favorable, as they tended to be at the sites where speed limits were increased. 9 While it is not possible to determine directly from the available data, this may help to explain why 10 crash risks tend to be exacerbated at higher speeds as this subset of drivers seems less apt to reduce 11 their speeds bas ed on contextual factors. This point will arise during subsequent portions of the 12 discussion, as well. 13 14 FIGURE 3 Plot of Parameter Estimates for Speed Quantiles for Passenger Car 15 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 12 Following the speed limit increases, significant i ncreases were experienced across the 1 entire speed distribution at sites where the limits were increased. Among passenger vehicles, these 2 increases were 2.3 mph, 4.2 mph, and 4.6 mph for the 15th, 50th, and 85th percentiles, respectively. 3 The corresponding speed increases for heavy vehicles were 2.5 mph, 4.3 mph, and 4.5 mph for 4 these same percentiles. The increase in speeds was again higher in the upper portion of the 5 distribution (i.e., the 50th and 85th percentile), suggesting that the most aggressive g roup of drivers 6 tended to increase their speeds by a greater margin. 7 In general, these results are also similar to findings from prior studies, which have shown 8 that operating speeds increase by roughly half the magnitude of the actual speed limit increas e (11, 9 13–15, 19). Interestingly, speeds either remained unchanged or decreased at the c ontrol sites across 10 all quartiles and for both vehicle types. This is in contrast to prior research, which has suggested a 11 potential spillover effect on adjacent roads (39). 12 13 TABLE 3 Linear Quantile Regression Model for Heavy Vehicle Speeds 14 Dependent Variable = Speed of HV (n = 4,939) ` τ =0.15 τ =0.50 τ =0.85 Parameters Estimate (Std. Error) P- value Estimate (Std. Error) P- value Estimate (Std. Error) P- value Intercept 54.35 (1.72) <0.01 61.48 (0.96) <0.01 65.85 (1.11) <0.01 Ln(Hourly T otal Volume) -0.73 (0.27) <0.01 -0.90 (0.15) <0.01 -1.03 (0.17) <0.01 Period and Site Type Before -control sites Base Condition Before -increase sites 1.45 (0.58) 0.01 0.59 (0.32) 0.07 0.16 (0.38) 0.66 After -control sites -0.62 (0.50) 0.21 -0.65 (0.28) 0.02 0.17 (0.32) 0.60 After -increase sites 3.95 (0.53) <0.01 4.90 (0.29) <0.01 4.65 (0.34) <0.01 Cross -section Normal/one -way passing Base Condition Two-way passing 0.20 (0.58) 0.72 0.29 (0.32) 0.36 2.05 (0.37) <0.01 Lane W idth 12 feet Base Condition 11 feet 0.95 (0.40) 0.02 0.20 (0.22) 0.36 0.69 (0.25) <0.01 Passing Restricted Base Condition Permitted 2.34 (0.47) <0.01 1.35 (0.26) <0.01 1.16 (0.30) <0.01 Degree of C urvature 0 Base Condition <5 -7.23 (0.71) <0.01 -3.66 (0.40) <0.01 -1.47 (0.46) <0.01 5-10 -12.60 (0.72) <0.01 -12.97 (0.40) <0.01 -10.30 (0.47) <0.01 >10 -27.71 (1.26) <0.01 -29.34 (0.70) <0.01 -18.04 (0.81) <0.01 MDOT Region Superior Base Condition Bay -4.27 (0.70) <0.01 -2.94 (0.39) <0.01 -2.60 (0.45) <0.01 North 0.09 (0.34) 0.79 0.01 (0.19) 0.99 0.71 (0.22) <0.01 Grand 0.16 (0.73) 0.83 0.06 (0.41) 0.88 -0.60 (0.47) 0.21 University -6.10 (1.50) <0.01 -4.19 (0.84) <0.01 -3.60 (0.97) <0.01 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 13 Effect s of Site Characteristics 1 Turning to the other site characteristics that were found to be related to speed selection, s everal of 2 the roadway-related variables also showed interesting associations with specific quartiles of the 3 speed distribution. First, speeds were consistently reduced during periods when traffic volumes 4 were higher. Since all of the vehicles included as a part of this analysis included headways of at 5 least 4.0 seconds, this is likely reflective of the relative density of traffic over the course of the 6 segment, including upstream of the speed observation location. This is reinforced by the fact that 7 the speed reductions were most pronounced among the highe st quartiles. If these segments tended 8 to experience higher volumes, there is less opportunity for the fastest vehicles to maintain t hese 9 higher speeds. 10 11 FIGURE 4 Plot of Parameter Estimates for S peed Quantiles for Heavy Vehicles 12 13 Similar findings emerged when considering the effects of geometric and traffic 14 characteristics that related to passing. Speeds tended to be marginally different among the 15th and 15 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 14 50th percentiles along four -lane cross -sections, which included passing relief lanes in both 1 directions. However, the 85th percentile speeds were 1.3 mph higher among passenger vehicles 2 and 2.0 mph higher among trucks. This shows that the most aggressive drive rs tend to increase 3 their speeds significantly along these extended passing sections. 4 Related to this same result, two -lane segments where passing was allowed (without passing 5 relief lanes) showed higher speeds across the entire distribution, although the magnitude of this 6 difference was greatest at lower speeds. This reinforces some of the same patterns alluded to 7 previously. The lowest speed drivers appear to adapt their speeds more based upon changes in the 8 driving environment. It is difficult to determ ine what the causes are for this behavior, though 9 potential explanations may include greater risk aversion among this group or lower levels of 10 comfort under higher stress driving environments. This finding generally aligns with previous 11 results (18, 20, 22). 12 One of the most interesting results related to horizontal curvature. There was significant 13 variability in the sharpness of the curves included in the sample of study sites. Each site was 14 classified into one of four groups based upon its degree of curvature, which ranged from 0 (tang ent 15 sections), to 5 degrees (radius = 1 ,146 ft), to 10 degrees (radius = 574 ft), or more. For both vehicle 16 types and all quartiles, speeds were consistently reduced as the horizontal curves became tighter. 17 These speed reductions were again consistently gr eater among the lowest speed quartiles and lower 18 among the highest speed quartiles. On the largest radius (i.e., broadest) curves, the 85th percentile 19 vehicles reduced their speeds by only 0.8 mph and 1.5 mph among passenger vehicles and trucks, 20 respective ly. In contrast, speed reductions among the 15th percentile were 5.3 and 7.2 mph. These 21 same general trends held for the intermediate radius curves. For the sharpest curves in the sample, 22 reductions among the 85th percentile vehicles were 15.6 mph and 18.0 mph among passenger 23 vehicles and trucks, while these reductions were 25.6 mph and 27.7 mph within the 15th percentile 24 vehicles. 25 Lastly, lane width had marginal impacts on speed selection. Passenger vehicles reduced 26 their speeds very slightly on 11 -ft lane s as compared to 12 -ft lanes, with the greatest differences 27 being only 0.3 mph. Among heavy vehicles, speeds were actually marginally higher on the 11 -ft 28 lanes. Collectively, these results suggest that lane widths do not have a substantive impact on 29 speeds at widths of 11 f eet or above. Pronounced differences were also exhibited within several 30 MDOT regions, though these are largely an artifact of the dataset since these regions tended to 31 include a disproportionately large number of control sites and very sm all numbers of segments 32 where speed limit increases occurred. 33 34 CONCLUSIONS 35 This study provides important insights into the im pacts of speed limit increases on the underlying 36 speed selection behavior of drivers. Spot speed data from 95 study locations prov ided very high - 37 fidelity data as to the speed selection of more than 46 ,000 drivers under free -flow conditions. This 38 included 67 road segments where speed limits were increased from 55 to 65 mph, as well as 28 39 control sites where the speed limit was a consi stent 55 mph over the three -year study period . Three 40 waves of s peed data were collected , including shortly before (2017) , one year after (2018), and 41 two years after (2019) the increases occurred . 42 From a big -picture perspective, the results show that the 10 -mph speed limit increases 43 resulted in travel speeds that were generally between 3 mph and 5 mph higher across the 44 distributions of both passenger vehicles and large trucks. These findings are lar gely consistent with 45 prior research and reinforce the fact that drivers adjust their speeds based upon the posted limit 46 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 15 and to their environments, particularly on two -lane highways. Notably, the travel speed increases 1 varied significantly among drivers: th e magnitude of these increases tend to be highest among the 2 top end of the speed distribution. In contrast, the lowest speed drivers increased their speeds by 3 the least amount. This is important from a safety management perspective as these differences in 4 speed selection behavior also tend to increase the variability in travel speeds, helping to explain 5 the increases in the standard deviation in speeds among both passenger vehicles and heavy vehicles 6 following the speed limit increases. For both vehicle typ es, these increases were generally in the 7 range of 0.8 to 0.9 mph. 8 This increase in variability runs counter to the frequent argument that speed limit increases 9 tend to reduce the variability in speeds, as well as the resultant crash risk. For example most of the 10 previous speed limit increases have been justified with the argument that existing operating speeds 11 on high -speed roadways tend to exceed the posted speed limit anyways, often by significant 12 amounts ( 40). It would be very interesting to examine how these effects extrapolate to speeds 13 beyond 65 mph or to other facility types, such as limited access freeways. 14 The magnitude of the changes in speed limits also varied significantly based upon roadway 15 characteristics, including between passing and no -passing zones, along passing relief lanes, and, 16 particularly, on horizontal curves. In each of these instances, a few co mmon trends emerged. When 17 opportunities to drive faster arose, the fastest drivers increased their speeds more so than middle 18 and lower spee d drivers. Consequently, an important next step is to determine how these trends in 19 driver speed selection impact safety performance. 20 Such research would provide important support to inform future speed limit policy 21 decisions. While the 85th percentile sp eed has historically been viewed as a de facto performance 22 measure for determining appropriate speed limits, a 2018 survey conducted by the National 23 Committee on Uniform Traffic Control Devices (NCUTCD) Task Force shows that those 24 professionals who perform posted speed limit studies rarely use only the 85th percentile speed and, 25 instead, consider the context of the roadway where the speed limit change is being considered (41). 26 This includes factors explicitly noted in the Manual of Uniform Traffic Control Devices (2) that 27 may be considered when establishing or reevaluating speed limit s, which include road 28 characteristics, roadside development, and reported crash experiences. Being able to relate 29 differences in speed distributions to these factors has the potential to provide a more robust, 30 quantitatively based analysis framework for se lecting appropriate speed limits for specific site 31 conditions. 32 Lastly, this study appears to be among the first in the traffic safety research literature to 33 exploit the advantages of quantile regression. As clearly demonstrated herein, reliance on OLS 34 regression allows for important insights into impacts on the conditional mean speed of traffic based 35 upon speed limit increases and other site characteristics. However, significant information is lost 36 by considering only the average speed of traffic. Quant ile regression is likely to provide valuable 37 insights across a range of other contexts in which there is particular interest amongst the highest 38 and lower quantiles of a distribution. 39 Lastly, there are several limitations that should be noted with respect to this study. First, 40 quantile regression as applied in this study allows for the investigation of differences in speed 41 selection behavior within the distribution of vehicles observed at specific roadway locations. 42 However, it is important to note that the se quantiles do not necessarily represent the speeds of the 43 same drivers across locations. For example, a driver may be in significantly different quantiles 44 across study locations or at the same study location during a different time period. Nonetheless, 45 the consistency of these results across vehicle types and quantiles suggest that important 46 Mahmud, Gupta, Safaei, Jashami, Gates, Savolainen, and Kassens -Noor 16 relationships do exist. This is an area where naturalistic driving study data, or other similar 1 methods, would be valuable as they would allow for inferences as to va rious quantiles of interest 2 while controlling for driver -specific effects. 3 Moving forward, the establishment of maximum speed limits on rural two -lane highways 4 will continue to be an area of substantive interest to researchers, legislatures, and the travel ing 5 public. Ultimately, additional research is warranted to fully understand the nature of these 6 relationship s. For example, t he impacts of emerging concerns, such as distracted driving and the 7 integration of connective and autonomous vehicles, are among t he issues that prompt the need for 8 such scrutiny. 9 10 DISCLAIMER 11 Funding for this research was provided by the Michigan Department of Transportation ( MDOT ). 12 This publication is disseminated in the interest of information exchange. MDOT expressly 13 disclaims any liability, of any kind, or for any reason that might otherwise arise out of any use of 14 this publication or the information or data provided in the publication. MDOT further disclaims 15 any responsibility for typographical errors or accuracy of the information provided or contained 16 within this publication. MDOT makes no warranties or representations whatsoever regarding the 17 quality, content, completeness, suitability, adequacy, sequence, accuracy or timeliness of the 18 information and data provided or that the contents represent standards, specifications, or 19 regulations. 20 21 CONTRIBUTIONS 22 The authors confirm contribution to the paper as follows: study concept and design: Timothy 23 Gates , Peter Savolainen , Eva Kassens -Noor, and Md Shakir Mahmud ; data coll ection: Timothy 24 Gates and Md Shakir Mahmud ; analysis and interpretation of results: Md Shakir Mahmud, Nischal 25 Gupta, Timothy Gates , Peter Savolainen , Hisham Jashami , and Eva Kassens -Noor ; dra ft 26 manuscript preparation: Md Shakir Mahmud, Nischal Gupta, Babak Safaei, and Peter Savolainen . 27 All authors reviewed the results and approved the final version of the manuscript. 28 29