--- category: literaturenote citekey: ahsancanmidblockpedestrian2025 title: Can mid-block pedestrian signals (MPS) provide greater safety benefits than other mid-block pedestrian crossings? authors: "Ahsan, Md Jamil; Abdel-Aty, Mohamed; Abdelrahman, Ahmed S." year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108105 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108105" zotero_key: 5KX5JJ9Q zotero_storage: 445IGPBS collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Ahsan, Md Jamil" status: converted --- ![](_page_0_Picture_1.jpeg) Contents lists available at [ScienceDirect](www.sciencedirect.com/science/journal/00014575) # Accident Analysis and Prevention journal homepage: [www.elsevier.com/locate/aap](https://www.elsevier.com/locate/aap) ![](_page_0_Picture_5.jpeg) ![](_page_0_Picture_6.jpeg) # Can mid-block pedestrian signals (MPS) provide greater safety benefits than other mid-block pedestrian crossings? Md Jamil Ahsan \* , Mohamed Abdel-Aty , Ahmed S. Abdelrahman *Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816, USA* ARTICLE INFO *Keywords:* Conflict Modification Factor Midblock Pedestrian Signal Pedestrian Hybrid Beacon Rectangular Rapid Flashing Beacon Before-After Study #### ABSTRACT The Florida Department of Transportation (FDOT) has recently implemented a new midblock signal system known as the Midblock Pedestrian Signal (MPS) to enhance pedestrian safety. This study evaluates the effectiveness of MPSs by comparing their safety performance with other existing midblock crossing treatments. Portable CCTV video data were collected from 14 MPS equipped locations, in addition to five reference sites, to calculate Conflict Modification Factors (CoMFs) using vehicle–pedestrian conflict data. Advanced computer vision techniques, specifically the RT-DETR model for object detection and the ByteTrack algorithm for tracking were utilized to process the video data. The study employed both Cross-Sectional (CS) and Before-After methods, incorporating the Comparison Group (CG) and Empirical Bayesian (EB) approaches to evaluate the safety impacts of MPSs. To address repeated observations at the same locations and minimize bias, Safety Performance Functions (SPFs) were developed using Generalized Estimating Equations (GEE) with a Negative Binomial distribution, which proved more robust than traditional Generalized Linear Models (GLMs). The results demonstrate that MPS systems outperform Rectangular Rapid Flashing Beacons (RRFBs) and Flashing Beacons in reducing pedestrian-vehicle conflicts. Furthermore, when compared to Pedestrian Hybrid Beacons (PHBs) which share similar functionalities but differ in signal phase management—MPS systems provided additional safety benefits. Compared to PHBs, MPS systems reduced serious and all conflicts by between 26–33% and 31–33%, respectively, using the EB, CG and the CS methods. These reductions highlight the superior safety performance of MPS systems compared to PHBs and other midblock crossing treatments. With their adaptability, cost-effectiveness, and enhanced safety benefits, MPS systems are a promising alternative for upgrading existing pedestrian crossings or installing new signal systems to improve pedestrian safety at midblock locations. ## **1. Introduction** In 2024, Florida reported a total of 10,272 pedestrian crashes, including 651 fatalities; a decrease of approximately 18 % compared to 2023 ([FLHSMV Crash Dashboard, 2025](#page-14-0)). This decline can be attributed to the proactive measures implemented by the Florida Department of Transportation (FDOT) to enhance pedestrian safety ([Florida Pedestrian](#page-14-0) [and Bicycle Strategic Safety Plan, 2021](#page-14-0)). These include increasing the deployment of pedestrian signal systems, enhancing pedestrian and driver education programs, adding more roadway signage, and enforcing traffic laws more rigorously. While the number of pedestrian fatalities remains high, the decreasing trend shows progress in improving pedestrian safety. Notably, a majority of pedestrian crashes occur in urban areas (82 %) and at non-intersection locations (75 %), such as mid-blocks [\(NHTSA, 2020](#page-14-0)). To mitigate these risks, FDOT has introduced three types of mid-block pedestrian signals: Rectangular Rapid Flashing Beacons (RRFBs), Pedestrian Hybrid Beacons (PHBs), and Flashing Beacons. RRFBs are designed as pedestrian-activated systems that use bright LED lights to warn drivers when a pedestrian crosses (refer to [Fig. 1](#page-1-0)). Researches have shown that RRFBs are most effective on roads with lower speeds and fewer pedestrian activity ([Goswamy et al., 2023; Ugan](#page-14-0) [et al., 2022](#page-14-0)). However, their visibility during daylight, particularly on sunny days, can be limited. This visibility challenge contributes to a continued risk of pedestrian crashes and vehicle rear-end crashes ([Ahsan](#page-14-0) [et al., 2024; Anwari et al., 2023](#page-14-0)). Flashing Beacons, though used less frequently, serve a similar purpose as RRFBs. RRFBs are rectangularshaped lights that flash rapidly in an alternating pattern when activated by pedestrians, in contrast, regular flashing beacons are typically circular, flash at a steady rate, both are used more generally for warning *E-mail addresses:* [mdjamil.ahsan@ucf.edu](mailto:mdjamil.ahsan@ucf.edu) (M.J. Ahsan), [m.aty@ucf.edu](mailto:m.aty@ucf.edu) (M. Abdel-Aty), [ahmed.abdelrahman@ucf.edu](mailto:ahmed.abdelrahman@ucf.edu) (A.S. Abdelrahman). \* Corresponding author. ![](_page_1_Picture_2.jpeg) ![](_page_1_Picture_4.jpeg) ![](_page_1_Picture_6.jpeg) ![](_page_1_Picture_8.jpeg) **Fig. 1.** Different types of signalized mid-block pedestrian crossings ([Google Street View, 2025\)](#page-14-0). purposes. RRFBs have a more prominent and rapid flash pattern, making them more visible compared to Flashing Beacons [\(Ahsan et al. 2025a, b,](#page-14-0) [c](#page-14-0)). PHBs are traffic control systems designed to improve pedestrian safety with a unique signal pattern. These beacons remain off when inactive and are activated by a pedestrian pressing a button. The sequence begins with a flashing yellow light to alert drivers, transitions to a steady yellow light as a warning to slow down, and then displays a solid red light, requiring vehicles to stop completely. Finally, the beacon switches to a flashing red, signaling drivers to stop and proceed only if the crosswalk is clear of pedestrians. The main drawback of PHBs is that drivers are often not familiar with their operation, as they resemble standard traffic signals but only activate when pressing the pushbutton ([Ahsan et al., 2024\)](#page-14-0). FDOT has recently introduced a new mid-block signal system known as the Mid-block Pedestrian Signal (MPS), starting its implementation in late 2022. Its implementation is still in the early stages, with 14 locations currently using this system across Florida. MPS shares certain similarities with PHBs; however, a notable distinction is that MPS does not remain dark when not activated(refer to Fig. 1). Instead, it displays a green light in the absence of pedestrian activity, enhancing its visibility and functionality [\(Ahsan et al., 2025a,c; Fitzpatrick et al., 2024](#page-14-0)). Despite its potential, detailed safety evaluation has not yet been conducted due to the limited number of installations. This study aims to assess the effectiveness of MPSs using conflict data and compare its safety performance with other mid-block crossing treatments, such as PHB, RRFB and Flashing Beacon. # **2. Related works** This section is divided into two parts: (i) Studies on the safety effectiveness of RRFB, PHB, and MPS (ii) Limitations of existing studies. ## *2.1. Safety effectiveness of RRFB, PHB and MPS* RRFBs are considered cost-effective pedestrian safety measures but have certain limitations, typically evaluated using Crash Modification Factors (CMFs). A CMF quantifies the expected change in crash frequency after a safety treatment is applied, where a CMF less than 1.0 indicates a crash reduction and a CMF greater than 1.0 suggests a crash increase. According to [Goswamy and Abdel-Aty, \(2023\),](#page-14-0) RRFBs have the potential to reduce pedestrian-involved crashes by 69 % (CMF 0.31). However, their impact on total vehicular crashes is minimal, and they may even increase rear-end collisions, as indicated by a CMF of 1.11. This suggests that vehicles slowing or stopping for pedestrians could result in more rear-end crashes. [Monsere et al., \(2017\)](#page-14-0) reported CMFs for pedestrian crashes as 0.64 and 0.26 using a simple before-and-after analysis, and a CMF of 0.93 for rear-end crashes using an empirical Bayes approach in Oregon. Similarly, studies by [Zegeer et al., \(2017\)](#page-14-0) found that RRFBs reduced pedestrian crashes by 47 %. However, PHBs were found to be more effective, reducing pedestrian crashes by 55 %. These findings highlight the enhanced safety potential of PHBs over RRFBs, though they may come at a higher cost. Fitzpatrick et al., in two separate studies [\(Fitzpatrick et al., 2010, 2019\)](#page-14-0), concluded that PHBs not only reduce pedestrian crashes but also decrease rear-end collisions, making them more effective than RRFBs. Additional research supports this conclusion, highlighting that PHBs outperform RRFBs in terms of overall safety benefits ([Ahsan et al., 2024; Anwari et al., 2023; Ugan](#page-14-0) [et al., 2022\)](#page-14-0). Regarding MPS, [Fitzpatrick et al., \(2024\)](#page-14-0) conducted the only known study, reporting that MPS reduced pedestrian crashes by 45 % and all crashes by 34 % using cross-sectional method. However, this analysis encompassed both traditional MPS (which display a flashing red light during both the pedestrian walk and clearance intervals) and modified MPS (which display a steady red light during the pedestrian walk interval and a flashing red during the clearance phase). These variations complicated isolating the specific effectiveness of each type of MPS. [Ahsan et al., \(2025a\)](#page-14-0) evaluated the performance of five newly installed MPSs in Florida at locations that previously lacked signal systems. Using extensive video footage, the study employed Relative Time-to-Collision (RTTC) metrics to classify and analyze different levels of pedestrianvehicle conflicts. The findings indicated that MPSs significantly enhance pedestrian safety by supporting safer crossings. However, the study did not compare MPSs with other mid-block signals. In another study by [Ahsan et al., \(2025c\)](#page-14-0) an analysis of driver braking behavior and the effectiveness of traffic control systems at mid-block pedestrian crossings in Florida was conducted using extensive video-based trajectory data. The findings showed that MPS improved safety by promoting more gradual speed reductions, while PHBs and RRFBs raised concerns due to potential sudden braking. A mixed logit model with heterogeneity in the means of random parameters revealed that factors such as vehicle speed, deceleration, pedestrian volumes, signal activation, and nighttime conditions significantly influenced pedestrian safety outcomes. The **Table 1** Studies on the safety effectiveness of RRFB, PHB, and MPS. | Study | Treatment | CMF | Methodology | Dependent
Variable | Explanatory variables | |-------------------------------------|----------------------|-------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------|------------------------------------------------------------------------------| | (Goswamy and
Abdel-Aty,
2023) | RRFB | 0.31 (pedestrian
crash)
1.14 (vehicular
crash)
1.11 (rear-end
crash) | Empirical Bayes | Crash data | AADT, median, speed limit | | (Monsere et al.,
2017) | RRFB | 0.64 (pedestrian
crash)
0.93 (rear end
crash) | Simple
before after and comparison group (CG) for ped crash;
Empirical Bayes and Cross-sectional including above two
methods for rear end crash | Crash data | AADT, bus stop | | (Zegeer et al.,
2017) | RRFB,
PHB | 0.53 (pedestrian
crash at RRFB)
0.45 (ped crash at
PHB) | Cross-sectional | Crash data | AADT | | (Fitzpatrick et al.,
2019) | PHB | 0.54 (pedestrian
crash)
0.71 (rear end
crash) | Empirical Bayes and Cross-sectional | Crash data | No. lanes, No. pf legs, median,
parking, Ped. Volume, speed
limit, ADT | | (Fitzpatrick et al.,
2010) | PHB | 0.71 (all crash)
0.85 (severe crash)
0.31 (ped crash) | Empirical Bayes | Crash data | Vehicle and ped volume, median | | (Fitzpatrick et al.,
2024) | MPS | 0.554 (ped crash)
0.660 (all crashes) | Cross-sectional | Crash data | Various road geometry, Avg. daily
traffic and pedestrian | | (Ahsan et al.,
2025a) | MPS,
Unsignalized | | Mixed logit model | Conflict data | Pedestrian-vehicle dynamics,
road geometry and temporal | | (Ahsan et al.,
2025c) | MPS, PHB,
RRFB | | Mixed logit model | Conflict data | Pedestrian-vehicle dynamics,
road geometry and temporal | study emphasized the importance of clear signal visibility and the benefits of MPS over other treatments in enhancing safety at mid-block crossings. To evaluate midblock signals, the referenced studies estimated CMFs using two primary methods: the Cross-Sectional (CS) approach and the Empirical Bayes (EB) Before-After technique. In these studies, Safety Performance Functions (SPFs) were developed using annual crash data to predict crash frequencies. Additional variables influencing safety, such as Annual Average Daily Traffic (AADT), Average Daily Traffic (ADT), speed limits, median presence, pedestrian volumes, and various road geometry features, were incorporated into the analysis (refer to Table 1). #### *2.2. Limitations of existing studies* One significant limitation of existing studies is their reliance on annual crash data for developing SPFs. Although annual crash data offers a broad understanding of crash trends, it lacks the level of detail required for precise and timely evaluations. In this study, since MPSs have been newly implemented, there is limited post-implementation crash data available. Additionally, FDOT aims to expand MPS installations to more locations. Waiting several years for sufficient crash data to assess their effectiveness would not be practical for implementing a potentially promising safety strategy. A more effective alternative involves using conflict based surrogate safety measures (SSMs), such as Post-Encroachment Time (PET), RTTC, and Deceleration Rate to Avoid a Collision (DRAC). These measures offer immediate insights into potential conflicts and near-misses, enabling faster and more accurate evaluations of safety interventions. For instance, [Shahdah](#page-14-0) [et al., \(2014\)](#page-14-0) proposed a conflict-based method to estimate CMFs, addressing the limitations of traditional crash-based approaches. By integrating simulated traffic conflicts with observed crash data, their method provided reliable CMF estimates while reducing the dependence on long-term crash data. [Hasanpour et al., \(2025\)](#page-14-0) employed SSMs to assess pedestrian-vehicle conflicts at intersections as an alternative to crash-based safety evaluations, recognizing the limitations posed by the low frequency of pedestrian crashes. Their study utilized conflict-based metrics to estimate pedestrian crash risks at signalized intersections, similar to how SPFs traditionally model crash frequency. While their work demonstrated the feasibility of using SSMs in safety performance assessments, it did not incorporate pedestrian-vehicle dynamics in the development of SPFs. Another limitation of the present studies is the heavy reliance on variables like AADT and posted speed limits in SPFs development. While these variables serve as useful indicators, they fail to account for dynamic factors such as actual vehicle speeds, variability in traffic flow, and temporal changes in pedestrian-vehicle interactions. Additionally, no existing studies have conducted a comprehensive comparison among all mid-block crossing treatments, such as MPS, PHB, RRFB, Flashing Beacons, and untreated crossings. This gap in the literature makes it challenging to assess the relative safety performance of different mid-block signal systems under varying conditions. Such comparisons are critical to identifying the most effective treatments and guiding evidence-based decision-making for pedestrian safety improvements. ### **3. Contribution of the study** This study addresses the limitations of traditional crash-based evaluations by utilizing vehicle–pedestrian conflict data from SSMs, such as RTTC. Furthermore, it applies the Conflict Modification Factor (CoMF) as an alternative metric to the conventional CMF to assess safety improvements. The study also incorporates dynamic data, including vehicle speeds, pedestrian volumes, and traffic volumes, to provide a more detailed and accurate evaluation of safety performance. This method captures important interactions that traditional crash data often misses. In addition, the study compares the effectiveness of MPSs relative to other mid-block crossing treatments, such as PHB, RRFB, and Flashing Beacon. #### **4. Data collection** This study collected data from 19 locations, including 5 reference sites and 14 treatment sites where MPSs were installed. Of the treatment sites, 7 were previously untreated (without any signal system), 5 had **Table 2** Study locations. | # | County | Route | Treatment
Type | Speed
limit
(mph) | Total
Lanes | Median
Type | |----|-----------------|---------------------|---------------------------|-------------------------|----------------|--------------------------| | | MPS sites | | | | | | | 1 | Alachua | SR 26 | Uncontrolled
to MPS | 25 | 4 | Paved | | 2 | Alachua | SR 26 | Uncontrolled
to MPS | 25 | 4 | Raised | | 3 | Duval | SR 212 | Uncontrolled
to MPS | 40 | 4 | Paved | | 4 | Franklin | US 98 | Uncontrolled
to MPS | 45 | 2 | Paved | | 5 | Brevard | SR A1A | Uncontrolled
to MPS | 35 | 4 | Paved | | 6 | Brevard | SR A1A | Uncontrolled
to MPS | 35 | 4 | Paved | | 7 | Miami
Dade | SW 1st
Street | Uncontrolled
to MPS | 30 | 3 | No | | 8 | Alachua | SR 24A/
SR 331 | Flashing
Beacon to MPS | 45 | 4 | Raised and
vegetation | | 9 | Marion | US 41 | RRFB to MPS | 35 | 4 | Paved | | 10 | St. Lucie | SR A1A | PHB to MPS | 45 | 2 | Paved | | 11 | St. Lucie | SR A1A | PHB to MPS | 45 | 2 | Paved | | 12 | St. Lucie | SR A1A | PHB to MPS | 45 | 2 | Paved | | 13 | St. Lucie | SR A1A | PHB to MPS | 45 | 2 | Paved | | 14 | St. Lucie | SR A1A | PHB to MPS | 45 | 2 | Paved | | | Reference Sites | | | | | | | 1 | St. Johns | SR 207 | PHB | 55 | 4 | Vegetation | | 2 | St. Johns | SR A1A | PHB | 30 | 2 | Paved | | 3 | Miami
Dade | W
Flagler
St. | PHB | 40 | 4 | Paved | | 4 | Brevard | SR A1A | RRFB | 35 | 2 | Paved | | 5 | Broward | SR A1A | Unsignalized | 35 | 2 | Paved | PHBs, 1 had RRFB, and 1 had a Flashing Beacon prior to the installation of MPSs. The reference groups included 3 locations with PHBs, 1 location with an RRFB, and 1 unsignalized location (refer to Table 2). This diverse selection of sites ensured a comprehensive evaluation of MPS effectiveness across different baseline conditions. Data collection was carried out using a portable CCTV camera setup, with multiple cameras strategically placed to capture activity from both directions for vehicles, pedestrians, and the signal phases. Recordings were conducted for 10 to 12 h per day during daytime only (approximately between 8:00 AM and 8:00 PM), including one weekday and one weekend, both before and after MPS installation, covering the period from morning to evening. Due to challenges in video processing under low-light conditions at some locations without proper lighting, data collected after sunset was excluded to maintain data quality. The same data collection protocol was applied at the reference groups to ensure consistency. In total, approximately 700 h of video footage were recorded, documenting over 2700 vehicle-pedestrian interactions. Approval was obtained from the Institutional Review Board (IRB) before the data collection began. More details about the data collection methodology can be found in a related study by the authors ([Ahsan et al.,](#page-14-0) [2025a\)](#page-14-0), where the same approach was used. A sample of the data collection setup and collected video screenshot are presented in [Fig. 2.](#page-4-0) Although previous studies used the same data collection methodology, they utilized only a portion of the available data and did not include reference sites for comparison. For instance, [Ahsan et al., 2025a\)](#page-14-0) focused solely on five previously unsignalized MPS locations, while another study [\(Ahsan et al., 2024; Anwari et al., 2023\)](#page-14-0) examined only PHB and RRFB sites. None of these studies conducted a comprehensive evaluation that included MPS, PHB, RRFB, flashing beacon, and unsignalized (non-treated locations) crossings. This limited their ability to perform a robust before-and-after analysis across various crossing types. ## **5. Data processing** The collected videos were processed in three main steps: object detection, object tracking, and converting pixel coordinates into GPS coordinates. These steps were critical for analyzing the movement and trajectories of road users. The GPS points were then used to calculate variables such as speed, direction, and other parameters required for the study. The video processing utilized advanced computer vision techniques, specifically the Real-Time DEtection TRansformer (RT-DETR) model for detection and the ByteTrack algorithm for tracking. The RT-DETR model is a cutting-edge method for object detection ([Lin et al., 2014; Zhao et al., 2024](#page-14-0)). It eliminates the need for Non-Maximum Suppression (NMS), which improves both speed and accuracy [\(Bochkovskiy et al., 2020; Li et al., 2023](#page-14-0)). RT-DETR achieves higher performance and processing speed on object detection ([Lin et al., 2014\)](#page-14-0) compared to other object detection models like YOLO models such as YOLOv7 and YOLOv8 ([Zhao et al., 2024](#page-14-0)). Once detected, objects were tracked across consecutive video frames using the ByteTrack algorithm. Unlike other approaches that discard low-confidence detections [\(Liang](#page-14-0) [et al., 2022\)](#page-14-0), the ByteTrack algorithm incorporates nearly all detection boxes, even those with lower confidence scores. This ensures better tracking accuracy, minimizes missed objects, and reduces fragmented trajectories [\(Zhang et al., 2022b](#page-14-0). By associating detection boxes with tracklets, ByteTrack enhances the overall tracking performance. Byte-Track achieved superior performance on the MOT17 dataset, with MOTA score of 80.3, IDF1 score of 77.3, and HOTA score of 63.1, running at 30 FPS on a single V100 GPU, outperforming many state-ofthe-art models [\(Liang et al., 2022](#page-14-0)). Once object trajectories were extracted from the video footage, perspective transformation was applied to convert the pixel-based coordinates to GPS coordinates. This process, implemented using the OpenCV library, mapped the image plane (in pixels) to the world plane (in GPS coordinates) for each camera location [\(Anwari et al., 2024;](#page-14-0) [Zhang et al., 2022a](#page-14-0)). Transforming the pixel data into GPS coordinates allowed the calculation of key variables such as distance, speed, and SSMs for pedestrians and vehicles. This method ensured precise analysis of interactions between road users. The same data processing procedure has been successfully used by the authors in a previous study ([Ahsan](#page-14-0) [et al., 2025a](#page-14-0)), where more details can be found. [Fig. 3](#page-5-0) provides a visual representation of the data processing technique and the resultant trajectories of the leading vehicles of each lane (blue lines) and the pedestrian (red line) of that pedestrian-vehicle interaction. For conflict calculations, the analysis considered the first point of the vehicle whether the front-left or front-right corner that would have initially made contact with the pedestrian. #### **6. Descriptive study** Previous studies have identified RTTC as one of the most effective SSMs for analyzing pedestrian-vehicle conflicts, outperforming other metrics such as PET, Spatial Gap, and Temporal Gap ([Ahsan et al., 2024,](#page-14-0) [2025a; Anwari et al., 2023; Chen et al., 2017\)](#page-14-0). RTTC is particularly advantageous as it captures the entire interaction between pedestrians and vehicles, taking into account their actual speeds and trajectories ([Ahsan et al., 2024, 2025a](#page-14-0)). RTTC is calculated (Eq. (1) as the absolute difference between the Time to Collision for a vehicle (TTCv) and that for a pedestrian (TTCp): $$RTTC = abs(TTCv - TTCp) \tag{1}$$ where, $$TTCp = \frac{Pedestrian distance from conflict point}{pedestrian speed}$$ TTCv = *Vehicle distance from conflict point vehicle speed* ![](_page_4_Picture_2.jpeg) ![](_page_4_Picture_3.jpeg) **Fig. 2.** Sample data collection from a MPS site. In this study, RTTC calculations considered only leading vehicles that first interacted with pedestrians, as trailing vehicles were unlikely to directly contribute to the conflict. The analysis identified the initial point of potential contact between the vehicle and the pedestrian, whether it was the front-left or front-right corner of the vehicle. RTTC was computed using the average values of the last 10 frames (videos are 20 frames/second) recorded before the vehicle reached the conflict point or came to a stop, ensuring that the analysis focused on the most critical moments of interaction. To maintain data relevance, any TTCp, or TTCv values exceeding 10 s were considered as non-conflicts, as they allowed sufficient time for the driver or pedestrian to respond. Following the methodology from a previous study ([Ahsan et al., 2025a](#page-14-0)), RTTC thresholds were defined as follows: RTTC ≤ 1.0 represents serious conflicts, 1.0 *<* RTTC ≤ 3.0 represents moderate conflicts, and values exceeding 3.0 s were not considered conflicts. The total number of serious and moderate conflicts was recorded for each 30-minute interval (refer [Table 3](#page-6-0)). This study incorporates three types of speed metrics: the speed of leading vehicles interacting with pedestrians, the average speed of all vehicles during each 30-minute interval, and the posted speed limit at each site. If a vehicle came to a complete stop before the crosswalk, the average speed was calculated including the rolling speed measured prior to stopping. All vehicle types were considered collectively, in alignment with the scope of the FDOT project; specific vehicle classes such as trucks or utility vehicles were not analyzed separately. At MPS locations, the pedestrian compliance rate defined as the percentage of pedestrians who activated the signal before crossing was 96.4 %. The dataset included all pedestrian crossings, including the 3.6 % who crossed without activating the signal. Most of these non-compliant crossings occurred when no vehicles were present and thus did not result in pedestrian-vehicle interactions. A dummy variable called "signal activation" (yes/no) was created to capture this behavior. However, this variable was not statistically significant in the modeling (EB, CG and CS) used in this study, likely due to the small number of non-compliant cases. Additionally, the study considers land-use mix data for each location which was extracted from FDOT GIS shape file ([FDOT GIS, 2024\)](#page-14-0). The land-use mix reflects the diversity of activities and services available in an area, influencing both pedestrian and vehicular traffic. Locations with a higher variety of land uses tend to attract a wider range of visitors and trip purposes, such as shopping, dining, or recreation. This diversity often results in increased pedestrian activity and vehicle flow due to the area's ability to meet various needs. Further insights including the calculation of land-use mix of each location can be found in studies by ([Ahsan et al., 2024, 2025a; Anwari et al., 2023; Goswamy and Abdel-](#page-14-0)[Aty, 2023\)](#page-14-0). Other variables used in the analysis, along with their brief descriptions, are provided in [Table 4.](#page-7-0) These variables are categorized into three main aspects: traffic and pedestrian dynamics, road characteristics, and contextual and temporal factors. All variables were ![](_page_5_Picture_2.jpeg) ![](_page_5_Picture_4.jpeg) **Fig. 3.** A sample data processing technique and resultant trajectories. manually reviewed to ensure consistency and accuracy. For distance and speed-related data, if any abrupt fluctuations were detected, a moving average technique was applied to smooth the measurements and improve data reliability. #### **7. Methodology** For calculating Crash Modification Factors (CMFs) to evaluate the safety impact of a treatment, studies commonly use both Cross-Sectional (CS) and Before–After methods, incorporating a Comparison Group (CG) and the Empirical Bayesian (EB) approach ([Hauer, 1997\)](#page-14-0). The CG method involves analyzing treated sites alongside reference groups with similar characteristics that remain unchanged, allowing for a robust comparison [\(Abuzwidah and Abdel-Aty, 2024](#page-14-0)). In this study, the same methodological framework used for calculating CMFs was adopted; however, since the analysis was based on conflict rather than crash data, Conflict Modification Factors (CoMFs) were used throughout. The interpretation of CoMF values is as follows: - CoMF *<* 1.0: The treatment (e.g., MPS) is effective in reducing conflicts. - CoMF = 1.0: The treatment has no effect; conflicts remain unchanged. - CoMF *>* 1.0: The treatment is associated with an increase in conflicts, indicating a potential negative safety impact. #### *7.1. Empirical Bayes Before-After method* The EB method is a statistical approach widely applied in beforeafter studies to evaluate the effectiveness of safety interventions, particularly in transportation safety research. Unlike traditional techniques, the EB method addresses challenges like random variability and regression-to-the-mean bias, which are common in observational data. This approach enables researchers to accurately estimate the impact of interventions (e.g., crash or conflict reduction) by isolating the treatment effect from external influences or natural variations in the data. By combining data from treated and reference groups, as suggested in previous studies ([Abuzwidah and Abdel-Aty, 2024; Hauer, 1997](#page-14-0)), the EB approach will offer a robust and reliable estimation of the expected impact of safety measures on conflict frequencies. The expected conflict frequency *E*̂*i*is calculated as Eq. (2): $$\widehat{E}_i = (\gamma_i \times y_i) + (1 - \gamma_i)\eta_i \tag{2}$$ Here, *γi*is the weight determined based on the negative binomial model's over-dispersion parameter and the predicted conflict frequency, *yi* is observed conflict count during the pre-treatment period, and *ηi*is observed conflict count from the reference sites. The weighting factor *γi*is calculated as Eq. [\(3\):](#page-6-0) **Table 3** Recorded serious and moderate conflicts from each study site. | # | District | Route | Treatment
Type | Before Period Data
Collection (Pre-MPS) | After Period Data
Collection (Post
MPS) | Serious
Conflict (Pre
MPS) | Moderate
Conflict (Pre
MPS) | Serious
Conflict (Post
MPS) | Moderate
Conflict (Post
MPS) | |----|-----------------|-------------------|---------------------------|--------------------------------------------|-----------------------------------------------|----------------------------------|-----------------------------------|-----------------------------------|------------------------------------| | | MPS sites | | | | | | | | | | 1 | Alachua | SR 26 | Uncontrolled to
MPS | Dec 19, Dec 21 2021 | Sept 5, Sept 7, 2024 | 19 | 29 | 12 | 21 | | 2 | Alachua | SR 26 | Uncontrolled to
MPS | Nov 7, Nov 9 2021 | Sept 5, Sept 7, 2024 | 18 | 27 | 9 | 17 | | 3 | Duval | SR 212 | Uncontrolled to
MPS | Oct 13, Nov 7 2021 | Jan 25, Jan 27, 2024 | 19 | 25 | 10 | 16 | | 4 | Franklin | US 98 | Uncontrolled to
MPS | Oct 17, Oct 19 2021 | April 13, April 15,
2024 | 16 | 27 | 8 | 20 | | 5 | Brevard | SR A1A | Uncontrolled to
MPS | Sept 21, Sept 25
2021 | Dec 19,
Dec 23,
2023 | 15 | 26 | 7 | 17 | | 6 | Brevard | SR A1A | Uncontrolled to
MPS | Sept 18, Sept 29
2021 | Dec 23, 2023
Jan 4, 2024 | 14 | 19 | 8 | 15 | | 7 | Miami
Dade | SW 1st
Street | Uncontrolled to
MPS | Nov 21, Dec 01,
2021 | Nov 6, 2022, and
Jan 11, 2023 | 25 | 36 | 16 | 23 | | 8 | Alachua | SR 24A/
SR 331 | Flashing Beacon
to MPS | Oct 13, Oct 17 2021 | May 23, May 25,
2024 | 15 | 22 | 8 | 14 | | 9 | Marion | US 41 | RRFB to MPS | July 10, July 12,
2021 | Dec 7,
Dec 9, 2023 | 18 | 27 | 12 | 18 | | 10 | St. Lucie | SR A1A | PHB to MPS | Sep 15, Oct 31 2021 | Jan 16, Jan 18, 2025 | 18 | 26 | 14 | 21 | | 11 | St. Lucie | SR A1A | PHB to MPS | Sep 12, Nov 11 2021 | Dec 19,
Dec 21, 2024 | 16 | 15 | 13 | 13 | | 12 | St. Lucie | SR A1A | PHB to MPS | Sep 12, Nov 11 2021 | Dec 19,
Dec 21, 2024 | 11 | 17 | 9 | 14 | | 13 | St. Lucie | SR A1A | PHB to MPS | Oct 28, Oct 31 2021 | Jan 16, Jan 18, 2025 | 13 | 18 | 10 | 15 | | 14 | St. Lucie | SR A1A | PHB to MPS | Sept 12, Sept 14,
2021 | Jan 16, Jan 18, 2025 | 15 | 17 | 13 | 14 | | | Reference Sites | | | | | | | | | | 1 | St. Johns | SR 207 | PHB | Sept 2. Sept 5, 2021 | May 4, May 6, 2024 | 21 | 28 | 25 | 31 | | 2 | St. Johns | SR A1A | PHB | Sept 2. Sept 5, 2021 | Feb 8, Feb 10, 2024 | 16 | 31 | 18 | 37 | | 3 | Miami
Dade | W Flagler
St. | PHB | Oct 6, Oct 9, 2021 | Sept. 19, Sept. 21,
2024 | 22 | 29 | 25 | 35 | | 4 | Brevard | SR A1A | RRFB | Sept 18. Sept 21,
2021 | May 11, May 13,
2023 | 16 | 28 | 19 | 38 | | 5 | Broward | SR A1A | Uncontrolled | Oct 9, Nov 22 2021 | | 12 | 19 | − | − | $$\gamma_i = \frac{1}{1 + k \times y_i} \tag{3}$$ Here, *k* is over-dispersion parameter, indicating the variance in crash frequencies relative to the mean. The standard deviation *σ*̂*i*of the predicted conflict frequency is calculated as Eq. (4): $$\widehat{\sigma}_i = \sqrt{(1 - \gamma_i) \cdot \widehat{E}_i} \tag{4}$$ Scaling factors for adjusting post-intervention period *ρ*var is for changes in variables like traffic volume or speed between the "Before" and "After" periods. It is given as Eq (5): $$\rho_{\text{var}} = \frac{\text{var}_{\text{after}}^{a_i}}{\text{var}_{\text{before}}^{a_i}}$$ (5) When there is no significant change between pre- and post-intervention conditions, the scaling factor becomes 1. *αi*is regression coefficient for each variable from SPF. The adjusted conflict frequency for the post-intervention period *π*̂*i*is: $$\widehat{\pi}_i = \widehat{E}_i \cdot \rho_{\text{var}} \tag{6}$$ The effectiveness of a safety intervention is assessed using the Effectiveness Index *θ* ̂*i*defined as Eq (7): $$\widehat{\theta}_i = \frac{\widehat{\lambda}_i/\widehat{\pi}_i}{1 + \widehat{(\sigma_i^2/\pi_i^2)}} \tag{7}$$ Here, *λ* ̂*i*is actual conflict count observed during the post-intervention period. If *θ* ̂*i*is less than 1, the treatment is considered to be effective in reducing the expected number of conflicts. The percentage reduction in conflict frequency *τ*̂*i*is given by Eq (8): $$\widehat{\tau}_i = (1 - \widehat{\theta}_i) \times 100\% \tag{8}$$ The aggregate effectiveness index ̂*θ* across all treated sites is calculated as Eq (9): $$\widehat{\theta} = \frac{\sum_{j=1}^{m-1} \widehat{t}_i}{1 + \left(\frac{\operatorname{var}\left(\sum_{j=1}^{m} \widehat{t}_i\right)}{\left(\sum_{j=1}^{m} \widehat{t}_i\right)^2}\right)}$$ $$(9)$$ Where *m* is the total number of treated sites. The variance of the aggregated prediction is: $$\operatorname{var}\left(\sum_{i=1}^{k} \widehat{\pi}_{i}\right) = \sum_{i=1}^{k} \rho_{\operatorname{var}}^{2} \cdot \operatorname{var}(\widehat{E}_{i})$$ (10) The standard deviation ̂*σ* for overall effectiveness is calculated as Eq [\(11\):](#page-7-0) **Table 4** Summary Statistics of each variable used in the final analysis. | Variable | Description | Value type | Mean | Std. Dev. | Max. | Min. | |----------------------------------|---------------------------------------------------------------------------------------------|--------------------------------|-------|-----------|-------|-------| | Traffic and Pedestrian Dynamics | | | | | | | | Average leading vehicle
speed | Average speed of each leading vehicle before stopping that interact with pedestrian,
mph | Continuous
variable | 26.6 | 8.60 | 59.81 | 1.72 | | Average vehicles' speed | Average speed of all vehicles during each 30-minute interval, mph | Continuous
variable | 34.2 | 12.94 | 61.04 | 11.91 | | Vehicle volume | Total vehicles passing the crosswalk during each 30-minute interval | Continuous
variable | 285 | 62.49 | 398 | 38 | | Pedestrian volume | Total no. of pedestrians crossed the road during each 30-minute interval | Continuous
variable | 4.8 | 4.72 | 29 | 0 | | Road Characteristics | | | | | | | | MPS treatment | MPS treatment | 1: Present
0: Otherwise | 0.52 | 0.49 | 1 | 0 | | Raised/vegetation median | Median those are raised or vegetation | 1: Raised/veg.
0: Otherwise | 0.18 | 0.38 | 1 | 0 | | Lane count | Total number of lanes | Continuous
variable | 2.98 | 0.36 | 4 | 2 | | Lane width | Lane width, feet | Continuous
variable | 10.38 | 1.64 | 14 | 11 | | Posted speed limit | Posted speed limit, mph | Continuous
variable | 36.80 | 17.43 | 55 | 25 | | Contextual and Temporal Factors | | | | | | | | Land-use mix | Land-use mix of each site, collected from FDOT GIS shape file | Continuous
variable | 0.45 | 0.07 | 0.57 | 0 | | Weekday | Day other than Saturday and Sunday | 1: Weekday
0: Otherwise | 0.46 | 0.49 | 1 | 0 | | Morning peak | Morning peak time (8am to 10am) | 1: Morning
0: Otherwise | 0.22 | 0.41 | 1 | 0 | | Afternoon Peak | Afternoon peak time (4 pm to 6 pm) | 1: Afternoon
0: Otherwise | 0.19 | 0.39 | 1 | 0 | $$\widehat{\sigma} = \sqrt{\frac{\theta^2 \left[ \left( \frac{\operatorname{var}\left(\sum_{i=1}^k \widehat{r_i}\right)}{\left(\sum_{i=1}^k \widehat{r_i}\right)^2} \right)^2 + \left( \frac{\operatorname{var}\left(\sum_{i=1}^k \widehat{\lambda_i}\right)}{\left(\sum_{i=1}^k \widehat{\lambda_i}\right)^2} \right)^2 \right]}}{\left[ 1 + \left( \frac{\operatorname{var}\left(\sum_{i=1}^k \widehat{r_i}\right)}{\left(\sum_{i=1}^k \widehat{r_i}\right)^2} \right) \right]^2}$$ (11) This method provides a comprehensive framework for accurately estimating the effectiveness of safety measures while accounting for variability and potential biases. #### *7.2. Safety Performance Functions (SPFs) for EB method* SPFs are predictive models used to estimate the expected number of crashes, conflicts, or other safety-related outcomes based on explanatory variables such as traffic volume, roadway characteristics, and environmental factors. Among the modeling approaches, Generalized Linear Models (GLMs) with a Negative Binomial (NB) distribution are widely used to account for the overdispersion typically observed in crash or conflict data ([Faden et al., 2025; Goswamy and Abdel-Aty, 2023;](#page-14-0) [Shahdah et al., 2014](#page-14-0)). However, in many real-world datasets, observations may not be independent but instead exhibit correlation within clusters. For instance, when data is collected repeatedly over time from the same location or across spatially related sites, the outcomes may be influenced by shared underlying characteristics. Ignoring such correlations can lead to biased parameter estimates and underestimated standard errors. To address this, Generalized Estimating Equations (GEE) with a Negative Binomial family are increasingly considered as an alternative to GLMs ([Abdel-Aty and Abdalla, 2004; Cui and Feng, 2008;](#page-14-0) [Mohammadi et al., 2014\)](#page-14-0). In this study, conflict data were aggregated every 30 min over a continuous period of 10 to 12 h per day for each location. This results in a dataset with repeated measures within each location, where conflicts observed at different time intervals are likely to be correlated due to shared traffic conditions, environmental factors, and spatial influences. The GEE framework is particularly suitable for this scenario, as it explicitly accounts for the within-location correlation through its working correlation structure (e.g., Exchangeable or AR-1) ([Cui and](#page-14-0) [Feng, 2008; Mohammadi et al., 2014](#page-14-0)). By modeling populationaveraged effects, GEE provides robust inferences even in the presence of intra-cluster dependencies, making it an essential addition to GLMs for estimating SPFs. This dual approach allows to capture both conditional effects (using GLMs) and robust population trends (using GEEs), ensuring comprehensive and reliable safety analysis. ## *7.3. Negative Binomial Generalized Linear model (NB-GLM)* GLM models the conditional mean of the response variable *Y* given the covariates. It assumes all observations are independent and is widely used for count data with overdispersion ([Abdel-Aty and Radwan, 2000;](#page-14-0) [Abuzwidah and Abdel-Aty, 2024; Hauer, 1997; Shirazi et al., 2016](#page-14-0)). Response variable *Yi* (e.g., conflict counts) follows: $$Y_i \sim \text{Negative Binomial}(\mu_i, \alpha)$$ (12) where, *μi*is expected conflicts for observation *i*, and *α* is dispersion parameter, controlling overdispersion. The variance of *Yi* is modeled as: $$Var(Y_i) = \mu_i + \alpha \mu_i^2 \tag{13}$$ where, α = Varobs(*Yi*)− μ*i* μ2 ; and Varobs(*Yi*) is the observed variance of the response variable. The following log-link function (Eq. (14) relates the mean response *μi* to the covariates. $$\log(\mu_i) = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \dots + \beta_p X_{pi}$$ (14) Here, *X*1*i, X*2*i,* ⋯*, Xpi* is predictors (e.g., traffic volume, pedestrian count), and β0*,* β1*,* ⋯*,* β: are model coefficients. Parameters *β* and *α* are estimated via maximum likelihood estimation (MLE). ## *7.4. Negative Binomial Generalized Estimating Equations (NB-GEE)* GEE models the population-averaged mean of the response variable, explicitly accounting for within-cluster correlation ([Mohammadi et al.,](#page-14-0) [2014\)](#page-14-0). It is ideal for repeated or grouped data as this study where conflict counts are recorded every 30 min across multiple locations. Response variable *Yij* for the *j*-th observation in the *i*-th cluster follows: $$Y_{ij} \sim \text{Negative Binomial} \Big( \mu_{ij}, \alpha \Big)$$ (15) where, *μij* is expected conflicts for observation *j* in cluster *i* , and α is dispersion parameter that accounts for overdispersion in the NB model. The variance of *Yij* is modeled as: $$Var(Y_{ij}) = \phi V(\mu_{ij}) = \mu_{ij} + \alpha \mu_{ij}^2$$ (16) Here, *ϕ* is scale parameter, and *V* ( *μij*) is the variance function specific to the NB distribution. The dispersion parameter *α* is calculated as: $$\alpha = \frac{\sum_{i=1}^{m} \sum_{j=1}^{n_i} \frac{(Y_{ij} - \mu_{ij})^2}{\mu_{ij}^2} - (N - p)}{N - p}$$ (17) Here, *N* − *p* is residual degrees of freedom. Although *ϕ* adjusts the variance for any additional variability in the GEE framework, we calculate *α* specifically to model the overdispersion inherent to the NB distribution. This ensures that the variance structure reflects the relationship Var( *Yij*) = *ϕ*(*μij* + *αμ*2 *ij*), aligning the NB assumptions with the GEE framework for accurate modeling of over dispersed count data. The log-link function relates the mean response μ*ij* to the predictors: $$\log(\mu_{ij}) = \beta_0 + \beta_1 X_{1ij} + \beta_2 X_{2ij} + \dots + \beta_p X_{pij}$$ (18) Here, *X*1*ij* represents a predictor variable (e.g., traffic volume, pedestrian count) for observation *j* in cluster *i*. GEE includes a working correlation matrix *R*(*ρ*) to model withincluster correlation ([Cui and Feng, 2008; Mohammadi et al., 2014](#page-14-0)); *Exchangeable*: equal correlation *ρ* between all observations within a cluster. *Autoregressive (AR-1):* correlation decreases with increasing time lag. *Independent*: assumes no correlation. Parameters *β* are estimated using quasi-likelihood estimation ([Cui](#page-14-0) [and Feng, 2008; Mohammadi et al., 2014](#page-14-0)): $$U(\beta) = \sum_{i=1}^{m} D_i^{\mathrm{T}} V_i^{-1}(Y_i - \mu_i) = 0$$ (19) where, *Di* is derivative of the mean vector *μi*with respect to *β*, and *Vi* is covariance matrix, incorporating *R*(ρ). The inclusion of *R*(ρ) allows GEE to account for within-cluster correlations, making it particularly suitable for clustered or repeated measures data where traditional NB models may fall short. # **8. Cross Sectional Method** The CS Method applies a similar framework to the SPFs but explicitly incorporates the treatment effect (e.g., MPS treatment) as an explanatory variable [\(Abuzwidah and Abdel-Aty, 2024; Park and Abdel-Aty,](#page-14-0) [2016\)](#page-14-0). This approach enables the evaluation of how the presence of a treatment modifies the expected conflict frequency across locations. ## *8.1. Model formulation* Using the same NB framework as the original SPF (see Eq. [\(14\),](#page-7-0) the expected number of conflicts is now modeled to include the treatment effect as Eq. (20): $$\log(\mu_i) = \beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \dots + \beta_p X_{pi} + \beta_T T_i$$ (20) Here, *βT*is coefficient representing the treatment effect, and *Ti* is binary indicator for the presence of treatment (*Ti* = 1 for treated locations, *Ti* = 0 for otherwise). The treatment's effect is quantified through the CoMF, which is calculated as Eq (21): $$CoMF_T = e^{\beta_T} \tag{21}$$ This allows the predicted conflict frequencies to vary based on the presence or absence of treatment. The standard error (SE) of the CoMF is calculated as ([Park and Abdel-Aty, 2016](#page-14-0)): $$SE_T = \frac{e^{\theta_T + SE_{T_x}} - e^{\theta_T - SE_{T_x}}}{2} \tag{22}$$ where, *βT*denotes the coefficient of treatment indicator variable *Ti* and *SETx* denotes the standard error of *βT*from the NB model. ## **9. Goodness of Fit** When comparing NB-GLM and NB-GEE, using Akaike Information Criterion (AIC) and Quasi-Likelihood Information Criterion (QIC) is not appropriate for direct comparison due to their differing frameworks. AIC, used in NB-GLM, evaluates model fit based on maximum likelihood, assuming independent observations, while QIC, used in NB-GEE, accounts for quasi-likelihood and within-cluster correlation [\(Abdel-Aty](#page-14-0) [and Abdalla, 2004; Cui and Feng, 2008; Mohammadi et al., 2014\)](#page-14-0). Since AIC and QIC rely on different likelihood structures, their values are not directly comparable. Instead of comparing AIC and QIC, alternative metrics such as Mean Absolute Error (MAE) or Mean Squared Error (MSE) can be used to assess predictive performance on the same test dataset, providing a common ground for evaluation. For NB-GLM, the log-likelihood measures how well the model explains the observed data, given the parameter estimates. It is expressed as: $$Log-Likelihood (NB GLM) = \sum_{i=1}^{n} log P(Y_i | \mu_i, \alpha)$$ (25) *Yi* is observed response for observation *i* (e.g. conflict counts), *μi*is predicted mean response for observation *i* and, *α* is dispersion parameter to account for overdispersion. The AIC evaluates model fit while penalizing complexity, defined as: $$AIC = 2k - 2\log L \tag{26}$$ Where, *k* is number of model parameters and log*L* is Log-likelihood of the model. For NB-GEE model that accounts for within-cluster correlation, the QIC is used as an analog to AIC ([Mohammadi et al., 2014\)](#page-14-0). It is defined as: $$QIC = -2l(\beta) + 2trace(W)$$ (27) where l(*β*) is quasi-likelihood under the working correlation and *W* is model-based covariance matrix. To evaluate predictive accuracy, MAE and MSE are defined as follows: $$MAE = \frac{1}{n} \sum_{i=1}^{n} |Y_i - \mu_i|$$ (28) **Table 5** Reference groups and final evaluation sites for EB method. | Reference Group | Ref. Group Sites | Evaluation Sites | | | | | | |---------------------------------------------------------------------------------------------------------|------------------|-------------------------------|--|--|--|--|--| | All | All | All | | | | | | | PHB | 1, 2, 3 | 10, 11, 12, 13, 14 | | | | | | | RRFB | 4 | 8a
, 9 | | | | | | | PHB and RRFB | 1, 2, 3, 4 | 8a
, 9, 10, 11, 12, 13, 14 | | | | | | | a: Flashing Beacon and RRFB have similar functionality; therefore, they were
evaluated collectively. | | | | | | | | $$MSE = \frac{1}{n} \sum_{i=1}^{n} (Y_i - \mu_i)^2$$ (29) *where n* is total number of observations. ## **10. Before-After comparison group study** A before-and-after CG study evaluates treated sites by comparing them with an untreated group of control or comparison sites. In this study, data were collected from reference sites during both the before period, when MPSs had not yet been installed at the treatment sites, and the after period, when MPSs were operational. Therefore, these reference sites served as comparison sites. This approach does not explicitly adjust for variations in traffic volume or temporal factors. Instead, it calculates the ratio of observed crashes or conflicts during the after period to those recorded during the before period for the comparison sites. CoMF is calculated from the following Eq. (30) [\(Gross, 2010;](#page-14-0) [Monsere et al., 2017](#page-14-0)). $$CoMF = \left(\frac{N_{\text{observed},TA}}{N_{\text{expected},TA}}\right) / \left(1 + \frac{\text{Var}(N_{\text{expected},TA})}{N_{\text{expected},TA}^2}\right)$$ (30) And variance of CoMF is: $$Variance (CoMF) = \frac{CoMF^{2} \left[ \left( \frac{1}{N_{observed,TA}} \right) + \left( \frac{Var(N_{expected,TA})}{N_{expected,TA}^{2}} \right) \right]}{1 + \frac{Var(N_{expected,TA})^{2}}{N_{expected,TA}^{2}}}$$ (31) where, $$N_{\text{expected},T,A} = N_{\text{observed},T,B} \left( \frac{N_{\text{observed},C,A}}{N_{\text{observed},C,B}} \right)$$ **Table 6** SPFs based on different reference groups for serious conflicts. | Variable | Estimate (std. error) based on different reference groups | | | | | | | | | | | |------------------------------------------------|-----------------------------------------------------------|-------------------------------|----------------------|-------------------------|---------------------|------------------------------|-------------------------------|-------------------------------|--|--|--| | | All | | | PHBs and RRFB | | PHBs | | RRFB | | | | | | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | | | | | Traffic and Pedestrian Dynamics | | | | | | | | | | | | | Constant | 1.312**
(0.0562) | 1.012**
(0.0292) | 1.561**
(0.0320) | 1.138** (0.088) | 1.287**
(0.1539) | 1.181**
(0.120) | 1.428**
(0.127) | 1.111**
(0.158) | | | | | Average leading vehicle | 0.561** | 0.1509* | 0.1725* (0.09) | 0.632** (0.095) | 0.433** | 0.393** | 0.593** | 0.918** | | | | | speed
Average vehicles' speed | (0.032)
0.787**
(0.200) | (0.088)
0.844**
(0.223) | | 0.319**
(0.1601) | (0.064) | (0.126)
0.710*
(0.399) | (0.222)
0.922**
(0.218) | (0.173)
1.076**
(0.109) | | | | | Ln (Vehicle volume) | 1.012**
(0.0292) | 0.634**
(0.301) | 0.844**
(0.2231) | 1.287** (0.153) | 0.751**
(0.015) | 0.741**
(0.253) | 1.46**
(0.134) | 1.257**
(0.113) | | | | | Pedestrian volume | 0.0854**
(0.022) | 0.644**
(0.093) | 0.274**
(0.073) | 0.261** (0.033) | | | | 0.676**
(0.236) | | | | | Road Characteristics | | | | | | | | | | | | | Lane count | 0.6007**
(0.298) | 0.547**
(0.222) | 0.100*
(0.0573) | 0.526* (0.313) | 0.4163*
(0.2301) | 0.6175*
(0.378) | | | | | | | Raised/vegetation Median | | − 0.094*
(0.054) | | − 0.163**
(0.0398) | | | | | | | | | Lane width | | − 0.234**
(0.110) | | | | − 0.847**
(0.024) | | | | | | | Posted speed limit | | 0.469**
(0.185) | 0.946**
(0.025) | 0.286**
(0.0630) | 0.634**
(0.071) | 0.163**
(0.039) | | | | | | | Contextual and Temporal Factors | | | | | | | | | | | | | Land-use mix | 0.243* (0.145) | 0.424* (0.246) | 0.9822**
(0.2437) | 0.658* (0.397) | 0.621**
(0.314) | 0.296**
(0.109) | | | | | | | Weekday | | 0.115**
(0.047) | | 0.963** (0.054) | | 0.286**
(0.063) | 0.768**
(0.154) | 0.425**
(0.156) | | | | | Morning peak | 0.559* (0.325) | 0.266**
(0.121) | 0.247**
(0.121) | 0.293* (0.177) | 0.119**
(0.055) | 0.213*
(0.109) | 0.502**
(0.128) | 0.804**
(0.260) | | | | | Afternoon Peak | | 1.137**
(0.086) | | 0.731** (0.054) | | | | | | | | | Goodness of Fit | | | | | | | | | | | | | AIC/QIC
Dispersion Parameter
Correlation | 10024/-
0.44 | − /10078
0.48
0.46 | 9647/-
0.31 | − /9826
0.37
0.39 | 9534/-
0.29 | − /9608
0.35
0.42 | 6727/-
0.31 | − /6859
0.35
0.42 | | | | | Coefficient,R(ρ)
MAE
MSE | 0.7026
1.7164 | 0.5259
0.9863 | 0.6943
1.7240 | 0.5586
1.3864 | 0.6536
1.7178 | 0.4735
1.2866 | 0.5346
1.5691 | 0.3950
0.8636 | | | | \*\*Significant at 95% confidence level. \*Significant at 90% confidence level. **Table 7** SPFs based on different reference group for all conflicts (serious and moderate). | Variable | Estimate (std. error) based on different reference groups | | | | | | | | | | | |----------------------------------|-----------------------------------------------------------|----------------------|----------------------|----------------------|--------------------|----------------------|--------------------|-------------------------------|--|--|--| | | All | | | PHBs and RRFB | | PHBs | RRFB | | | | | | | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | | | | | Traffic and Pedestrian Dynamics | | | | | | | | | | | | | Constant | 2.138**
(0.109) | 2.010** (0.215) | 1.010** (0.208) | 1.625** (0.130) | 1.757**
(0.106) | 1.064** (0.095) | 1.010**
(0.208) | 1.368**
(0.171) | | | | | Average leading vehicle
speed | 0.210**
(0.029) | 0.186** (0.032) | 0.916** (0.241) | 0.154** (0.039) | 0.265**
(0.105) | 0.298** (0.113) | 0.916**
(0.241) | 0.894**
(0.198) | | | | | Average vehicles' speed | | 0.423** (0.110) | 0.334** (0.114) | 0.224* (0.13) | | 0.305** (0.104) | 0.334** | 0.521** | | | | | Ln (Vehicle volume) | 0.774** | 0.692** (0.231) | 0.500* (0.281) | 0.352** (0.176) | 0.883** | 0.466** (0.113) | (0.114)
0.500* | (0.123)
0.529** | | | | | Pedestrian volume | (0.218) | 0.106* (0.062) | | 0.399** (0.135) | (0.298) | 0.357** (0.123) | (0.281) | (0.162)
0.301**
(0.101) | | | | | Road Characteristics | | | | | | | | | | | | | Lane count | | 0.499** (0.118) | | 0.501** (0.202) | 0.399**
(0.134) | 0.982** (0.226) | | | | | | | Raised/vegetation Median | | − 0.521**
(0.149) | | − 0.051**
(0.010) | | − 0.490**
(0.108) | | | | | | | Lane width | | − 0.817**
(0.119) | − 0.916**
(0.130) | − 0.778**
(0.212) | | − 0.806**
(0.227) | | | | | | | Posted speed limit | 0.825**
(0.271) | 0.770** (0.252) | 0.949** (0.212) | 0.789** (0.238) | 0.658**
(0.272) | 0.664** (0.154) | | | | | | | Contextual and Temporal Factors | | | | | | | | | | | | | Land-use mix | | 0.629** (0.167) | | 0.1.301**
(0.106) | | 0.309** (0.110) | | | | | | | Weekday | 0.536**
(0.210) | 0.613** (0.103) | 0.990** (0.121) | 1.00** (0.141) | 0.445**
(0.151) | 0.630** (0.166) | 0.974**
(0.251) | 0.734**
(0.111) | | | | | Morning peak | | 0.095** (0.012) | | 0.107** (0.020) | 0.466**
(0.094) | 0.601** (0.072) | 1.084**
(0.132) | 1.153**
(0.289) | | | | | Afternoon Peak | | | | 0.691** (0.101) | | | | | | | | | Goodness of Fit | | | | | | | | | | | | | AIC/QIC | 9307/- | − /9439 | 9325/- | − /9427 | 8946/- | − /9026 | 6426/- | − /6503 | | | | | Dispersion Parameter | 0.47 | 0.46 | 0.30 | 0.33 | 0.32 | 0.36 | 0.33 | 0.36 | | | | | Correlation | | 0.36 | | 0.32 | | 0.38 | | 0.40 | | | | | Coefficient,R(ρ) | | | | | | | | | | | | | MAE | 1.1945 | 0.7233 | 0.9867 | 0.3365 | 0.9521 | 0.5055 | 0.9645 | 0.4260 | | | | | MSE | 2.1055 | 1.2951 | 2.0740 | 1.0521 | 2.0546 | 1.1318 | 1.9809 | 0.7399 | | | | \*\*Significant at 95% confidence level. $$\mathrm{Var}(N_{\mathrm{expected},T,A}) = N_{\mathrm{expected},T,A}^2 \left(\frac{1}{N_{\mathrm{observed},T,B}} + \frac{1}{N_{\mathrm{observed},C,B}} + \frac{1}{N_{\mathrm{observed},C,A}}\right)$$ *N*observed*,T,B*= The total number of conflicts recorded during the before period of MPS installation. *N*observed*,T,A*= The total number of conflicts recorded during the after MPS installation. *N*observed*,C,B*= The total number of conflicts recorded during the before period for sites in the comparison (untreated) group. *N*observed*,C,A*= The total number of conflicts recorded during the after period for sites in the comparison (untreated) group. ## **11. Results and discussion** #### *11.1. Empirical Bayes and comparison group methods* To develop SPFs for the EB method, data were analyzed across four reference groups: PHB sites, RRFB site, a combination of PHB and RRFB sites, and all sites combined. Observations were aggregated in 30-minute intervals for all locations. For CoMF evaluation, when PHBs were used as the reference group, only sites that initially operated as PHBs and later transitioned to MPSs were considered. The same approach was applied to other reference groups (RRFB and combination of PHB and RRFB) to ensure consistency in evaluation. In the CG method, untreated sites were excluded from the reference group, as data was not collected from that location after MPS installation at other untreated sites. For further details, refer to [Table 5](#page-9-0). Location numbers align with those provided in [Table 2](#page-3-0). For the final CoMF evaluation, the NB-GEE model was selected due to its better performance across multiple evaluation metrics compared to NB-GLM. The NB-GEE model consistently demonstrated lower MAE and MSE, indicating more accurate predictions with smaller residuals (refer to [Table 6](#page-9-0) and Table 7). Additionally, it accounts for within-cluster correlation through the correlation coefficient *R*(*ρ*), which is crucial for clustered traffic data. Since AIC and QIC rely on different likelihood structures, their values are not directly comparable. These findings emphasize the reliability of the NB-GEE model for CoMF development in this study. All three correlation structures: Exchangeable, Autoregressive (AR-1), and Independent were tested to evaluate their performance in the GEE model. Based on the results, the Exchangeable correlation structure provided the best fit, as indicated by MAE and MSE compared to the other two. [Fig. 4](#page-11-0) highlights a sample of the prediction results and accuracy for the PHB reference group, demonstrating the robustness of the NB-GEE model for CoMF evaluation. In the NB-GEE model (refer to [Table 6](#page-9-0) and Table 7), average leading vehicle speed, average vehicles' speed, vehicle volume, pedestrian volume, lane count, \*Significant at 90% confidence level. ![](_page_11_Figure_2.jpeg) **Fig. 4.** Conflict prediction and their residuals from NB-GEE and NB-GLM models for reference group: PHBs. **Table 8** CoMFs of MPSs based on EB method and CG method. | Conflict
Type | | CoMF (std. error) of MPSs based on different reference groups | | | | | | | | | | |------------------|----------------|---------------------------------------------------------------|-----------------|------------------|---------------------|----------------|----------------|--|--|--|--| | | | | Empirical Bayes | Comparison Group | | | | | | | | | | All | PHBs,
RRFB | PHBs | RRFB | PHBs
and
RRFB | PHBs | RRFB | | | | | | Serious | 0.55
(0.03) | 0.67
(0.07) | 0.73
(0.04) | 0.53
(0.06) | 0.62
(0.13) | 0.67
(0.16) | 0.45
(0.17) | | | | | | All | 0.52
(0.04) | 0.62
(0.03) | 0.67
(0.03) | 0.46
(0.02) | 0.63
(0.09) | 0.69
(0.11) | 0.47
(0.12) | | | | | posted speed limit, land-use mix, weekday, morning peak, and afternoon peak have positive and statistically significant coefficients, indicating an increased expected conflict frequency as these variables increase. Conversely, raised/vegetation median and lane width have negative coefficients, suggesting that the presence of raised/vegetation median and wider lanes are associated with a reduction in conflicts. Table 8 summarizes the CoMFs for MPSs across different reference groups, evaluated using EB and CG methods. For all sites combined, MPSs reduced serious conflicts by 45 %, and reductions for all conflicts were 48 % using the EB method. For the combined PHB and RRFB reference group, serious conflicts decreased by 33 % using the EB method and 38 % with the CG method, while reductions for all conflicts were 38 % and 37 %. Using PHBs as the reference group, MPSs reduced serious conflicts by 27 % and 33 % for the EB and CG methods, respectively, and all conflicts by 33 % and 31 %. For RRFBs as the reference group, serious conflicts were reduced by 47 % and 55 %, while reductions for all conflicts were 54 % and 53 %. ## *11.2. Cross sectional method* The CS method evaluated the impact of MPSs across different reference categories. The first category included all locations that transitioned to MPSs, irrespective of whether they were previously PHB, RRFB, untreated, or remained unchanged. The second category focused on PHB, RRFB and Flashing Beacon locations, including those that transitioned to MPSs or remained same during both periods. The third category specifically analyzed PHB locations, considering those that either transitioned to MPSs or remained as PHBs throughout the study period. Lastly, the fourth category examined RRFB and Flashing Beacon locations, including those that transitioned to MPSs or remained as RRFBs during the analysis period. The NB-GEE model was also selected for this analysis, as it effectively accounts for within-cluster correlations and consistently demonstrates lower MAE and MSE values (refer to [Table 9 and 10\)](#page-12-0). Here also all variables except raised/vegetation median and lane width have positive and statistically significant coefficients, indicating an increased expected conflict frequency as these variables increase. Conversely, raised/vegetation median and lane width have negative coefficients, suggesting that presence of raised/vegetation median and higher lane width are associated with a reduction in conflicts. [Table 11](#page-13-0) highlights the CoMFs for MPSs derived from the CS method across various site categories. Compared to all locations, MPSs achieved a 45 % reduction in serious conflicts and a 50 % reduction in all conflicts. Relative to PHBs, RRFB, and Flashing Beacon sites, MPSs resulted in a 32 % reduction in serious conflicts and a 51 % reduction in all conflicts. When compared specifically to PHBs, MPSs demonstrated a 26 % reduction in serious conflicts and a 36 % reduction in all conflicts. Lastly, compared to RRFB and Flashing Beacon sites, MPSs achieved a 46 % reduction in serious conflicts and a 53 % reduction in all conflicts. ## **12. Conclusions and future work** MPSs represent a relatively new traffic control measure recommended by the National Committee on Uniform Traffic Control Devices (NCUTCD) Signal Technical Committee (STC). FDOT began implementing MPS systems in November 2022, currently operational at 14 locations across Florida. This study evaluates the effectiveness of MPSs in improving pedestrian safety and comparing their performance with other mid-block pedestrian crossings such as PHB, RRFB and Flashing Beacon. For evaluation, extensive CCTV video data was collected from each location before and after MPS installation, including five reference sites. These videos were processed using computer vision technology, specifically the RT-DETR model for detection and the ByteTrack algorithm for tracking. Instead of relying on traditional annual crash data, which may not be available or sufficient for newly implemented systems, this study utilized vehicle–pedestrian conflict data derived from SSMs such as **Table 9** SPFs based on different reference groups for serious conflicts. | Variable | Estimate (std. error) based on different reference groups | | | | | | | | | | | |---------------------------------|-----------------------------------------------------------|--------------------|----------------|-----------------------------|----------------|-----------|-----------------------|-----------|--|--|--| | | All locations | | | PHBs, RRFB, Flashing Beacon | PHBs | | RRFB, Flashing Beacon | | | | | | | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | | | | | Traffic and Pedestrian Dynamics | | | | | | | | | | | | | Constant | 1.258** | 1.211** | 1.445* (0.209) | 1.386** | 1.462** | 1.343** | 1.191** | 1.423** | | | | | | (0.106) | (0.229) | | (0.128) | (0.160) | (0.192) | (0.182) | (0.212) | | | | | Average leading vehicle | 0.395* (0.235) | 0.493** | 0.289* (0.161) | 0.290** | 0.388* (0.228) | 0.402** | 0.195* (0.105) | 0.229** | | | | | speed | | (0.151) | | (0.128) | | (0.099) | | (0.108) | | | | | Average vehicles' speed | 0.762** | 0.749** | 0.977* (0.206) | 0.679** | 0.949** | 1.351** | 0.551** | 0.565** | | | | | | (0.165) | (0.215) | | (0.229) | (0.168) | (0.277) | (0.238) | (0.149) | | | | | Ln (Vehicle volume) | 1.018** | 0.893** | 0.560** | 0.591** | 0.580** | 0.527** | 0.724** | 0.811** | | | | | | (0.155) | (0.122) | (0.262) | (0.196) | (0.124) | (0.215) | (0.273) | (0.154) | | | | | Pedestrian volume | | 0.899**
(0.240) | | | | | | | | | | | | | | | | | | | | | | | | Road Characteristics | | | | | | | | | | | | | MPS treatment | ¡0.550** | − 0. 597** | − 0.409** | − 0.386** | − 0.284** | − 0.301** | − 0.639** | − 0.616** | | | | | | (0.017) | (0.010) | (0.090) | (0.066) | (0.012) | (0.018) | (0.080) | (0.074) | | | | | Lane count | 0.906** | 1.420* (0.244) | | 0.611** | | | | 0.607** | | | | | | (0.141) | | | (0.099) | | | | (0.177) | | | | | Raised/vegetation | | − 0.904** | | − 0.544** | | − 0.881** | | | | | | | Median | | (0.264) | | (0.101) | | (0.111) | | | | | | | Lane width | − 0.860** | − 0.686** | | | | − 0.970** | | | | | | | | (0.125) | (0.200) | | | | (0.193) | | | | | | | Posted speed limit | 0.995** | 1.158** | | 1.238** | | − 0.740** | | 0.197** | | | | | | (0.108) | (0.144) | | (0.149) | | (0.101) | | (0.051) | | | | | Contextual and Temporal Factors | | | | | | | | | | | | | Land-use mix | 0.921** | 1.269** | | 0.633** | | 0.431** | 0.568** | 0.703** | | | | | | (0.124) | (0.186) | | (0.256) | | (0.108) | (0.164) | (0.229) | | | | | Weekday | | 1.218** | 0.957** | 0.666** | | 1.500** | 0.561** | 0.612** | | | | | | | (0.242) | (0.200) | (0.181) | | (0.153) | (0.227) | (0.198) | | | | | Morning peak | 0.683** | 0.434** | 0.630** | 0.643** | 0.775** | 0.895** | 0.596** | 0.409** | | | | | | (0.241) | (0.106) | (0.280) | (0.290) | (0.161) | (0.225) | (0.137) | (0.108) | | | | | Afternoon Peak | 0.115** | 0.098* (0.054) | | | | | | | | | | | | (0.023) | | | | | | | | | | | | Goodness of Fit | | | | | | | | | | | | | AIC/QIC | 8834/- | − /8941 | 9267/- | − /9351 | 9119/- | − /9180 | 6213/- | − /6289 | | | | | Dispersion Parameter | 0.49 | 0.44 | 0.28 | 0.27 | 0.29 | 0.31 | 0.32 | 0.34 | | | | | Correlation
Coefficient,R(ρ) | | 0.35 | | 0.35 | | 0.37 | | 0.41 | | | | | MAE | 0.5406 | 0.3246 | 0.6155 | 0.4001 | 0.5628 | 0.3410 | 0.5246 | 0.2080 | | | | | MSE | 1.5523 | 0.8295 | 1.6208 | 0.9132 | 1.5711 | 0.7521 | 1.5296 | 0.5110 | | | | \*\*Significant at 95% confidence level. RTTC. RTTC thresholds were defined as follows: RTTC ≤ 1.0 represents serious conflicts, 1.0 *<* RTTC ≤ 3.0 represents moderate conflicts, and. RTTC *>* 3.0 was not considered a conflict. The number of serious and moderate conflicts was recorded for each 30-minute interval to comprehensively assess pedestrian-vehicle interactions. The effectiveness of MPSs was evaluated by calculating Conflict Modification Factors (CoMFs) and comparing their safety performance with other midblock crossing systems. The study employed both Cross-Sectional (CS) and Before-After evaluation methods, incorporating a Comparison Group (CG) and the Empirical Bayesian (EB) approach to calculate CoMFs. Prior studies have consistently demonstrated that PHB are generally safer than RRFB or Flashing Beacon. The primary reason for this is the mandatory stop requirement for vehicles during the red phase of PHB, ensuring driver compliance and pedestrian safety. In contrast, RRFB and Flashing Beacon serve only as visual warnings and do not require vehicles to stop unless a pedestrian is actively crossing, leading to inconsistent driver behavior. This study compared the safety performance of MPSs against different reference groups, including PHBs, RRFB, combinations of PHBs, RRFB and Flashing Beacon. Across all categories, MPSs demonstrated consistent reductions in serious and moderate conflicts. Notably, when compared to PHBs which share similar functionalities but differ in signal phase management; MPSs provided additional safety benefits by reducing both serious and total conflicts. Unlike PHBs, which remain dark when inactive, MPS systems operate seamlessly with regular traffic signals, maintaining a green phase until pedestrian activation. Importantly, even at locations where PHBs were replaced with MPS systems, no changes were made to the signal architecture (except for signal heads) or road geometry. The transition to MPS involved only reprogramming the signal phases, highlighting the adaptability and cost-effectiveness of this intervention. The results showed that, compared to PHBs, MPSs reduced serious and total conflicts by 27 % and 33 % using the EB method, 33 % and 31 % using CG method, and 26 % and 36 % using CS method, respectively. These consistent reductions demonstrate that MPS systems provide greater safety benefits than PHBs and other signalized mid-block crossings. Given their adaptability, ease of implementation, and improved safety performance, MPS systems can be considered as a preferred alternative when upgrading existing crossings or installing \*Significant at 90% confidence level. **Table 10** SPFs based on different reference groups for all conflicts. | Variable | | | | | | Estimate (std. error) based on different reference groups | | | | | | | | | | | |---------------------------------|--------------------|--------------------|-----------|-----------------------------|-----------|-----------------------------------------------------------|-----------------------|--------------------|--|--|--|--|--|--|--|--| | | All locations | | | PHBs, RRFB, Flashing Beacon | PHBs | | RRFB, Flashing Beacon | | | | | | | | | | | | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | NB-GLM | NB-GEE | | | | | | | | | | Traffic and Pedestrian Dynamics | | | | | | | | | | | | | | | | | | Constant | 1.368** | 1.099** | 1.184** | 1.382** | 1.297** | 1.436** | 1.404** | 1.342** | | | | | | | | | | | (0.200) | (0.281) | (0.242) | (0.284) | (0.229) | (0.102) | (0.237) | (0.140) | | | | | | | | | | Average leading vehicle | 0.504** | 0.604** | 0.962** | 0.800** | 1.138** | 0.988** | 0.425* (0.257) | 0.622** | | | | | | | | | | speed | (0.227) | (0.233) | (0.218) | (0.225) | (0.131) | (0.105) | | (0.175) | | | | | | | | | | Average vehicles' speed | 0.931** | 0.974** | 0.732** | 1.095** | 0.668** | 0.397** | 1.069** | 0.883** | | | | | | | | | | | (0.247) | (0.220) | (0.117) | (0.209) | (0.201) | (0.072) | (0.107) | (0.092) | | | | | | | | | | Ln (Vehicle volume) | 1.047** | 1.128** | 0.762** | 0.604** | 0.319** | 0.428** | 0.402* (0.211) | 0.519** | | | | | | | | | | | (0.145) | (0.131) | (0.118) | (0.099) | (0.108) | (0.100) | | (0.120) | | | | | | | | | | Pedestrian volume | 0.056* (0.031) | 0.040* (0.021) | | | | | | 0.0875*
(0.046) | | | | | | | | | | Road Characteristics | | | | | | | | | | | | | | | | | | MPS treatment | − 0.615** | − 0.693** | − 0.815** | − 0.720** | − 0.427** | − 0.447** | − 0.823** | − 0.755** | | | | | | | | | | | (0.032) | (0.091) | (0.039) | (0.028) | (0.065) | (0.081) | (0.110) | (0.091) | | | | | | | | | | Lane count | 0.399** | 0.500** | | 0.209** | | 0.397** | | | | | | | | | | | | | (0.107) | (0.118) | | (0.050) | | (0.095) | | | | | | | | | | | | Raised/vegetation | | − 0.496** | | − 0.821** | | − 0.510** | | − 0.464** | | | | | | | | | | Median | | (0.095) | | (0.141) | | (0.108) | | (0.224) | | | | | | | | | | Lane width | − 0.230** | − 0.355** | | | | | | | | | | | | | | | | | (0.101) | (0.109) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Posted speed limit | 0.336**
(0.091) | 0.314**
(0.013) | | 0.297**
(0.117) | | 0.566**
(0.240) | 0.109**
(0.022) | 0.111* (0.065) | | | | | | | | | | Contextual and Temporal Factors | | | | | | | | | | | | | | | | | | Land-use mix | 0.404** | 0.577** | | | 0.332** | 0.439** | | | | | | | | | | | | | (0.100) | (0.104) | | | (0.106) | (0.093) | | | | | | | | | | | | Weekday | 0.503** | 0.628** | 0.421** | 0.467** | 0.862** | 0.619** | 0.384* (0.209) | 0.918** | | | | | | | | | | | (0.221) | (0.210) | (0.123) | (0.208) | (0.110) | (0.091) | | (0.110) | | | | | | | | | | Morning peak | 0.499** | 0.506** | 0.636** | 0.731** | 0.062** | 0.049** | 0.749** | 0.521** | | | | | | | | | | | (0.170) | (0.113) | (0.184) | (0.266) | (0.006) | (0.002) | (0.111) | (0.100) | | | | | | | | | | Afternoon Peak | | | | | | | 0.093** | 0.019* | | | | | | | | | | | | | | | | | (0.044) | (0.011) | | | | | | | | | | Goodness of Fit | | | | | | | | | | | | | | | | | | AIC/QIC | 9046/- | − /9109 | 9431/- | − /9503 | 9315/- | − /9397 | 6419/- | − /6501 | | | | | | | | | | Dispersion Parameter | 0.40 | 0.42 | 0.31 | 0.32 | 0.28 | 0.32 | 0.31 | 0.35 | | | | | | | | | | Correlation
Coefficient,R(ρ) | | 0.34 | | 0.37 | | 0.36 | | 0.40 | | | | | | | | | | MAE | 0.7565 | 0.4267 | 0.8551 | 0.2278 | 0.8012 | 0.3761 | 0.5562 | 0.1034 | | | | | | | | | | MSE | 1.7630 | 0.7295 | 1.8603 | 0.4360 | 1.8087 | 0.8790 | 1.5605 | 0.3086 | | | | | | | | | \*\*Significant at 95% confidence level. **Table 11** CoMFs of MPSs based on Cross Sectional Method. | Conflict | | CoMF (std. error) of MPSs based on different reference groups | | | | | | | | |----------|------------------|---------------------------------------------------------------|----------------|-----------------------------|--|--|--|--|--| | types | All
locations | PHBs, RRFB and
Flashing Beacon | PHBs | RRFB and
Flashing Beacon | | | | | | | Serious | 0.55
(0.01) | 0.68 (0.06) | 0.74
(0.02) | 0.54 (0.07) | | | | | | | All | 0.50
(0.09) | 0.49 (0.03) | 0.64
(0.08) | 0.47 (0.09) | | | | | | new pedestrian signal systems. In the future, there will be the need to incorporate crash data alongside conflict data to validate and refine the current findings. Additionally, as more MPS systems are implemented across Florida and beyond, further research would involve larger datasets including nighttime observations and more detailed evaluation to enhance the understanding of their long-term safety impact. #### **CRediT authorship contribution statement** **Md Jamil Ahsan:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Mohamed Abdel-Aty:** Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. **Ahmed S. Abdelrahman:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Formal analysis, Data curation. #### **Declaration of competing interest** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ## **Acknowledgement** The authors wish to thank the Florida Department of Transportation \*Significant at 90% confidence level. for funding this research. The results and opinions are those of the authors and do not present the opinion of FDOT. The authors would also like to express their sincere appreciation to both current and former members of the UCF Smart and Safe Transportation (UCF-SST) Lab— Dr. Zubayer Islam , B. M. Tazbiul Hassan Anik, Dr. Tarek Hasan, Dr. Nafis Anwari, Md Mushtaque Tahmid, Insan Arafat Jahan, and Shaoyan Zhai—for their valuable assistance with data collection, and to Siyuan Tang for help with data processing. ## **Data availability** Data will be made available on request. ## **References** - Abdel-Aty, M.A., Radwan, A.E., 2000. Modeling traffic accident occurrence and involvement. Accident Analysis and Prevention 32 (5), 633–642. [https://doi.org/](https://doi.org/10.1016/S0001-4575(99)00094-9) [10.1016/S0001-4575\(99\)00094-9.](https://doi.org/10.1016/S0001-4575(99)00094-9) - Abdel-Aty, M., Abdalla, M.F., 2004. Modeling drivers' diversion from normal routes under ATIS using generalized estimating equations and binomial probit link function. Transportation 31 (3), 327–348. 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