Crash Modification Factors for Dynamic Speed Feedback Signs on Rural Curves
Affiliation(s)
1 Center for Transportation Research and Education, Iowa State University, Ames, Iowa, USA. 2 Plymouth Rock Assurance Inc., Boston, MA, USA.
1 Center for Transportation Research and Education, Iowa State University, Ames, Iowa, USA. 2 Plymouth Rock Assurance Inc., Boston, MA, USA.
ABSTRACT
A large number of crashes occur on curves even though they account for only a small percentage of a system’s mileage. Excessive speed has been identified as a primary factor in both lane departure and curve-related crashes. A number of countermeasures have been proposed to reduce driver speeds on curves, which ideally result in successful curve negotiation and fewer crashes. Dynamic speed feedback sign (DSFS) systems are traffic control devices that have been used to reduce vehicle speeds successfully and, subsequently, crashes in applications such as traffic calming on urban roads. DSFS systems show promise, but they have not been fully evaluated for rural curves. To better understand the effectiveness of DSFS systems in reducing crashes on curves, a national field evaluation of DSFS systems on curves on rural two lane roadways was conducted. Two different DSFS systems were selected and placed at 22 sites in seven states. Control sites were also identified. A full Bayes modeling methodology was utilized to develop crash modification factors (CMFs) for several scenarios including total crashes for both directions, total crashes in the direction of the sign, total single-vehicle crashes, and single-vehicle crashes in the direction of the sign. Using quarterly crash frequency as the response variable, crash modification factors were developed and results showed that crashes were 5% to 7% lower after installation of the signs depending on the model.
A large number of crashes occur on curves even though they account for only a small percentage of a system’s mileage. Excessive speed has been identified as a primary factor in both lane departure and curve-related crashes. A number of countermeasures have been proposed to reduce driver speeds on curves, which ideally result in successful curve negotiation and fewer crashes. Dynamic speed feedback sign (DSFS) systems are traffic control devices that have been used to reduce vehicle speeds successfully and, subsequently, crashes in applications such as traffic calming on urban roads. DSFS systems show promise, but they have not been fully evaluated for rural curves. To better understand the effectiveness of DSFS systems in reducing crashes on curves, a national field evaluation of DSFS systems on curves on rural two lane roadways was conducted. Two different DSFS systems were selected and placed at 22 sites in seven states. Control sites were also identified. A full Bayes modeling methodology was utilized to develop crash modification factors (CMFs) for several scenarios including total crashes for both directions, total crashes in the direction of the sign, total single-vehicle crashes, and single-vehicle crashes in the direction of the sign. Using quarterly crash frequency as the response variable, crash modification factors were developed and results showed that crashes were 5% to 7% lower after installation of the signs depending on the model.
KEYWORDS
CMF, Curve Warning, Dynamic Speed Feedback Sign, Bayesian Modeling, Horizontal Curve, Rural Curve, Speed Warning, Rural Safety
CMF, Curve Warning, Dynamic Speed Feedback Sign, Bayesian Modeling, Horizontal Curve, Rural Curve, Speed Warning, Rural Safety
Cite this paper
Hallmark, S. , Qiu, Y. , Hawkins, N. and Smadi, O. (2015) Crash Modification Factors for Dynamic Speed Feedback Signs on Rural Curves. Journal of Transportation Technologies, 5, 9-23. doi: 10.4236/jtts.2015.51002.
Hallmark, S. , Qiu, Y. , Hawkins, N. and Smadi, O. (2015) Crash Modification Factors for Dynamic Speed Feedback Signs on Rural Curves. Journal of Transportation Technologies, 5, 9-23. doi: 10.4236/jtts.2015.51002.
References
[1] Glennon, J.C., Neuman, T.R. and Leisch, J.E. (1985) Safety and Operational Considerations for Design of Rural Highway Curves. Federal Highway Administration. FHWA/RD-86-035. [2] Preston, H. and Schoenecker, T. (1999) Potential Safety Effects of Dynamic Signing at Rural Horizontal Curves. Minnesota Local Road Research Board. [3] Shankar, V.N., Albin, R.B., Milton, J.C. and Mannering, F.L. (1998) Evaluating Median Crossover Likelihoods with Clustered Accident Counts: An Empirical Inquiry Using the Random Effects Negative Binomial Model. Transportation Research Record: Journal of the Transportation Research Board, 1635, 44-48. [4] Farmer, C.M. and Lund, A.K. (2002) Rollover Risk of Cars and Light Trucks after Accounting for Driver and Environmental Factors. Accident Analysis and Prevention, 34, 163-173.
http://dx.doi.org/10.1016/S0001-4575(01)00010-0 [5] AASHTO (2008) Driving Down Lane-Departure Crashes: A National Priority. American Association of State Highway and Transportation Officials. [6] Luediger L., Choueiri, E.M., Hayward, J.C. and Paluri, A. (1988) Possible Design Procedure to Promote Design Consistency in Highway Geometric Design on Two-Lane Rural Roads. Transportation Research Record: Journal of the Transportation Research Board, 1195, 111-122. [7] Miaou, S. and Lum, H. (1993) Statistical Evaluation of the Effects of Highway Geometric Design on Truck Accident Involvements. Transportation Research Record: Journal of the Transportation Research Board, 1407, 11-24. [8] Vogt, A. and Bared, J. (1998) Accident Models for Two-Lane Rural Segments and Intersections. Transportation Research Record: Journal of the Transportation Research Board, 1635, 18-29. [9] Zegeer, C.V., Stewart, R., Council, F.M., Reinfurt, D.W. and Hamilton, E. (1992) Safety Effects of Geometric Improvements on Horizontal Curves. Transportation Research Record: Journal of the Transportation Research Board, 1356, 11-19. [10] Caliendo, C., Guida, M. and Parisi, A. (2007) A Crash-Prediction Model for Multi-lane Roads. Accident Analysis and Prevention, 39, 657-670.
http://dx.doi.org/10.1016/j.aap.2006.10.012 [11] Findley, D.J., Hummer, J.E., Rasdorf, W., Zegeer, C.V. and Fowler, T.J. (2012) Modeling the Impacts of Spatial Relationships on Horizontal Curve Safety. Accident Analysis and Prevention, 45, 296-304.
http://dx.doi.org/10.1016/j.aap.2011.07.018 [12] Council, F.M., Srinivasan, R., Masten, S., Carter, D. and Reurings, M. (2005) Development of a Speeding-Related Crash Typology: Summary Report. Federal Highway Administration, FHWA-HRT-10-039. [13] NHTSA (2011) Traffic Safety Facts 2011 Data—Speeding. National Highway Traffic Safety Administration, DOT HS 811 751. [14] Jorgensen and Associates, Inc. (1978) NCHRP Report 197: Cost and Safety Effectiveness of Highway Design Elements. National Cooperative Highway Research Program, Washington DC. [15] Hallmark, S., McDonald, T.J., Tian, Y. and Andersen, D. (2010) Safety Benefits of Paved Shoulders. Center for Transportation Research and Education, Iowa State University, Ames. [16] Zador, P.L., Wright, P.H. and Karpf, R.S. (1982) Effect of Pavement Markers on Nighttime Crashes in Georgia. Insurance Institute for Highway Safety, Washington DC. [17] Hammond, J.L. and Wegmann, F.J. (2001) Daytime Effects of Raised Pavement Markers on Horizontal Curves. ITE Journal, 71, 38-41. [18] Bahar, G., Mollett, C., Persuad, B., Lyon, C., Smiley, A., Smahel, T. and McGee, H. (2004) NCHRP Report 518: Safety Evaluation of Raised Pavement Markers. National Cooperative Highway Research Program, Washington DC. [19] Tsyganov, A.R., Machemehl, R.B. and Warrenchuk, N.M. (2005) Safety Impact of Edge Lines or Rural Two-Lane Highways. Center for Transportation Research, University of Texas at Austin, Austin. [20] Potts, I.B., Harwood, D.W., Bokenkroger, C.D. and Hutton, J.M. (2008) Benefit-Cost Evaluation of MoDOT’s Total Striping and Delineation Program. Midwest Research Institute and the Missouri Department of Transportation, Kansas City. [21] Hughes, W.E., McGee, H.W., Hussain, S. and Keegel, J. (1989) Field Evaluation of Edge Line Widths. Federal Highway Administration, Washington DC. [22] Hall, J. (1987) Evaluation of Wide Edgelines. Transportation Research Record, 1114, 21-27. [23] Cottrell, B.H., Lee, D., Molino, J. and Opiela, K.S. (2007) Can Pavement Marking Curve Delineation Improve the Consistency of Vehicle Speed and Lane Position? Results from a Nighttime Driving Experiment. Proceedings of the 2007 Annual Meeting of the Transportation Research Board, Washington DC, January 2007. [24] Park, E., Carlson, P.J., Porter, R.J. and Anderson, C.K. (2012) Safety Effects of Wider Edge Lines on Rural Two-Lane Highways. Accident Analysis and Prevention, 48, 317-325.
http://dx.doi.org/10.1016/j.aap.2012.01.028 [25] Chrysler, S.T. and Schrock, S.D. (2005) Field Evaluation and Driver Comprehension Studies of Horizontal Signing. Texas Transportation Institute, College Station. [26] Retting, R.A. and Farmer, C.M. (1998) Use of Pavement Markings to Reduce Excessive Traffic Speeds on Hazardous Curves. ITE Journal, 68, 30-36. [27] Hallmark, S., Hawkins, N. and Smadi, O. (2012) Evaluation of Low-Cost Treatments on Rural Two-Lane Curves. Center for Transportation Research and Education, Iowa State University, Ames. [28] Vest, A., Stamatiadis, N., Clayton, A. and Pigman, J. (2005) Effect of Warning Signs on Curve Operating Speeds. Kentucky Transportation Center, Lexington. [29] Molino, J.A., Katz, B.J., Hermosillo, M.B., Dagnall, E.E. and Kennedy, J.F. (2010) Simulator Evaluation of Low-Cost Safety Improvements on Rural Two-Lane Undivided Roads: Nighttime Delineation for Curves and Traffic Calming for Small Towns. U.S. Department of Transportation, Federal Highway Administration, Washington DC. [30] FHWA (2011) Highways for LIFE Technology Partnership Program. Light Emitting Diode Raised Pavement Markers, Federal Highway Administration. www.fhwa.dot.gov/hfl/partnerships/safety_eval/led.cfm [31] Torbic, D.J., Harwood, D., Gilmore, D.K., Pfefer, R., Neuman, T.R., Slack, K.L. and Hardy, K.K. (2004) NCHRP Report 500 Volume 7: A Guide for Reducing Collisions on Horizontal Curves. National Cooperative Highway Research Program, Washington DC. [32] Griffin, L.I. and Reinhart, R.N. (1995) Patterns That Have Been Developed to Reduce Traffic Speeds and Crashes. AAA Foundation for Traffic Safety, Washington DC. [33] Patel, R.B., Council, F.M. and Griffith, M.S. (2007) Estimating the Safety Benefits of Shoulder Rumble Strips on Two Lane Rural Highways in Minnesota: An Empirical Bayes Observational Before-After Study. 2007 TRB 86th Annual Meeting: Compendium of Papers CD-ROM, Washington DC, Vol. TRB#07-1924. [34] Bertini, R.L., Monsere, C., Nolan, C., Bosa, P. and Abou El-Seoud, T. (2006) Field Evaluation of the Myrtle Creek Advance Curve Warning System, SPR 352, FHWA-OR-RD-05_13. Portland State University, Portland. [35] Tribbett, L., McGowen, P. and Mounce, J. (2000) An Evaluation of Dynamic Curve Warning Systems in the Sacramento River Canyon. Western Transportation Institute.
www.coe.montana.edu/ce/patm/pubs/files/2000curve.pdf [36] City of Bellevue Transportation Department (2009) Stationary Radar Sign Program 2009 Report. Bellevue. [37] Mattox, J.H., Sarasua, W.A., Ogle, J.H., Eckenrode, R.T. and Dunning, A. (2007) Development and Evaluation of a Speed Activated Sign to Reduce Speeds in Work Zones. Proceedings of the 2007 Annual Meeting of the Transportation Research Board, Washington DC, January 2007. [38] 3M (2006) A Before and After Study of 3M Driver Feedback Signs. Traffic Safety Systems, 3M United Kingdom PLC, Berkshire.
www.morelock.co.uk/assets/3M/3M%20DFS%20field%20study%20results.pdf [39] Winnett, M.A. and Wheeler, A.H. (2002) Vehicle Activated Signs—A Large Scale Evaluation. TRL548, Road Safety Division, Department for Transport, Wokingham, Berkshire. [40] Santiago-Chaparra, K.R., Chitturi, M., Bill, A. and Noyce, D. (2012) Spatial Effectiveness of Speed Feedback Signs. Journal Transportation Research Record: Journal of the Transportation Research Board, 2281, 8-15.
http://dx.doi.org/10.3141/2281-02 [41] FHWA (2009) Manual on Uniform Traffic Control Devices (MUTCD) for Streets and Highways. U.S. Department of Transportation, Federal Highway Administration, Washington DC. [42] Hauer, E., Harwood, D.W., Council, F.M. and Griffith, M. (2002) Estimating Safety by the Empirical Bayes Method: A Tutorial. Journal Transportation Research Record: Journal of the Transportation Research Board, 1784, 126-131.
http://dx.doi.org/10.3141/1784-16 [43] Hovey, P.W. and Chowdhury, M. (2005) Development of Crash Reduction Factors. 14801(0) Ohio Department of Transport, Columbus. [44] Persaud, B. and Lyon, C. (2007) Empirical Bayes Before-After Safety Studies: Lessons Learned from Two Decades of Experience and Future Directions. Accident Analysis and Prevention, 39, 546-555.
http://dx.doi.org/10.1016/j.aap.2006.09.009 [45] Hauer, E. (1997) Observational Before-After Studies in Road Safety. Emerald Group Publishing Limited, Bingley. [46] Carriquiry, A.L. and Pawlovich, M. (2004) From Empirical Bayes to Full Bayes: Methods for Analyzing Traffic Safety Data, White Paper. Iowa Department of Transportation, Ames, Iowa. [47] Lan, B., Persaud, B., Lyon, C. and Bhim, R. (2009) Validation of a Full Bayes Methodology for Observational Before-After Road Safety Studies and Application to Evaluation of Rural Signal Conversions. Accident Analysis and Prevention, 41, 574-580.
http://dx.doi.org/10.1016/j.aap.2009.02.010 [48] Congdon, P. (2001) Bayesian Statistical Modeling. John Wiley & Sons Ltd., West Sussex. [49] Persaud, B., Lord, D. and Palmisano, J. (2002) Calibration and Transferability of Accident Prediction Models for Urban Intersections. Journal Transportation Research Record: Journal of the Transportation Research Board, 1784, 57-64.
http://dx.doi.org/10.3141/1784-08 [50] Spiegelhalter, D., Thomas, A., Best, N. and Lunn, D. (2003) WinBUGS Version 1.4 User Manual. MRC Biostatistics Unit, Cambridge. [51] Gamerman, D. (2006) Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference. Taylor & Francis, Boca Raton. [52] Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman and Hall, London. [53] Hallmark, S., Hawkins, N. and Smadi, O. (2013) Evaluation of Dynamic Speed Feedback Signs on Curves: A National Demonstration Project. Draft Final Report, FHWA Project DTFH61-07-H-00022.
[1] Glennon, J.C., Neuman, T.R. and Leisch, J.E. (1985) Safety and Operational Considerations for Design of Rural Highway Curves. Federal Highway Administration. FHWA/RD-86-035. [2] Preston, H. and Schoenecker, T. (1999) Potential Safety Effects of Dynamic Signing at Rural Horizontal Curves. Minnesota Local Road Research Board. [3] Shankar, V.N., Albin, R.B., Milton, J.C. and Mannering, F.L. (1998) Evaluating Median Crossover Likelihoods with Clustered Accident Counts: An Empirical Inquiry Using the Random Effects Negative Binomial Model. Transportation Research Record: Journal of the Transportation Research Board, 1635, 44-48. [4] Farmer, C.M. and Lund, A.K. (2002) Rollover Risk of Cars and Light Trucks after Accounting for Driver and Environmental Factors. Accident Analysis and Prevention, 34, 163-173.
http://dx.doi.org/10.1016/S0001-4575(01)00010-0 [5] AASHTO (2008) Driving Down Lane-Departure Crashes: A National Priority. American Association of State Highway and Transportation Officials. [6] Luediger L., Choueiri, E.M., Hayward, J.C. and Paluri, A. (1988) Possible Design Procedure to Promote Design Consistency in Highway Geometric Design on Two-Lane Rural Roads. Transportation Research Record: Journal of the Transportation Research Board, 1195, 111-122. [7] Miaou, S. and Lum, H. (1993) Statistical Evaluation of the Effects of Highway Geometric Design on Truck Accident Involvements. Transportation Research Record: Journal of the Transportation Research Board, 1407, 11-24. [8] Vogt, A. and Bared, J. (1998) Accident Models for Two-Lane Rural Segments and Intersections. Transportation Research Record: Journal of the Transportation Research Board, 1635, 18-29. [9] Zegeer, C.V., Stewart, R., Council, F.M., Reinfurt, D.W. and Hamilton, E. (1992) Safety Effects of Geometric Improvements on Horizontal Curves. Transportation Research Record: Journal of the Transportation Research Board, 1356, 11-19. [10] Caliendo, C., Guida, M. and Parisi, A. (2007) A Crash-Prediction Model for Multi-lane Roads. Accident Analysis and Prevention, 39, 657-670.
http://dx.doi.org/10.1016/j.aap.2006.10.012 [11] Findley, D.J., Hummer, J.E., Rasdorf, W., Zegeer, C.V. and Fowler, T.J. (2012) Modeling the Impacts of Spatial Relationships on Horizontal Curve Safety. Accident Analysis and Prevention, 45, 296-304.
http://dx.doi.org/10.1016/j.aap.2011.07.018 [12] Council, F.M., Srinivasan, R., Masten, S., Carter, D. and Reurings, M. (2005) Development of a Speeding-Related Crash Typology: Summary Report. Federal Highway Administration, FHWA-HRT-10-039. [13] NHTSA (2011) Traffic Safety Facts 2011 Data—Speeding. National Highway Traffic Safety Administration, DOT HS 811 751. [14] Jorgensen and Associates, Inc. (1978) NCHRP Report 197: Cost and Safety Effectiveness of Highway Design Elements. National Cooperative Highway Research Program, Washington DC. [15] Hallmark, S., McDonald, T.J., Tian, Y. and Andersen, D. (2010) Safety Benefits of Paved Shoulders. Center for Transportation Research and Education, Iowa State University, Ames. [16] Zador, P.L., Wright, P.H. and Karpf, R.S. (1982) Effect of Pavement Markers on Nighttime Crashes in Georgia. Insurance Institute for Highway Safety, Washington DC. [17] Hammond, J.L. and Wegmann, F.J. (2001) Daytime Effects of Raised Pavement Markers on Horizontal Curves. ITE Journal, 71, 38-41. [18] Bahar, G., Mollett, C., Persuad, B., Lyon, C., Smiley, A., Smahel, T. and McGee, H. (2004) NCHRP Report 518: Safety Evaluation of Raised Pavement Markers. National Cooperative Highway Research Program, Washington DC. [19] Tsyganov, A.R., Machemehl, R.B. and Warrenchuk, N.M. (2005) Safety Impact of Edge Lines or Rural Two-Lane Highways. Center for Transportation Research, University of Texas at Austin, Austin. [20] Potts, I.B., Harwood, D.W., Bokenkroger, C.D. and Hutton, J.M. (2008) Benefit-Cost Evaluation of MoDOT’s Total Striping and Delineation Program. Midwest Research Institute and the Missouri Department of Transportation, Kansas City. [21] Hughes, W.E., McGee, H.W., Hussain, S. and Keegel, J. (1989) Field Evaluation of Edge Line Widths. Federal Highway Administration, Washington DC. [22] Hall, J. (1987) Evaluation of Wide Edgelines. Transportation Research Record, 1114, 21-27. [23] Cottrell, B.H., Lee, D., Molino, J. and Opiela, K.S. (2007) Can Pavement Marking Curve Delineation Improve the Consistency of Vehicle Speed and Lane Position? Results from a Nighttime Driving Experiment. Proceedings of the 2007 Annual Meeting of the Transportation Research Board, Washington DC, January 2007. [24] Park, E., Carlson, P.J., Porter, R.J. and Anderson, C.K. (2012) Safety Effects of Wider Edge Lines on Rural Two-Lane Highways. Accident Analysis and Prevention, 48, 317-325.
http://dx.doi.org/10.1016/j.aap.2012.01.028 [25] Chrysler, S.T. and Schrock, S.D. (2005) Field Evaluation and Driver Comprehension Studies of Horizontal Signing. Texas Transportation Institute, College Station. [26] Retting, R.A. and Farmer, C.M. (1998) Use of Pavement Markings to Reduce Excessive Traffic Speeds on Hazardous Curves. ITE Journal, 68, 30-36. [27] Hallmark, S., Hawkins, N. and Smadi, O. (2012) Evaluation of Low-Cost Treatments on Rural Two-Lane Curves. Center for Transportation Research and Education, Iowa State University, Ames. [28] Vest, A., Stamatiadis, N., Clayton, A. and Pigman, J. (2005) Effect of Warning Signs on Curve Operating Speeds. Kentucky Transportation Center, Lexington. [29] Molino, J.A., Katz, B.J., Hermosillo, M.B., Dagnall, E.E. and Kennedy, J.F. (2010) Simulator Evaluation of Low-Cost Safety Improvements on Rural Two-Lane Undivided Roads: Nighttime Delineation for Curves and Traffic Calming for Small Towns. U.S. Department of Transportation, Federal Highway Administration, Washington DC. [30] FHWA (2011) Highways for LIFE Technology Partnership Program. Light Emitting Diode Raised Pavement Markers, Federal Highway Administration. www.fhwa.dot.gov/hfl/partnerships/safety_eval/led.cfm [31] Torbic, D.J., Harwood, D., Gilmore, D.K., Pfefer, R., Neuman, T.R., Slack, K.L. and Hardy, K.K. (2004) NCHRP Report 500 Volume 7: A Guide for Reducing Collisions on Horizontal Curves. National Cooperative Highway Research Program, Washington DC. [32] Griffin, L.I. and Reinhart, R.N. (1995) Patterns That Have Been Developed to Reduce Traffic Speeds and Crashes. AAA Foundation for Traffic Safety, Washington DC. [33] Patel, R.B., Council, F.M. and Griffith, M.S. (2007) Estimating the Safety Benefits of Shoulder Rumble Strips on Two Lane Rural Highways in Minnesota: An Empirical Bayes Observational Before-After Study. 2007 TRB 86th Annual Meeting: Compendium of Papers CD-ROM, Washington DC, Vol. TRB#07-1924. [34] Bertini, R.L., Monsere, C., Nolan, C., Bosa, P. and Abou El-Seoud, T. (2006) Field Evaluation of the Myrtle Creek Advance Curve Warning System, SPR 352, FHWA-OR-RD-05_13. Portland State University, Portland. [35] Tribbett, L., McGowen, P. and Mounce, J. (2000) An Evaluation of Dynamic Curve Warning Systems in the Sacramento River Canyon. Western Transportation Institute.
www.coe.montana.edu/ce/patm/pubs/files/2000curve.pdf [36] City of Bellevue Transportation Department (2009) Stationary Radar Sign Program 2009 Report. Bellevue. [37] Mattox, J.H., Sarasua, W.A., Ogle, J.H., Eckenrode, R.T. and Dunning, A. (2007) Development and Evaluation of a Speed Activated Sign to Reduce Speeds in Work Zones. Proceedings of the 2007 Annual Meeting of the Transportation Research Board, Washington DC, January 2007. [38] 3M (2006) A Before and After Study of 3M Driver Feedback Signs. Traffic Safety Systems, 3M United Kingdom PLC, Berkshire.
www.morelock.co.uk/assets/3M/3M%20DFS%20field%20study%20results.pdf [39] Winnett, M.A. and Wheeler, A.H. (2002) Vehicle Activated Signs—A Large Scale Evaluation. TRL548, Road Safety Division, Department for Transport, Wokingham, Berkshire. [40] Santiago-Chaparra, K.R., Chitturi, M., Bill, A. and Noyce, D. (2012) Spatial Effectiveness of Speed Feedback Signs. Journal Transportation Research Record: Journal of the Transportation Research Board, 2281, 8-15.
http://dx.doi.org/10.3141/2281-02 [41] FHWA (2009) Manual on Uniform Traffic Control Devices (MUTCD) for Streets and Highways. U.S. Department of Transportation, Federal Highway Administration, Washington DC. [42] Hauer, E., Harwood, D.W., Council, F.M. and Griffith, M. (2002) Estimating Safety by the Empirical Bayes Method: A Tutorial. Journal Transportation Research Record: Journal of the Transportation Research Board, 1784, 126-131.
http://dx.doi.org/10.3141/1784-16 [43] Hovey, P.W. and Chowdhury, M. (2005) Development of Crash Reduction Factors. 14801(0) Ohio Department of Transport, Columbus. [44] Persaud, B. and Lyon, C. (2007) Empirical Bayes Before-After Safety Studies: Lessons Learned from Two Decades of Experience and Future Directions. Accident Analysis and Prevention, 39, 546-555.
http://dx.doi.org/10.1016/j.aap.2006.09.009 [45] Hauer, E. (1997) Observational Before-After Studies in Road Safety. Emerald Group Publishing Limited, Bingley. [46] Carriquiry, A.L. and Pawlovich, M. (2004) From Empirical Bayes to Full Bayes: Methods for Analyzing Traffic Safety Data, White Paper. Iowa Department of Transportation, Ames, Iowa. [47] Lan, B., Persaud, B., Lyon, C. and Bhim, R. (2009) Validation of a Full Bayes Methodology for Observational Before-After Road Safety Studies and Application to Evaluation of Rural Signal Conversions. Accident Analysis and Prevention, 41, 574-580.
http://dx.doi.org/10.1016/j.aap.2009.02.010 [48] Congdon, P. (2001) Bayesian Statistical Modeling. John Wiley & Sons Ltd., West Sussex. [49] Persaud, B., Lord, D. and Palmisano, J. (2002) Calibration and Transferability of Accident Prediction Models for Urban Intersections. Journal Transportation Research Record: Journal of the Transportation Research Board, 1784, 57-64.
http://dx.doi.org/10.3141/1784-08 [50] Spiegelhalter, D., Thomas, A., Best, N. and Lunn, D. (2003) WinBUGS Version 1.4 User Manual. MRC Biostatistics Unit, Cambridge. [51] Gamerman, D. (2006) Markov Chain Monte Carlo Stochastic Simulation for Bayesian Inference. Taylor & Francis, Boca Raton. [52] Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (1996) Markov Chain Monte Carlo in Practice. Chapman and Hall, London. [53] Hallmark, S., Hawkins, N. and Smadi, O. (2013) Evaluation of Dynamic Speed Feedback Signs on Curves: A National Demonstration Project. Draft Final Report, FHWA Project DTFH61-07-H-00022.