Guidelines for the Development and Application of Crash Modification Factors (2022) / Chapter Skim
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From page 105... ...
A-1 A P P E N D I X A Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site
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From page 106... ...
A-2 A-3 Chapter 1 Introduction A-5 Chapter 2 Procedure A-5 Step 1 Identify Proposed Treatment and Subject Site A-5 Step 2 Identify Characteristics of Subject Site A-7 Step 3 Identify Existing CMFs for Proposed Treatment A-9 Step 4 Compare Subject Site Characteristics to Known CMF Influential Factors A-14 Step 5 Convert CMF to Disaggregate CMFs A-33 Step 6 Process Disaggregate CMFs A-39 Step 7 Develop Aggregate CMF Using Crash Distribution at Subject Site A-42 Result A-43 Chapter 3 Example Application of Procedure A-50 Additional Example Applications of the Step 5 Disaggregation Process A-68 Chapter 4 Supporting Research A-68 Development of Crash Modification Functions to Identify Influential Factors A-77 Evaluation of Two Estimators of Combined Average CMF A-83 References C O N T E N T S
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From page 107... ...
A-3 C H A P T E R 1 Introduction Safety practitioners must often adopt CMFs developed in other geographic areas and apply those CMFs to their own intersection or road section of interest. In many cases, there are differences between the sites where the CMF was developed and the site(s)
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From page 108... ...
A-4 Guidelines for the Development and Application of Crash Modification Factors In this regard, the treatment is presumed to affect both travel directions for the length of the segment and all intersection legs. Hence, the CMF is accurately represented as a "spatially aggregate" CMF because the treatment influences the safety of the entire site.
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From page 109... ...
A-5 The procedure presented in this appendix provides a step-by-step approach to selecting and adjusting a CMF for a proposed treatment to assure its suitability for a site of interest. The procedure consists of the following major steps, which are discussed individually in the following sections.
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From page 110... ...
A-6 Guidelines for the Development and Application of Crash Modification Factors Figure A1. Procedure for selecting and adjusting a CMF for a subject site.
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From page 111... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-7 In addition to physical and operational characteristics, it is necessary to know information about the crash history of the site for some steps of this process. In particular, the following crash information may be required.
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From page 112... ...
A-8 Guidelines for the Development and Application of Crash Modification Factors Determining whether a CMF is high quality can be done by viewing the star quality rating (if the CMF has been rated on the CMF Clearinghouse) , seeing if the CMF was included in the HSM, or by considering the criteria above.
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From page 113... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-9 Step 4 Compare Subject Site Characteristics to Known CMF Influential Factors In an ideal situation, the CMFs identified in Step 3 would have been developed using data from sites that are identical to the subject site. However, the reality is that the CMFs identified for the proposed treatment will often differ from the subject site on at least a few, if not many, characteristics.
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From page 114... ...
A-10 Guidelines for the Development and Application of Crash Modification Factors Countermeasure Crash Severity Crash Type Area Type Geographic Area of Origin Traffic Volume (AADT) Other References Increase access point density Total Total Increasing the access point density is more harmful for lower AADT compared to higher AADT Harwood et al.
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From page 115... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-11 information on the effect of various physical or operational characteristics. Note that these columns are not the same for every table.
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From page 116... ...
A-12 Guidelines for the Development and Application of Crash Modification Factors Countermeasure Crash Severity Crash Type Area Type Geographic Area of Origin Number of Lanes / Roadway Type Traffic Volume (AADT) Shoulder Width Degree of Curvature Other References Install permanent raised pavement markers Total Nighttime More beneficial for higher AADT (for fourlane freeways)
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From page 117... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-13 Countermeasure Crash Severity Crash Type Area Type Number of Lanes/Roadway Type Traffic Volume (AADT) Number of Intersection Legs Intersection Traffic Control References Convert signal to roundabout Total Total More beneficial in suburban areas compared to urban areas Data available, but could not conclude that it was an influential factor Less beneficial at sites with higher AADT More beneficial on 4-leg intersections compared to 3-leg Srinivasan et al.
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From page 118... ...
A-14 Guidelines for the Development and Application of Crash Modification Factors Data Analysis to Identify Influential Factors The project team conducted analyses of the various raw data sets to develop CMFunctions and identify influential factors. These included raw data that could be extracted from study reports as well as raw data sets available to the team from previous research projects.
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From page 119... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-15 Countermeasure Crash Severity Crash Type Geographic Area of Origin Traffic Volume (AADT) Shoulder Width Other References Decrease lane width Total Head-on, Run-offroad, Sideswipe, Single vehicle More harmful for higher AADT roads Less harmful for roads with wider shoulders Zegeer et al.
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From page 120... ...
A-16 Guidelines for the Development and Application of Crash Modification Factors Countermeasure Crash Severity Crash Type Geographic Area of Origin Number of Lanes / Roadway Type Traffic Volume (AADT) Road Division Shoulder Type Shoulder Width References Install Safetyedge Total Total Data available, but could not conclude that it was an influential factor (between GA and IN)
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From page 121... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-17 Countermeasure Crash Severity Crash Type Geographic Area of Origin Number of Lanes / Roadway Type Traffic Volume (AADT) Road Division Shoulder Type Shoulder Width References Install shoulder rumble strips Total Total Data available, but could not conclude that it was an influential factor More beneficial at higher AADT Data available, but could not conclude that it was an influential factor More beneficial on roads with narrow (4–6 ft)
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From page 122... ...
A-18 Guidelines for the Development and Application of Crash Modification Factors Countermeasure Crash Severity Crash Type Geographic Area of Origin Number of Lanes / Roadway Type Traffic Volume (AADT) Road Division Shoulder Type Shoulder Width References Widen shoulder Total Total More beneficial on roads with narrow (4–6 ft)
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From page 123... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-19 Required Data This section describes the number of aggregate CMFs needed for the procedure, the characteristics of the crash distribution used in the procedure, the statistical weight associated with each CMF observation, and a technique for estimating CMFs from a function of variables. Number of Aggregate CMFs Step 5 is used to estimate disaggregate CMFs for n categories of crash type or crash severity.
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From page 124... ...
A-20 Guidelines for the Development and Application of Crash Modification Factors If the sites were selected for treatment for reasons that do not include a recent increase in crashes, then the crash distribution can be obtained from the crash history of the treatment sites. This approach requires the crash distribution to be available in the original publication or from the researchers.
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From page 125... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-21 Standard Error and Weight The standard error is needed for each aggregate CMF observation. This statistic is used to determine the weight of the CMF observation, relative to other observations.
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From page 126... ...
A-22 Guidelines for the Development and Application of Crash Modification Factors where CMFb:a,i = value of CMF observation i when variable of interest changes from b to a (i = 1 to M2)
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From page 127... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-23 Based on the preceding discussion, the following equation is used to estimate the standard error of the regression coefficient associated with the variable of interest. This standard error is used in Equation A3 to estimate the weight associated with the CMF observation.
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From page 128... ...
A-24 Guidelines for the Development and Application of Crash Modification Factors The proportions included in Equation A8 must add to 1.0 for each observation in the regression database. The exponential function is used with each regression coefficient to ensure that the estimated CMF is non-negative.
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From page 129... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-25 where CMFagg = aggregate CMF bi,j = regression coefficient for crash type category i (i = mv: multiple vehicle, sv: single vehicle) and crash severity category j (j = fi: fatal-and-injury, pdo: property damage only)
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From page 130... ...
A-26 Guidelines for the Development and Application of Crash Modification Factors All models described in this subsection apply to four-leg intersections. When applied to three-leg intersections, the fourth term (i.e., with subscripts indicating leg 4)
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From page 131... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-27 intersection leg. This model can be used to estimate disaggregated CMFs when the aggregated CMFs are available in the literature.
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From page 132... ...
A-28 Guidelines for the Development and Application of Crash Modification Factors where LLi = log likelihood for observation i v = predicted variance scale parameter wi = weight of CMF observation i (from Equation A3) CMFi = value of CMF observation i CMFi = predicted value of the CMF for observation i When the weight of each CMF observation is defined using Equation A3, the variance term v in Equation A17 represents a scale parameter.
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From page 133... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-29 Steps for Disaggregating CMFs This section outlines the steps within Step 5 for disaggregating CMFs (Steps 5.1 through 5.4)
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From page 134... ...
A-30 Guidelines for the Development and Application of Crash Modification Factors Area Type Roadway Type Median State Crash Type Severity CMF Urban Freeway Divided Pennsylvania All All 0.9862 Rural Freeway Divided Missouri All All 1.0789 Pennsylvania All All 1.0033 Multilane Divided Minnesota All All 1.1022 Missouri All All 1.2200 Pennsylvania All All 0.8671 Two-lane Undivided Minnesota All All 1.1438 Missouri All All 1.4049 Pennsylvania All All 0.7560 Urban Freeway Divided Pennsylvania All Fatal & Injury 0.8399 Rural Freeway Divided Missouri All Fatal & Injury 0.9416 Pennsylvania All Fatal & Injury 0.8739 Multilane Divided Minnesota All Fatal & Injury 0.7779 Missouri All Fatal & Injury 0.9475 Pennsylvania All Fatal & Injury 0.5988 2-lane Undivided Minnesota All Fatal & Injury 1.0513 Missouri All Fatal & Injury 0.8076 Pennsylvania All Fatal & Injury 0.8203 Urban Freeway Divided Pennsylvania SV-ROR All 0.9419 Rural Freeway Divided Missouri SV-ROR All 0.9209 Pennsylvania SV-ROR All 0.8229 Multilane Divided Minnesota SV-ROR All 1.3836 Missouri SV-ROR All 1.4478 Pennsylvania SV-ROR All 0.7454 Two-lane Undivided Minnesota SV-ROR All 1.1072 Missouri SV-ROR All 1.1687 Pennsylvania SV-ROR All 0.5641 Urban Freeway Divided Pennsylvania SV-ROR Fatal & Injury 0.9257 Rural Freeway Divided Missouri SV-ROR Fatal & Injury 0.8436 Pennsylvania SV-ROR Fatal & Injury 0.7680 Multilane Divided Minnesota SV-ROR Fatal & Injury 0.8971 Missouri SV-ROR Fatal & Injury 1.0016 Pennsylvania SV-ROR Fatal & Injury 0.8014 2-lane Undivided Minnesota SV-ROR Fatal & Injury 0.6759 Missouri SV-ROR Fatal & Injury 0.5541 Pennsylvania SV-ROR Fatal & Injury 0.6334 Abbreviation: SV-ROR, single-vehicle run-off-road crash. Table A12.
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From page 135... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-31 type and severity categories would have its proportions computed using a denominator equal to the count of all crashes, regardless of crash type or severity. The numerator of each proportion would be equal to the count of crashes associated with a specific combination of crash type and severity.
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From page 136... ...
A-32 Guidelines for the Development and Application of Crash Modification Factors The observations in Table A13 are organized into four groups according to crash type and severity (i.e., All/All, All/FI, SV-ROR/All, and SV-ROR/FI)
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From page 137... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-33 The chi-square treatment is found to have a chi-square value of 47.4 (8 degrees of freedom, = 7+1)
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From page 138... ...
A-34 Guidelines for the Development and Application of Crash Modification Factors For each crash distribution category of interest, the user must determine how many CMFs were identified for that category. If more than one CMF was identified for a particular category, Steps 6a and 6b or 6c must be applied.
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From page 139... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-35 The homogeneity test should be based on CMFs that are associated with a weight of about 4.0 or more. CMFs with a smaller weight are less reliable because they are based on a relatively small sample size (i.e., a small number of observed crashes)
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From page 140... ...
A-36 Guidelines for the Development and Application of Crash Modification Factors chi-square value is 2.968. Relating this value to the chi-square distribution with for 1 degree of freedom (= 2−1)
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From page 141... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-37 Using the data in Table A15, the value of eL – is computed as 0.717. The value of sCMF is computed as 0.034 (= 0.717/[351.6+106.8]
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From page 142... ...
A-38 Guidelines for the Development and Application of Crash Modification Factors Criterion 1. Implementation.
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From page 143... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-39 Step 7 Develop Aggregate CMF Using Crash Distribution at Subject Site The previous step resulted in a final set of disaggregate CMFs for the treatment of interest. If the user needs to arrive at an aggregate (total crash)
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From page 144... ...
A-40 Guidelines for the Development and Application of Crash Modification Factors where pint,i = proportion of crashes associated with intersection leg i (i = 1, 2, 3, 4) AADTi = annual average daily traffic volume for intersection leg i (i = 1, 2, 3, 4)
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From page 145... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-41 The proportions included in Equation A34 must add to 1.0. If Equation A34 is used for a three-leg intersection, then the fourth term in brackets (i.e., with subscripts indicating leg 4)
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From page 146... ...
A-42 Guidelines for the Development and Application of Crash Modification Factors Result At the conclusion of the process, the user will have a CMF or set of CMFs that can be used to estimate the effect of the proposed treatment. If the user desired an aggregate (total crash)
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From page 147... ...
A-43 A city engineer is seeking to improve the safety of an intersection in her city. The inter section is currently stop-controlled, and her diagnosis of the intersection crash patterns shows that installing a traffic signal would be an appropriate countermeasure.
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From page 148... ...
A-44 Guidelines for the Development and Application of Crash Modification Factors Step 4 Compare Subject Site Characteristics to Known CMF Influential Factors The engineer consults Table A7 and sees that traffic volume, number of intersection legs, speed limit, and frequency of expected crashes before treatment are influential factors on the effect of a traffic signal installation. To use the CMFs identified in Step 3, the characteristics of the subject site must match the data of the CMF on these influential factors.
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From page 149... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-45 If the homogeneity test in Step 6a indicates that the differences among CMF values are small, then the individual CMFs can be combined into a single CMF average value for the given category (Step 6b)
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From page 150... ...
A-46 Guidelines for the Development and Application of Crash Modification Factors Step 6a.5 Check Results. The last step is to add the chi-square values and compare this result with the chi-square distribution for n − 1 degrees of freedom, where n is the number of CMF observations.
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From page 151... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-47 Step 6b.3 Compute Confidence Interval. The engineer calculates a confidence interval for the combined CMF using 95% confidence (z-value of 1.96)
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From page 152... ...
A-48 Guidelines for the Development and Application of Crash Modification Factors Step 6a.3 Compute Average Log. The third step is to compute the weighted average value of L
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From page 153... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-49 At the end of Step 6, she has identified or calculated the following disaggregate CMFs for each severity level. • Fatal 0.57 • A-injury 0.80 • B-injury 0.80 • C-injury 0.83 • PDO 1.15 The engineer can end the procedure here and apply these CMFs in the benefit-cost analysis.
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From page 154... ...
A-50 Guidelines for the Development and Application of Crash Modification Factors Result The engineer has identified a set of CMFs for the traffic signal that are specific to each level of severity. She can now use these CMFs to calculate the anticipated change in for each category of crash severity and use the resulting benefit in the benefit-cost analysis.
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From page 155... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-51 safety can vary widely from site to site. This observation is supported by a homogeneity test that indicates that the null hypothesis (i.e., that all sites have the same CMF value)
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From page 156... ...
A-52 Guidelines for the Development and Application of Crash Modification Factors disaggregate CMF for possible-injury-and-property-damage-only crashes (i.e., n = 2)
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From page 157... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-53 where CMFagg = aggregate CMF CMFKAB = disaggregate CMF for fatal-and-severe-injury (i.e., KAB) crashes CMFCO = disaggregate CMF for possible-injury-and-property-damage-only (i.e., CO)
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From page 158... ...
A-54 Guidelines for the Development and Application of Crash Modification Factors The chi-square treatment is found to have a chi-square value of 277 (6 degrees of freedom)
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From page 159... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-55 Installation of Permanent Raised Pavement Markings This section describes the disaggregation of aggregate CMFs that quantify the safety effect of installing permanent raised pavement markings (PRPMs) on two-lane highways and four-lane freeways.
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From page 160... ...
A-56 Guidelines for the Development and Application of Crash Modification Factors with CMF b b AADT CMF b b AADT CMF b b AADT CMF b b AADT day fi day fi AADT day day pdo day pdo AADT day night fi night fi AADT night night pdo night pdo AADT night exp ln exp ln exp ln exp ln , , , , , , , , , , , , ( )
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From page 161... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-57 bday,fi = regression coefficient for daytime FI crashes bday,pdo = regression coefficient for daytime PDO crashes bnight,fi = regression coefficient for nighttime FI crashes bnight,pdo = regression coefficient for nighttime PDO crashes bAADT,day = regression coefficient for AADT adjustment to daytime crashes bAADT,night = regression coefficient for AADT adjustment to nighttime crashes pday,fi = proportion of daytime FI crashes pday,pdo = proportion of daytime PDO crashes pnight,fi = proportion of nighttime FI crashes pnight,pdo = proportion of nighttime PDO crashes AADT = annual average daily traffic volume (two-way total) , veh/d Convert Crash Distribution and Other CMF Characteristics into Observations The third step of the disaggregation procedure is to determine the proportion of crashes for the time-of-day and severity categories associated with each CMF observation.
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From page 162... ...
A-58 Guidelines for the Development and Application of Crash Modification Factors The chi-square treatment is found to have a chi-square value of 40.6 (6 degrees of freedom)
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From page 163... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-59 Table A25 illustrates the magnitude of CMF values obtained from the calibrated equation. The values listed apply to two-lane highways and four-lane freeways -- other CMF values would be obtained for other facility types.
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From page 164... ...
A-60 Guidelines for the Development and Application of Crash Modification Factors Bauer et al. speculated that the addition of an HOV lane (as opposed to a general-purpose lane)
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From page 165... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-61 The preceding analysis indicates that operating a lane as an HOV lane reduced crashes 1.0 percent (CMF = 0.99) on the segments in Bundle H
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From page 166... ...
A-62 Guidelines for the Development and Application of Crash Modification Factors Based on the findings regarding Bundle H (discussed in the previous section) and a preliminary examination of the data, it was concluded that the CMFs for Bundle H are likely to be influenced by other, unknown factors.
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From page 167... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-63 Given the positive correlation between the changes in inside shoulder width and outside shoulder width in the data, it is rationalized that variables wis,a and wis,b in Equation A41 could be replaced with ws,a and ws,b and that these new variables could be used to describe the total change in both the inside and outside shoulder widths. The chi-square treatment is found to have a chi-square value of 85.8 (5 degrees of freedom)
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From page 168... ...
A-64 Guidelines for the Development and Application of Crash Modification Factors regression models. The functions reported by Harkey et al.
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From page 169... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-65 wm,a,i = median width for "after" condition of observation i, ft wm,b,i = median width for "before" condition of observation i, ft x–j = independent variable j having a value representative of the site of interest bj = regression coefficient associated with variable xj To compute the CMF observations, the median width variable for the "before" and the "after" conditions is varied over the range of 10 to 90 ft, reflecting the range in the calibration database assembled by Harkey et al.
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From page 170... ...
A-66 Guidelines for the Development and Application of Crash Modification Factors median vs. the non-cross median crashes so "area type" was represented using two regression coefficients (i.e., m = 3)
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From page 171... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-67 standard errors. The analysis can also be undertaken with Excel Solver to obtain the coefficient and parameter values (although Solver does not report the standard error of each value)
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From page 172... ...
A-68 This chapter provides details on the research conducted in Project 17-63 to develop and support portions of this appendix's step-by-step procedure for estimating the effect of a proposed treatment at a subject site. The supporting research in this chapter is presented as two major parts.
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From page 173... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-69 where CMFi* = the biased estimate of the CMF for a particular site i CMFi = the unbiased estimate of the CMF λi = the actual number of crashes in the after period πi = the expected number of crashes in the after period had the treatment not been implemented The unbiased estimate is different from the biased estimate because the expected value of the ratio of two random numbers is different from the ratio of their expected values [i.e., if A and B are two random numbers, E(A/B)
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From page 174... ...
A-70 Guidelines for the Development and Application of Crash Modification Factors In this case, Equation A51 was estimated as a negative binomial regression model. The functional form for the negative binomial regression model was the typical log-linear form (investigation of other forms could be a topic for future research)
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From page 175... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-71 Analysis of Maximum Likelihood Parameter Estimates Parameter DF Estimate Standard Error Wald 95% Confidence Limits Wald ChiSq Pr > ChiSq Intercept 1 -0.7474 0.7190 -2.1566 0.6618 1.08 0.2986 State CO 1 -1.5127 0.6713 -2.8284 -0.1970 5.08 0.0242 State FL 1 0.9984 0.9121 -0.7892 2.7861 1.20 0.2737 State IN 1 0.0083 0.8360 -1.6303 1.6469 0.00 0.9921 State MD 1 -0.7587 0.7142 -2.1585 0.6411 1.13 0.2881 State MI 1 -0.4236 0.5901 -1.5802 0.7330 0.52 0.4728 State NC 1 0.2277 0.7601 -1.2620 1.7174 0.09 0.7645 State NY 1 -0.0098 0.6213 -1.2276 1.2079 0.00 0.9874 State SC 1 -1.6153 0.8827 -3.3453 0.1148 3.35 0.0673 State VT 1 -0.1100 0.8268 -1.7304 1.5105 0.02 0.8942 State WA 0 0.0000 0.0000 0.0000 0.0000 .
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From page 176... ...
A-72 Guidelines for the Development and Application of Crash Modification Factors CMFunctions for Fatal and Injury Crashes Table A36 shows the function for fatal and injury crashes. Lg_total_AADT_before_s represents ln(total intersection AADT/10000)
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From page 177... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-73 The CMF associated with Missouri is significantly lower compared to that associated Pennsylvania after accounting for AADT and the expected crashes in the before period. As seen with the roundabout treatment, higher AADTs are associated with higher CMFs.
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From page 178... ...
A-74 Guidelines for the Development and Application of Crash Modification Factors one state to the other. The following site characteristics were available: AADT, expected crashes per mile in the first year of the before period, number of lanes, right-side shoulder width, left side shoulder width, and area type.
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From page 179... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-75 Analysis of Maximum Likelihood Parameter Estimates Parameter DF Estimate Standard Error Wald 95% Confidence Limits Wald ChiSq Pr > ChiSq Intercept 1 0.3189 0.2266 -0.1253 0.7631 1.98 0.1593 State MN 1 -0.6692 0.1746 -1.0114 -0.3270 14.69 0.0001 State NC 0 0.0000 0.0000 0.0000 0.0000 .
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From page 180... ...
A-76 Guidelines for the Development and Application of Crash Modification Factors Analysis of Maximum Likelihood Parameter Estimates Parameter DF Estimate Standard Error Wald 95% Confidence Limits Wald ChiSq Pr > ChiSq Intercept 1 0.6334 0.4567 -0.2616 1.5285 1.92 0.1654 State MN 1 -0.8196 0.2653 -1.3396 -0.2996 9.54 0.0020 State NC 0 0.0000 0.0000 0.0000 0.0000 .
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From page 181... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-77 CMFunction for Wet Night Crashes For wet night crashes, only the expected crashes per mile in the first year of the before period and area type are significant for this crash type. Evaluation of Two Estimators of Combined Average CMF This section describes the findings from an evaluation of two alternative estimators of the combined average CMF.
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From page 182... ...
A-78 Guidelines for the Development and Application of Crash Modification Factors The standard error of the combined CMF is computed using the following equation. s s CMF v ii Equation A5411, 2∑ = where sCMF v, = overall average standard error of CMFv based on variance weighting Estimator B Griffin and Flowers (1997)
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From page 183... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-79 Comparing Performance A simulation program was constructed to evaluate the two estimators. The program replicated the results from 1,000 before-after studies (i.e., 1,000 observations)
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From page 184... ...
A-80 Guidelines for the Development and Application of Crash Modification Factors CMFs to compute an estimate of the overall average CMF. Finally, Estimator B was used with the CMFs to compute an estimate of the overall average CMF.
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From page 185... ...
Procedure for Estimating the Effect of a Proposed Treatment at a Subject Site A-81 Data Set 2 The evaluation of Estimators A and B indicated that the amount of bias for a given estimator was influenced by the standard error associated with each observation. These standard errors are included in the weighted average technique associated with each estimator.
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From page 186... ...
A-82 Guidelines for the Development and Application of Crash Modification Factors Model Statistics Value R2: 0.99 Root mean square error: 0.042 Observations no: 200 data points (1,000 obs. per data point)
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From page 187... ...
A-83 American Association of State Highway and Transportation Officials (AASHTO)
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From page 188... ...
A-84 Guidelines for the Development and Application of Crash Modification Factors Hauer, E
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