Application of Crash Modification Factors for Access Management, Volume 1: Practitioner's Guide (2021)

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77   This chapter introduces the general methodology for quantifying safety performance at the corridor level. The methodology provides a structured approach to incorporate access- management-related variables in estimating the crash frequency, by crash type and severity, for urban and suburban corridors. Topics include the recommended predictive method for corridor- level analysis; guidance on considering key variables, including a discussion of nuances and limi- tations; and examples that demonstrate how to use the methods with different levels of data. Predictive Method Options There are two primary options for corridor-level analysis: (1) combine results from segment- and intersection-level analysis (from Chapter 4) and (2) use a corridor-level prediction model devel- oped in previous research (Gross et al. 2018). Predictive Method Option 1: Combine Segment- and Intersection-Level Results This option may be selected when access management strategies target one or more segments or intersections along the corridor, with the following three conditions: 1. A procedure is available for estimating the individual and cumulative effects of those strategies. 2. The expected safety impacts of the strategies are assumed to be independent (i.e., the strategies target different locations with no expected interaction effects). For example, if the strategy is to close one driveway within a segment and install a left-turn lane at two intersections within the corridor, then it may be appropriate to assume these strategies are independent. 3. The safety performance of adjacent sites is assumed to be independent (i.e., the safety perfor- mance of the segment does not impact the safety performance of a nearby or adjacent inter- section). For example, if two alternatives include different spacing distances for unsignalized intersections, then the safety performance for the corridor may differ even though the number of intersections remains the same. In this example, the safety effects of the intersections are not independent. If these three conditions are met, it is reasonable to aggregate the safety performance of indi- vidual segments and intersections to estimate the safety performance of the corridor. Chapter 4 presented the analysis methodologies for estimating the effects of individual segments and inter- sections, including the impacts of various access management variables. Those methodologies are essentially the same as those in the Highway Safety Manual (1st Edition) (AASHTO 2010) with the addition of select new adjustment factors for access management variables developed in this research (NCHRP Project 17-74). The Highway Safety Manual (1st Edition) provides a C H A P T E R   5 Predictive Method for Corridor-Level Analysis

78 Application of Crash Modification Factors for Access Management detailed procedure for aggregating individual segment- and intersection-level crash predictions into a corridor-level prediction. If one or more of the three conditions previously mentioned are not met, then it is more appropriate to estimate the safety performance of the corridor using corridor-level prediction methods. While the results from NCHRP Project 17-74 indicate that the Highway Safety Manual (1st Edition) predictive method performs relatively well for estimating the safety performance of individual (and independent) segments and intersections with different access management characteristics, the method does not account for the potential interactions among adjacent or nearby sites (e.g., access spacing and density). It also does not account for the potential inter- actions among multiple access management strategies. As such, the corridor-level predictive method presented in Predictive Method Option 2 (see the next section) is more appropriate for estimating safety performance at the corridor level when it is necessary to consider interactions among nearby sites and multiple access management features. Predictive Method Option 2: Apply Corridor-Level Prediction Models For some situations, corridor-level crash predictions are more influenced by variables defined at the corridor level. For example, some access management strategies may shift turning traffic from one location to another (e.g., converting an undivided road to a physically divided road). In other cases, detailed access design (e.g., intersection or median opening spacing) will impact the safety performance of the corridor beyond the simple presence of the feature. Research con- ducted under NCHRP Project 17-74 suggests that in such cases, corridor-level crash predictions should be applied. The remainder of this chapter presents the corridor-level predictive method developed in this research. Corridor-Level Prediction Models This section is intended to guide a user through the steps required to select and apply the most appropriate model(s) for estimating the safety impacts of an access management strategy or combination of strategies at the corridor level. The model selection and application process involves the following four steps: 1. Select land use and region. 2. Select crash types and variables of interest. 3. Select analysis level of interest. 4. Select applicable model(s) and perform analysis. The remainder of this section provides a detailed discussion of the four-step process and sample problems to illustrate the application of each step. Step 1: Select Land Use and Region Corridor-level prediction models are available for different land use and regional character- istics. As such, the first step is to select the applicable land use and region based on the applica- tion context. The land use categories include mixed-use, commercial, or residential (categories are defined in Table 66). Figure 84 provides two examples of corridors and the corresponding land use. Regions include North Carolina, Minnesota, Northern California, or Southern California based on the data used to develop the models. One consideration in selecting an applicable region is a comparison of local values with the mean values of the variables in each region (see

Predictive Method for Corridor-Level Analysis 79   Appendix D). It is recommended to select an applicable region based on the summary statistics that most closely match the study corridor of interest rather than selecting the region based on geographic proximity. The result of this step is the identification of the most-applicable land use type and region. Step 2: Select Crash Types and Variables of Interest The second step is to select the crash types and variables of interest. The selection of crash types and variables determines which model(s) will be needed. Table 67 presents a list of poten- tial crash types and definitions. North Carolina crashes coded as rear-end turn crashes are included in both rear-end and turning crashes. Since the specific crash types cannot be summed to get total crashes, double-counting should not pose a problem for the crash type models. General variables of interest included in the models are AADT and corridor length. Table 68 presents the access-related characteristics included in the models. Step 3: Select Analysis Level of Interest The next step is to select the analysis level of interest. There are two options, and the choice of one option or the other will be based on the intended application of results and the availability and applicability of crash history. If the intent is to compare the relative safety performance Residential Area Commercial Area Figure 84. Examples of land use along urban and suburban arterials. heavy vehicles. As defined for these models, commercial areas do not include large shopping centers (e.g., malls) that have a larger percentage of trips on the weekends. Mixed Use Mixed-use area types are defined as those areas with a balanced mix of both commercial and residential establishments and access. Land Use Definition Residential Residential areas are characterized by the type of development (i.e., primarily single- or multi-family housing) and serve mainly passenger cars. Commercial Commercial areas are defined as those areas with office buildings and other businesses that operate during normal business hours on weekdays and serve a larger proportion of Table 66. Land use category definitions.

80 Application of Crash Modification Factors for Access Management of different alternatives or if the crash history is unavailable or not applicable, then Analysis Level 1 (relative comparison of safety performance) is appropriate. If the intent is to estimate or compare the number of crashes for one or more alternatives and an applicable crash history is available, then Analysis Level 2 (absolute comparison of safety performance) is appropriate. Analysis Level 1: Relative Comparison of Safety Performance This option applies to both existing corridors and new construction and provides an estimate of the change in predicted crashes or the percent change in crashes based on a proposed change in corridor characteristics (e.g., traffic volume, corridor length, and access management strategies). The results are presented as the change in predicted crash frequency or the percent change in crashes per year for alternative scenarios (e.g., scenario B is expected to result in 10 percent more injury crashes per year than scenario A). It is not appropriate to use this type of analysis in an economic evaluation because it does not account for the expected number of crashes (only the relative change). Note: Apply Analysis Level 1 in Step 4. Analysis Level 2: Absolute Comparison of Safety Performance This option applies to existing corridors with an available crash history and provides an estimate of the expected crashes per year; however, it requires the observed crash history for the study corridor. The EB method is employed, combining the observed crash history and the predicted crashes from the model to obtain the expected number of crashes. The EB method corrects for several potential sources of bias, including variables that are not in the model. Crash Type Definition Total All crashes Injury KABC on KABCO scale Turning California: any involved vehicle making a turn Minnesota: left turn or right turn North Carolina: rear-end turn, left-turn same roadway, left-turn different roadway, right- turn same roadway, right-turn different roadway Rear-End California and Minnesota: rear-end North Carolina: rear-end slow or stop and rear-end turn Right-Angle California: broadside and no vehicle was turning Minnesota: right-angle North Carolina: angle Table 67. Crash types and definitions. Strategy Variable Name Definition Access density ACCDENS Number of driveways plus unsignalized intersections per mile UNSIGDENS Number of unsignalized intersections per mile SIGDENS Number of signalized intersections per mile MEDOPDENS Number of median openings per mile Median type PROPDIV Proportion of corridor length with divided median PROPTWLTL Proportion of corridor length with TWLTL Roadside development PROPFULLDEV Proportion of corridor length with full roadside development PROPNODEV Proportion of length with no roadside development Number of lanes PROPLANE1 Proportion of corridor length with two lanes Visual clutter PROPVC Proportion of length with visual clutter (i.e., excessive signage, roadside advertisements, or banners) Table 68. Access-related variables and definitions.

Predictive Method for Corridor-Level Analysis 81   The results are presented as the expected crash frequency per year for each alternative. The results from this analysis may be used to compare the expected number of crashes by type among various scenarios and can be used in an economic evaluation (e.g., benefit-cost analysis). The models should be calibrated to local conditions when possible (see Appendix C for a discus- sion of model calibration). Note: Apply Analysis Level 2 in Step 4. Step 4: Select Applicable Model(s) and Perform Analysis The final step is to select and apply the applicable model(s). Use Tables 69 through 71, which present models by respective land use, to determine which model is applicable. The models are presented in one of two forms. In most cases, the model form is represented by the equation shown in Figure 85. In these cases, the result is expressed as crashes per mile per year. In other cases, the traffic volume variable is not statistically significant, indicating a linear relationship between traffic volume and crashes. In these limited cases, the model form is reduced to the equation shown in Figure 86, and the result is expressed as crashes per million vehicle miles traveled (MVMT). To express the result as crashes per mile per year, multiply the result from the equation in Figure 86 by MVMT. Crash Type Variables Available for Specified Land Use Applicable Model (Table No.) Variables Available Through Extrapolation Applicable Model for Extrapolation of Variables (Table No.) Applicable Base Model for Extrapolation and EB Method (Table No.) Total ACCDENS 1 (Table E-1) — — 2 (Table E-2) Total PROPLANE1 2 (Table E-2) — — 2 (Table E-2) Total PROPNODEV 3 (Table E-3) — — 2 (Table E-2) Total SIGDENS 2 (Table E-2) — — 2 (Table E-2) Total UNSIGDENS 2 (Table E-2) — — 2 (Table E-2) Total — — PROPFULLDEV Res1 (Table E-26) 2 (Table E-2) Injury PROPLANE1 2 (Table E-5) — — 2 (Table E-5) Injury PROPNODEV 2 (Table E-5) — — 2 (Table E-5) Injury SIGDENS 1 (Table E-4) — — 2 (Table E-5) Injury — — ACCDENS Com1 (Table E-16) 2 (Table E-5) Injury — — PROPVC Com3 (Table E-18) 2 (Table E-5) Injury — — PROPFULLDEV Res2 (Table E-31) 2 (Table E-5) Turning ACCDENS 1 (Table E-6) — — 2 (Table E-7) Turning PROPNODEV 3 (Table E-8) — — 2 (Table E-7) Turning SIGDENS 1 (Table E-6) — — 2 (Table E-7) Turning UNSIGDENS 2 (Table E-7) — — 2 (Table E-7) Turning — — PROPLANE1 Com2 (Table E-21) 2 (Table E-7) Rear-end PROPLANE1 2 (Table E-10) — — 2 (Table E-10) Rear-end SIGDENS 2 (Table E-10) — — 2 (Table E-10) Rear-end — — PROPTWLTL Res2 (Table E-37) 2 (Table E-10) Right-angle ACCDENS 1 (Table E-11) — — 1 (Table E-11) Right-angle MEDOPDENS 2 (Table E-12) — — 1 (Table E-11) Right-angle PROPDIV 2 (Table E-12) — — 1 (Table E-11) Right-angle PROPFULLDEV 3 (Table E-13) — — 1 (Table E-11) Right-angle SIGDENS 1 (Table E-11) — — 1 (Table E-11) Right-angle — — PROPLANE1 Res2 (Table E-40) 1 (Table E-11) — Not applicable. Table 69. Relevant models by crash type of interest—mixed land use.

— Not applicable. Crash Type Variables Available for Specified Land Use Applicable Model (Table No.) Variables Available Through Extrapolation Applicable Model for Extrapolation of Variables (Table No.) Applicable Base Model for Extrapolation and EB Method (Table No.) PROPLANE1 1 (Table E-26) — — 1 (Table E-26) SIGDENS 1 (Table E-26) — — 1 (Table E-26) PROPFULLDEV 1 (Table E-26) — — 1 (Table E-26) ACCDENS 3 (Table E-28) — — 1 (Table E-26) Total Total Total Total Total PROPNODEV 4 (Table E-29) — — 1 (Table E-26) PROPLANE1 2 (Table E-31) — — 1 (Table E-30) SIGDENS 1 (Table E-30) — — 1 (Table E-30) PROPFULLDEV 2 (Table E-31) — — 1 (Table E-30) — — ACCDENS Com1 (Table E-16) 1 (Table E-30) — — PROPNODEV Mix2 (Table E-5) 1 (Table E-30) Injury Injury Injury Injury Injury Injury — — PROPVC Com3 (Table E-18) 1 (Table E-30) UNSIGDENS 2 (Table E-33) — — 2 (Table E-33) SIGDENS 3 (Table E-34) — — 2 (Table E-33) ACCDENS 3 (Table E-34) — — 2 (Table E-33) PROPNODEV 4 (Table E-35) — — 2 (Table E-33) Turning Turning Turning Turning Turning — — PROPLANE1 Com2 (Table E-21) 2 (Table E-33) SIGDENS 1 (Table E-36) — — 2 (Table E-37) PROPLANE1 2 (Table E-37) — — 2 (Table E-37) Rear-end Rear-end Rear-end PROPTWLTL 2 (Table E-37) — — 2 (Table E-37) Right-angle SIGDENS 2 (Table E-40) — — 2 (Table E-40) Right-angle PROPLANE1 2 (Table E-40) — — 2 (Table E-40) Right-angle PROPFULLDEV 2 (Table E-40) — — 2 (Table E-40) Right-angle ACCDENS 3 (Table E-41) — — 2 (Table E-40) Table 71. Relevant models by crash type of interest—residential land use. — Not applicable. Crash Type Variables Available for Specified Land Use Applicable Model (Table No.) Variables Available Through Extrapolation Applicable Model for Extrapolation of Variables (Table No.) Applicable Base Model for Extrapolation and EB Method (Table No.) Total ACCDENS 1 (Table E-14) — — 1 (Table E-14) Total SIGDENS 1 (Table E-14) — — 1 (Table E-14) Total PROPNODEV 2 (Table E-15) — — 1 (Table E-14) Total — — UNSIGDENS Mix2 (Table E-2) 1 (Table E-14) Total — — PROPLANE1 Mix1 (Table E-1) 1 (Table E-14) Total — — PROPFULLDEV Res1 (Table E-26) 1 (Table E-14) Injury ACCDENS 1 (Table E-16) — — 4 (Table E-19) Injury SIGDENS 4 (Table E-14) — — 4 (Table E-19) Injury PROPNODEV 2 (Table E-17) — — 4 (Table E-19) Injury PROPLANE1 4 (Table E-19) — — 4 (Table E-19) Injury PROPVC 3 (Table E-18) — — 4 (Table E-19) Injury — — PROPFULLDEV Res2 (Table E-31) 4 (Table E-19) Turning ACCDENS 1 (Table E-20) — — 1 (Table E-20) Turning SIGDENS 1 (Table E-20) — — 1 (Table E-20) Turning PROPNODEV 2 (Table E-21) — — 1 (Table E-20) Turning PROPLANE1 2 (Table E-21) — — 1 (Table E-20) Turning — — UNSIGDENS Mix2 (Table E-7) 1 (Table E-20) Rear-end SIGDENS 2 (Table E-23) — — 2 (Table E-23) Rear-end PROPLANE1 2 (Table E-23) — — 2 (Table E-23) Rear-end — — PROPTWLTL Res2 (Table E-37) 2 (Table E-23) Right-angle ACCDENS 1 (Table E-24) — — 1 (Table E-24) Right-angle SIGDENS 1 (Table E-24) — — 1 (Table E-24) Right-angle PROPFULLDEV 2 (Table E-25) — — 1 (Table E-24) Right-angle — — MEDOPDENS Mix2 (Table E-12) 1 (Table E-24) Right-angle — — PROPDIV Mix2 (Table E-12) 1 (Table E-24) Right-angle — — PROPLANE1 Res2 (Table E-40) 1 (Table E-24) Table 70. Relevant models by crash type of interest—commercial land use.

Predictive Method for Corridor-Level Analysis 83   Variables for the equations shown in Figures 85 and 86 are defined as follows: • intercept = coefficient estimated for the model to account for unobserved variables. • Region = coefficient estimated for the model when the applicable region is North Carolina or Minnesota; a value of 0 is used if the applicable region is Northern California or Southern California. • AADT = annual average daily two-way traffic for the corridor. • b = coefficient estimated for the AADT term in the model. • ci = a vector of coefficients estimated for the other independent variables included in the model. • xi = a vector of other independent variables included in the model (i.e., the specific roadway attributes such as access density). The regional indicator variable accounts for differences between regions such as those related to crash reporting practices, driver demographics, weather, and other non-access-related factors affecting reported crashes. The regional indicators for Northern and Southern California were sufficiently close to be considered as one region. Similarly, the regional indicators for Minnesota and North Carolina were sufficiently close to be considered as one region. As previously stated, when applying the models, select an applicable region based on a comparison between the corridor of interest and the summary statistics in Appendix D, not on geographic proximity. The final models are presented in Appendix E, organized by land use (mixed-use, commer- cial, and residential) and crash type (total, injury, turning, rear-end, and right-angle). Tables 69 through 71 provide an overview of the structure of Appendix E, including a summary of the models and explanatory variables for each land use and crash type combination. The following specific notes should be considered when applying the models: • Specific crash types cannot be summed to calculate total crashes because models were not developed for all possible crash types. • North Carolina crashes coded as rear-end turn crashes are included in both rear-end and turning crashes. The specific crash types cannot be summed to calculate total crashes, so double-counting should not pose a problem for the crash type models. • Models are not provided for PDO crashes because of the inconsistent reporting of these crashes. The national focus is on fatal and injury crashes, and models are provided to assess the impacts on these severe crashes. • A single model could not accommodate all explanatory variables; hence, there are alternate model forms with various combinations of variables: – In some cases, it is necessary to select from multiple available models because one or more models were successfully developed for each land use/crash type combination. The following factors are considered in selecting the preferred model when more than one option is available for the land use and crash type of interest: (1) the statistical signifi- cance of the coefficients for the variables of interest as indicated by the size of the p-value (a lower p-value indicates a higher level of significance) and (2) model fit (a smaller value of k indicates a better-fitting model). Figure 85. Crash prediction model with regional calibration. Figure 86. Normalized crash prediction model with regional calibration.

84 Application of Crash Modification Factors for Access Management – In some cases, explanatory variables are included for a specific crash type but not for the land use of interest. Further consideration of these variables in this section follows. – In some cases, explanatory variables could not be included in any models due to a lack of statistical significance or an illogical direction of effect. Further consideration of these variables in this section follows and is also provided in Appendix F. Continue to Analysis Level 1 or Analysis Level 2 based on the selection in Step 3 and the appli- cable models identified in Tables 69 through 71. The following guiding principles are common to all scenarios: • If necessary, models may be extrapolated with caution across land use types for a given crash type; however, models for one crash type may not be extrapolated to another crash type. • In some situations, it may not be possible to estimate the impacts of a strategy for all or some crash types. • If several crash types are selected, the sum of differences between two alternatives for specific crash types cannot be greater than the number of all crash types combined. If this occurs, the estimate for all crash types combined should be equal to the sum of the specific crash types. Similarly, the estimate for injury crashes cannot be greater than total crashes. • The analyst should review the minimum and maximum values of each variable of interest for the given land use and region (see Appendix D). If an entered value is outside the range of data on which the model is based, the analyst should note that the model may not provide a reliable estimate of the effect of that variable. Step 4—Analysis Level 1: Relative Comparison of Safety Performance Analysis Level 1 is applicable when comparing the relative safety impact of two alternatives, Alternative A and Alternative B, one of which can be a do-nothing alternative. Step 4.1.1: Data for Conditions of Interest Identify the values for Alternative A and Alternative B, including corridor length, AADT, and all variables of interest for all models to be used in the analysis. A value must be provided for corridor length and AADT. For all other variables, a default value may be used if a value cannot be entered (default values are given in Appendix D). The default value is the mean value for the variable of interest and is determined by the land use and region selected. Step 4.1.2: Calculations for Non-Extrapolated Variables Using the model(s) listed in the “Applicable Model” column in Tables 69 through 71, com- pute the predicted crashes for existing conditions based on the values identified for Alterna- tive A. The next calculation only changes the variable(s) of interest, and the following two cases may be distinguished: • Case 1. All variables of interest appear in one model for the crash type of interest. In this case, compute the predicted crashes for proposed conditions based on the values identified for Alternative B. • Case 2. One or more variables of interest exist in multiple models for the crash type of interest. In this case, it is necessary to avoid double-counting the effect of variables. From a computa- tional perspective, it is important to focus on one variable at a time. For each variable of interest, separately compute the predicted crashes for proposed conditions using the applicable model and the value identified for Alternative B. The predicted crashes for each proposed condi- tion are subtracted from the predicted crashes for the existing conditions (Alternative A) to estimate the impact of each individual variable of interest. The impacts of the individual vari- ables are then summed to estimate the aggregate impact of Alternative B. Similarly, if either

Predictive Method for Corridor-Level Analysis 85   corridor length or AADT changes in Alternative B, these changes are considered in isolation. The appropriate model for considering corridor length or AADT changes is identified in the “Applicable Base Model for Extrapolation and EB Method” column of Tables 69 through 71. In this case, all variables, with the exception of corridor length and AADT, are kept constant, and the predicted crashes are computed for Alternative B. Step 4.1.3: Calculations for Extrapolated Variables Variables available through extrapolation of another land use model are identified in the “Variables Available Through Extrapolation” column of Tables 69 through 71. The extrapola- tion method first requires the use of a base model from the land use and crash type of interest to predict crashes for existing conditions. Then, a model is selected from another land use to estimate the impacts of the variables of interest. For each variable to be considered through extrapolation, take the following steps. Step 4.1.3a: Baseline Predicted Crashes for Existing Condition. Use the applicable base model from Tables 69 through 71 with the values from the existing condition (Alternative A) to estimate the baseline predicted crashes for the existing condition. Step 4.1.3b: Estimate the Impacts of the Variables of Interest for Existing Conditions. The effects of the variables of interest for the existing conditions are estimated using the equation shown in Figure 87. In the equation shown in Figure 87, the coefficient is obtained for the variable of interest from the extrapolation model identified in the “Applicable Model for Extrapolation of Variables” column of Tables 69 through 71. The Variable Actual Value is obtained from the existing condition (Alternative A). The Variable Default Value is the mean value of the variable of interest for the region and land use type from which that model was developed. Default values can be found in Appendix D. Figure 87. Equation to estimate effects of variables of interest for existing conditions. Step 4.1.3c: Adjusted Predicted Crashes for Existing Condition. The estimate from Step 4.1.3b is then multiplied by the estimate from Step 4.1.3a to compute the adjusted predicted crashes for existing conditions. Step 4.1.3d: Baseline Predicted Crashes for Proposed Condition. Use the applicable base model from Tables 69 through 71 with the values from the proposed condition (Alternative B) to estimate the baseline predicted crashes for the proposed condition. Step 4.1.3e: Estimate the Impacts of the Variables of Interest for Proposed Conditions. The effects of the variables of interest for the proposed conditions are estimated using the equa- tion shown in Figure 88. In the equation shown in Figure 88, the coefficient is obtained for the variable of interest from the extrapolation model identified in the “Applicable Model for Extra p- olation of Variables” column of Tables 69 through 71. The Variable Proposed Value is obtained from the proposed condition (Alternative B). The Variable Default Value is the mean value of the variable of interest for the region and land use type from which that model was developed. Default values can be found in Appendix D. Figure 88. Equation to estimate effects of variables of interest for proposed conditions.

86 Application of Crash Modification Factors for Access Management Step 4.1.4: Estimated Safety Impacts The results of Steps 4.1.2 and 4.1.3 can be used to compare the predicted crashes per year for Alternative A and Alternative B. The results may be presented as the difference or the percent change in predicted crashes per year. Step 4—Analysis Level 2: Absolute Comparison of Safety Performance Analysis Level 2 is applicable when comparing expected crashes for existing and proposed conditions. Recall that one of the conditions is the existing condition because a crash history is required to apply Analysis Level 2. In this context, Alternative A is the existing condition, and Alternative B is the proposed condition. Step 4.2.1: Data for Conditions of Interest Identify values for Alternative A and Alternative B, including corridor length, AADT, and all variables of interest for all models to be used in the analysis. A value must be provided for corridor length and AADT. For all other variables, a default value may be used if a value cannot be entered (default values are given in Appendix D). The default value is the mean value for the variable of interest and is determined by the land use and region selected. The observed crash history for the existing condition is also identified, including the number of years of crash data and crash totals for each crash type selected. Finally, the user must identify a calibration factor for all crash types selected. The default value is 1.0, but a user may compute a local calibration factor based on the procedure described in Appendix C. Step 4.2.2: Prediction for Existing Condition Steps 4.2.2a through 4.2.2d are completed for each crash type selected. The baseline predicted crashes for the existing condition are modified using the EB method, which uses the crash history of the corridor. The EB method is used to compute the expected crashes (Hauer 1997). Step 4.2.2a: Baseline Predicted Crashes for Existing Conditions. Use the applicable base model from the column titled “Applicable Base Model for Extrapolation and EB Method” column of Tables 69 through 71 with the values from Alternative A to estimate the baseline predicted crashes for the existing condition. Step 4.2.2b: Estimated EB Weight. The EB weight (w) is estimated using the equation shown in Figure 89. Note that k is given for each specific model in Appendix E. Step 4.2.2c: Expected Crashes for Existing Conditions. The annual expected crash fre- quency (EB estimate) for existing conditions is calculated using the equation shown in Figure 90. Figure 90. Equation to estimate the annual expected crash frequency (EB estimate). Figure 89. Equation to estimate EB weight (w).

Predictive Method for Corridor-Level Analysis 87   Step 4.2.2d: Estimated EB Correction Factor. The EB correction factor is calculated as the expected crashes for existing conditions (Step 4.2.2c) divided by the baseline predicted crashes for existing conditions (Step 4.2.2a). Step 4.2.3: Prediction for Proposed Condition Step 4.2.3a: Difference in Predicted Crashes for Existing and Proposed Conditions. Apply Steps 4.1.2 through 4.1.4 from Analysis Level 1 using the existing and proposed conditions as inputs. The result is an estimate of the difference in predicted crash frequency for the existing and proposed conditions. Step 4.2.3b: Adjusted Predicted Crashes for the Existing Condition. Add the difference in predicted crashes from Step 4.2.3a to the baseline predicted crashes for existing conditions from Step 4.2.2a. Step 4.2.3c: Expected Crashes for Proposed Condition. Multiply the adjusted predicted crashes for the existing condition from Step 4.2.3b by the EB correction factor from Step 4.2.2d. Step 4.2.4: Estimated Safety Impacts The results from Analysis Level 2 can be used to compare the expected crashes per year for Alternative A and Alternative B. The expected crashes for the existing condition are esti- mated from Step 4.2.2c. The expected crashes for the proposed condition are estimated from Step 4.2.3c. The results may be presented as the difference or the percent change in expected crashes per year. Sample Problems to Illustrate Corridor-Level Prediction Models Seven sample problems are presented in this section to illustrate the use of the corridor-level prediction models. The seven sample problems apply to the following scenarios and apply the four-step process previously presented: • Sample Problem 4. All variables of interest are available in one (and only one) model for the land use and crash type of interest. Analysis Level 1 is selected to estimate the safety perfor- mance for existing conditions. • Sample Problem 5. All variables of interest are available in one (and only one) model for the land use and crash type of interest. Analysis Level 1 is selected to estimate the relative safety impacts of alternatives. • Sample Problem 6. Variables of interest appear in different models for the same land use and crash type of interest (i.e., using a combination of models to assess the impacts of multiple variables because some variables of interest are in one model, while other variables of interest are in another model). Analysis Level 1 is selected to estimate the relative safety impacts of alternatives. • Sample Problem 7. Variables of interest appear in models for different crash types (i.e., assessing the impacts of a variable over different crash types). Analysis Level 1 is selected to estimate the relative safety impacts of alternatives. • Sample Problem 8. All variables of interest are available in one or more models for the land use and crash type of interest and an applicable crash history is available. Analysis Level 2 is selected to estimate the expected crashes for the given alternatives. • Sample Problem 9. Variables of interest are available for a given crash type but not for the land use type of interest (i.e., extrapolating the impacts of a variable on a given crash type

88 Application of Crash Modification Factors for Access Management from models related to a different land use). Analysis Level 1 is selected to estimate the relative safety impacts of alternatives. • Sample Problem 10. Variables of interest do not appear in any models for any crash type or land use. Analysis Level 1 and Analysis Level 2 are not applicable. Instead, there is an oppor- tunity to draw inferences from the correlation matrix presented in Appendix F. Sample Problem 4 Estimate the safety performance of a corridor based on predicted crashes when all variables of interest are in the same model. Problem Definition This sample problem is based on Sample Problem 3 from Chapter 4 of this guide. In Chapter 4, Predictive Method Option 1 (i.e., combine segment- and intersection-level results) was used to estimate the predicted crashes for the segment and intersections separately, and the results were combined to estimate the predicted crashes for the corridor. In this sample problem (Sample Problem 4), Predictive Method Option 2 (i.e., apply corridor-level prediction models) is used with the corridor-level models to estimate the predicted crashes for the corridor. As shown in Figure 91, the corridor of interest is 1.5 miles of an urban two-lane arterial with a TWLTL, 10 unsignalized intersections, and a mix of 30 commercial, industrial, and residential driveways. A prediction of the number of total crashes for the existing conditions is needed. The predicted number of crashes could be used as a basis to estimate the relative impacts of proposed changes. Step 1: Select Land Use and Region This is a mixed-use corridor (i.e., mix of 30 commercial, industrial, and residential drive- ways). After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them to the local data, it is determined that the corridor is most comparable to the data from North Carolina. Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, total crashes are of interest. In this case, the variables of interest are driveway density, unsignalized intersection density, number of lanes, and the pres- ence of a TWLTL. Step 3: Select Analysis Level of Interest It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, Analysis Level 1 is applicable because the objective is to compare the relative safety impacts. Figure 91. Illustration of Sample Problem 4.

Predictive Method for Corridor-Level Analysis 89   Step 4: Select Applicable Model(s) and Perform Analysis Table 69 presents the applicable models for mixed land use. The applicable models for total crashes are Mixed-Use Total Model 1 (Table E-1), Mixed-Use Total Model 2 (Table E-2), and Mixed-Use Total Model 3 (Table E-3). The objective is to predict the total crashes for the cor- ridor, as opposed to predicting or comparing the relative safety performance of different alter- natives (i.e., changes in specific variables). As such, the most appropriate model is the one that includes the most variables relevant to the corridor of interest. From Table E-1 through Table E-3, Model 1 includes ACCDENS, SIGDENS, and PROPLANE1, Model 2 includes UNSIGDENS, SIGDENS, and PROPLANE1, and Model 3 includes PROPNODEV. In this case, Model 1 and Model 2 include the same number of variables, but Model 1 is slightly more appropriate because it allows for the consideration of ACCDENS, which includes both driveways and unsignalized intersections. Note that all variables are available to apply this model, so no default values are required. The model coefficients from Table E-1 are as follows: intercept (–3.1845); region (1.1410 if North Carolina or Minnesota, zero otherwise); AADT (0.5187); ACCDENS (0.0053); SIGDENS (0.1095); and PROPLANE1 (–0.5185). The equation in Figure 85 is applicable to this model and shown again here for ease of reference: ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn Step 4.1.1: Data for Conditions of Interest. The following are the data for the existing corridor: • Corridor length = 1.5 miles. • AADT = 11,000 vehicles per day. • 30 mixed-use driveways. • 10 unsignalized intersections. • Total access density: ACCDENS = (30+10)/1.5 = 26.67 unsignalized access points per mile. • No signalized intersections: SIGDENS = 0 signals per mile. • Entire length of corridor is three lanes (two through lanes with TWLTL): PROPLANE1 = 0. Step 4.1.2: Calculations for Non-Extrapolated Variables. Case 1 applies when all variables of interest appear in only one model. Figure 92 shows the calculation of predicted total crashes per year for existing conditions. Predicted Total Crashes/Year = (length)exp(Intercept+Region)(AADT)0.5187exp(0.0053*ACCDENS+0.1095*SIGDENS-0.5185*PROPLANE1) = (1.5)exp(-3.1845+1.1410)(11,000)0.5187exp(0.0053*26.67+0.1095*0-0.5185*0) = 27.94 total crashes/year Figure 92. Calculation of predicted total crashes/year. Step 4.1.3: Calculations for Extrapolated Variables. There are no extrapolated variables, so this step is not applicable. Step 4.1.4: Estimated Safety Impacts. Because this is Case 1 in Step 4.1.2, the number of predicted crashes per year is obtained directly from the model predictions obtained in Step 4.1.2. The results could be used as a basis for comparing the safety performance of proposed alterna- tives. For illustrative purposes, the results are also compared to the results from Sample Problem 3

90 Application of Crash Modification Factors for Access Management in Chapter 4. Recall from Chapter 4, using Predictive Method Option 1 (i.e., combine segment- and intersection-level results), the predicted crash frequency for the same corridor was 19.4 crashes per year. In this chapter (Chapter 5), using Predictive Method Option 2 (i.e., apply corridor-level prediction models), the predicted crash frequency was 27.9 crashes per year. The two methods do not produce the same results. Predictive Method Option 1 does not consider the poten- tial interactions among adjacent or nearby sites (e.g., access spacing and density). As such, the corridor-level predictive method is more appropriate for considering interactions among access management features and estimating the safety effect of variables related to access spacing and density. Either method (Predictive Method Option 1 or Predictive Method Option 2) should be calibrated to reflect current local conditions. Refer to Appendix B: Overview of Quantitative Safety Analysis for more background on calibration and refer to Appendix C: Calibration for details on how to calibrate predictive methods. Sample Problem 5 Estimate the effect of multiple variables that are all in the same model. Problem Definition A planned development is expected to increase existing traffic volumes by 50 percent and change the general characteristics of a residential corridor in an urbanizing area. The new development will increase the frontage from 30 to 100 percent. A new signalized intersection is proposed in the middle of the corridor to help accommodate the expected growth. Figure 93 shows the existing conditions (A) and proposed conditions (B). A concern has been raised regarding the potential increase in right-angle crashes because these tend to be severe. It is desired to predict the number of right-angle crashes for both the existing and proposed condi- tions. The predicted crashes will be compared to estimate the relative impacts of the proposed changes. Step 1: Select Land Use and Region This is a residential corridor. After reviewing the summary statistics for residential land use in each of the four regions from which the models were developed and comparing them to the local data, it is determined that the corridor is most comparable to the data from North Carolina. Figure 93. Illustration of Sample Problem 5.

Predictive Method for Corridor-Level Analysis 91   Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, right-angle crashes are of interest. In this case, the variables of interest are proportion of full development (PROPFULLDEV) and signal density (SIGDENS). Step 3: Select Analysis Level of Interest It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, Analysis Level 1 is applicable because the objective is to compare the relative safety impacts. Step 4: Select Applicable Model(s) and Perform Analysis Table 71 presents the applicable models for residential land use. The applicable model for right-angle crashes and PROPFULLDEV is Residential Right-Angle Model 2 (Table E-40). The applicable model for right-angle crashes and SIGDENS is Residential Right-Angle Model 2 (Table E-40). The applicable model is the same for the variables of interest, so multiple models and extrapolated variables are not required. Note that all variables are available to apply this model, so no default values are required. The model coefficients from Table E-40 are as follows: intercept (–1.4079), region (0.8858 if North Carolina or Minnesota, zero otherwise), AADT (0.1332), SIGDENS (0.2267), PROPLANE1 (–0.3633), and PROPFULLDEV (0.4295). The equation in Figure 85 is applicable to this model and shown again here for ease of reference: ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn Step 4.1.1: Data for Conditions of Interest. The following are the data for the existing condition (Do-Nothing Alternative A): • Corridor length = 1.25 miles. • AADT = 15,000 vehicles per day. • No signalized intersections: SIGDENS = 0 signals/mile. • Entire length of corridor is two lanes: PROPLANE1 = 1.0. • Current frontage development is 30 percent: PROPFULLDEV = 0.30. The following are the data for the proposed condition (Alternative B): • Corridor length = 1.25 miles. • AADT = 22,500 vehicles per day (50-percent increase). • 1 new signal: SIGDENS = 1 signal/1.25 miles = 0.8 signals/mile. • Entire length of corridor is two lanes: PROPLANE1 = 1.0 (unchanged). • Frontage development increased from 30 to 100 percent: PROPFULLDEV = 1.0. Step 4.1.2: Calculations for Non-Extrapolated Variables. Case 1 applies when all variables of interest appear in only one model. Figure 94 shows the calculation of predicted right-angle crashes per year for existing conditions and Figure 95 shows the calculation of predicted right- angle crashes per year for proposed conditions. Predicted Right-Angle Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.1332exp(0.2267*SIGDENS-0.3633*PROPLANE1+0.4295*PROPFULLDEV) = (1.25)exp(-1.4079+0.8858)(15,000)0.1332exp(0.2267*0-0.3633*1.0+0.4295*0.3) = 2.11 right-angle crashes/year Figure 94. Calculation of predicted right-angle crashes/year (existing).

92 Application of Crash Modification Factors for Access Management Step 4.1.3: Calculations for Extrapolated Variables. There are no extrapolated variables, so this step is not applicable. Step 4.1.4: Estimated Safety Impacts. Because this is Case 1 in Step 4.1.2, the difference in predicted crashes per year between the two alternatives is obtained directly from the model predictions obtained in Step 4.1.2. The estimated effect of increasing development over the entire corridor, adding the signalized intersection, and the associated growth in mainline AADT is an increase of 1.50 right-angle crashes/year (3.61 crashes/year – 2.11 crashes/year). The proposed alternative is predicted to increase right-angle crashes by 71 percent (i.e., 3.61/2.11). In this sample problem, the aim was to compare the predicted right-angle crashes for existing and proposed conditions. The following computations are provided to illustrate the process for comparing the percent change in crashes related to the change in each individual variable: • The relative effect of increasing the signal density is exp(0.2267) = 1.25 (i.e., a 25-percent increase in right-angle crashes for each additional signal per mile). In this case, the signal density was increased from 0.0 to 0.8 signals/mile, so the relative impact for this corridor is exp(0.2267 ∗ (0.8 – 0.0)) = 1.20 (i.e., a 20-percent increase in right-angle crashes). • The relative effect of increasing the proportion of frontage development from 30 to 100 per- cent is exp(0.4295 ∗ (1.0 – 0.3)) = 1.35 (i.e., a 35-percent increase in right-angle crashes for a 70-percent increase in frontage development). Sample Problem 6 Estimate the effect of changes in two or more variables that are not all accommodated in the same model. Problem Definition On a mixed-use corridor, changes are being proposed that would eliminate existing roadside development while reducing the overall access density. This would involve the removal of several access points in parts of the corridor, which would reduce the corridor totals by five driveways and two unsignalized intersections. The proportion of the corridor with no development will increase from 0 to 15 percent. Figure 96 shows the existing conditions (A) and proposed con- ditions (B). It is desired to estimate the relative effect of the proposed changes on total crashes. It is assumed that all other variables, including AADT on the mainline, would not change. Step 1: Select Land Use and Region This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to the data from Northern California. Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, total crashes are of interest. In this case, the variables of interest are access density (ACCDENS) (i.e., density of driveways plus unsignalized inter- sections) and proportion of no development (PROPNODEV). Predicted Right-Angle Crashes/Year (Proposed) = (length)exp(Intercept+Region)(AADT)0.1332exp(0.2267*SIGDENS-0.3633*PROPLANE1+0.4295*PROPFULLDEV) = (1.25)exp(-1.4079+0.8858)(22,500)0.1332exp(0.2267*0.8-0.3633*1.0+0.4295*1.0) = 3.61 right-angle crashes/year Figure 95. Calculation of predicted right-angle crashes/year (proposed).

Predictive Method for Corridor-Level Analysis 93   Step 3: Select Analysis Level of Interest It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, Analysis Level 1 is applicable because the objective is to compare the relative safety impacts. Step 4: Select Applicable Model(s) and Perform Analysis Table 69 presents the applicable models for mixed land use. The applicable model for total crashes and ACCDENS is Mixed/Total Model 1 (Table E-1). The applicable model for total crashes and PROPNODEV is Mixed/Total Model 3 (Table E-3). The applicable model is different for the variables of interest, so it is necessary to apply multiple models to estimate the effects. In this case, extrapolated variables are not required. Note that all variables are available to apply the models, so no default values are required. The model coefficients for total crashes from Table E-1 are intercept (–3.1845), region (1.1410 if North Carolina or Minnesota, 0 otherwise), AADT (0.5187), ACCDENS (0.0053), SIGDENS (0.1095), and PROPLANE1 (–0.5185). The equation in Figure 85 is applicable to this model and shown again here for ease of reference: ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn The model coefficients for total crashes from Table E-3 are intercept (–0.8926), region (0.6166 if North Carolina or Minnesota, 0 otherwise), AADT (0.3766), and PROPNODEV (–0.4252). Again, the equation in Figure 85 is applicable to this model. Step 4.1.1: Data for Conditions of Interest. The following are the data for the existing condition (Do-Nothing Alternative A): • Corridor length = 4 miles. • AADT = 30,000 vehicles per day. • 5 signalized intersections: SIGDENS = 5 signals/4 miles = 1.25 signals/mile. • 16 unsignalized intersections and 20 driveways: ACCDENS = 36 access points/4 miles = 9.0 access points/mile. • Length of roadway with two lanes is 3 miles: PROPLANE1 = 3/4 = 0.75. • Length of roadway with no roadside development is 0 miles: PROPNODEV = 0. Figure 96. Illustration of Sample Problem 6.

94 Application of Crash Modification Factors for Access Management The following are the data for the proposed condition (Alternative B): • Corridor length = 4 miles (unchanged). • AADT = 30,000 vehicles per day (unchanged). • 5 signalized intersections: SIGDENS = 5 signals/4 miles = 1.25 signals/mile (unchanged). • 14 unsignalized intersections and 15 driveways: ACCDENS = 29 access points/4 miles = 7.25 access points/mile. • Length of roadway with two lanes is 3 miles: PROPLANE1 = 3/4 = 0.75 (unchanged). • Length of roadway with no roadside development: PROPNODEV = 0.15. Step 4.1.2: Calculations for Non-Extrapolated Variables. Case 2 applies when the two variables of interest (ACCDENS and PROPNODEV) appear in separate models. Therefore, it is necessary to consider the effects of each variable separately and then combine the effects to estimate the total impact of Alternative B. For the effect of access density, Figures 97 and 98 show the calculations of predicted total crashes per year for existing and proposed conditions, respectively, based on the coefficients in Table E-1. For the effect of the proportion of develop- ment, Figures 99 and 100 show the calculations of predicted total crashes per year for existing and proposed conditions, respectively, based on the coefficients in Table E-3. Effect of PROPNODEV: Predicted Total Crashes/Year (Proposed) = (length)exp(Intercept+Region)(AADT)0.3766exp(-0.4252*PROPNODEV) = (4.0)exp(-0.8926+0)(30,000)0.3766exp(-0.4252*0.15) = 74.61 total crashes/year Figure 100. Effect of PROPNODEV: predicted total crashes/year (proposed). Effect of ACCDENS: Predicted Total Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.5187exp(0.0053*ACCDENS+0.1095*SIGDENS-0.5185*PROPLANE1) = (4.0)exp(-3.1845+0)(30,000)0.5187exp(0.0053*9+0.1095*1.25-0.5185*0.75) = 28.35 total crashes/year Figure 97. Effect of ACCDENS: predicted total crashes/year (existing). Effect of ACCDENS: Predicted Total Crashes/Year (Proposed) = (length)exp(Intercept+Region)(AADT)0.5187exp(0.0053*ACCDENS+0.1095*SIGDENS-0.5185*PROPLANE1) = (4.0)exp(-3.1845+0)(30,000)0.5187exp(0.0053*7.25+0.1095*1.25-0.5185*0.75) = 28.09 total crashes/year Figure 98. Effect of ACCDENS: predicted total crashes/year (proposed). Effect of PROPNODEV: Predicted Total Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.3766exp(-0.4252*PROPNODEV) = (4.0)exp(-0.8926+0)(30,000)0.3766exp(-0.4252*0) = 79.52 total crashes/year Figure 99. Effect of PROPNODEV: predicted total crashes/year (existing). Step 4.1.3: Calculations for Extrapolated Variables. There are no extrapolated variables, so this step is not applicable. Step 4.1.4: Estimated Safety Impacts. The change in total crashes is estimated as the sum of changes from the individual models. The change in total predicted crashes related to the

Predictive Method for Corridor-Level Analysis 95   change in ACCDENS is 0.26 crashes/year (28.35 crashes/year – 28.09 crashes/year), and the change in total predicted crashes related to the change in PROPNODEV is 4.91 crashes/year (79.52 crashes/year – 74.61 crashes/year). The change in total predicted crashes from all modi- fications (Alternative B as a whole) is a reduction of 5.18 total crashes/year (0.26 crashes/year + 4.91 crashes/year). The proposed alternative is predicted to reduce total crashes by 5 percent: (28.09 + 74.61)/(28.35 + 79.52). Sample Problem 7 Estimate the effect of a change in a single variable that is accommodated in models for dif- ferent crash types. Problem Definition For a mixed-use corridor, a proposal has been made to increase the number of driveways by five and the number of unsignalized intersections by one. Figure 101 shows the existing condi- tions (A) and proposed conditions (B). It is desired to estimate the relative effect of the proposed changes on all available crash types. All other corridor characteristics, including the mainline AADT, are assumed to remain constant. Step 1: Select Land Use and Region This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to the data from Southern California. Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, it is desired to estimate the relative effect of the pro- posed changes on all available crash types. In this case, the variable of interest is access density (ACCDENS), which is the number of driveways plus unsignalized intersections per mile. Step 3: Select Analysis Level of Interest It is desired to estimate the relative safety between two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, Analysis Level 1 is applicable because the objective is to compare the relative safety impacts. Figure 101. Illustration of Sample Problem 7.

96 Application of Crash Modification Factors for Access Management Step 4: Select Applicable Model(s) and Perform Analysis Table 69 presents the applicable models for various crash types in mixed land use. For mixed land use, ACCDENS is directly available in models for total crashes, turning crashes, and right- angle crashes. ACCDENS is not included in any mixed land use models for injury or rear-end crashes without extrapolating from another land use type. Extrapolation is covered in Sample Problem 9. The applicable models for ACCDENS include Mixed/Total Model 1 (Table E-1), Mixed/Turning Model 1 (Table E-6), and Mixed/Right-Angle Model 1 (Table E-11). The appli- cable models are for different crash types, so it is necessary to apply the models separately to estimate the effects by crash type. In this case, extrapolated variables are not considered. All variables are available to apply the models, so no default values are required. The model coefficients for total crashes are given in Table E-1 as intercept (–3.1845), region (1.1410 if North Carolina or Minnesota, 0 otherwise), AADT (0.5187), ACCDENS (0.0053), SIGDENS (0.1095), and PROPLANE1 (–0.5185). The model coefficients for right-angle crashes are given in Table E-11 as intercept (–5.8048), region (1.8390 if North Carolina or Minnesota, 0 otherwise), AADT (0.4656), ACCDENS (0.0112), and SIGDENS (0.2284). The equation in Figure 85 is applicable to both of these models and shown again here for ease of reference: ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn The model coefficients for turning crashes are given in Table E-6 as intercept (–2.1083), region (0.9647 if North Carolina or Minnesota, 0 otherwise), SIGDENS (0.1865), and ACCDENS (0.0088). The equation in Figure 86 is applicable to this model and shown again here for ease of reference. The result is expressed as crashes per MVMT. Multiply the result by MVMT to express crashes per mile per year. = ∗ ( )( )+ ∗ + + ∗Crashes MVMT exp expintercept Region c1 X1 . . . cn Xn Step 4.1.1: Data for Conditions of Interest. The following are the data for the existing condition (Do-Nothing Alternative A): • Corridor length = 2.5 miles. • AADT = 25,000 vehicles per day. • 5 signalized intersections: SIGDENS = 5 signals/2.5 miles = 2.0 signals/mile. • 10 unsignalized intersections and 25 driveways: ACCDENS = (25 driveways + 10 unsignalized intersections)/2.5 miles = 14.0 access points/mile. • Length of roadway with two lanes is 0.625 miles: PROPLANE1 = 0.625/2.5 = 0.25. The following are the data for the proposed condition (Alternative B): • Corridor length = 2.5 miles. • AADT = 25,000 vehicles per day (unchanged). • 5 signalized intersections: SIGDENS = 2.0 signals/mile (unchanged). • 11 unsignalized intersections and 30 driveways: ACCDENS = (30 driveways + 11 unsignalized intersections)/2.5 miles = 16.4 access points/mile. • Length of roadway with two lanes is 0.625 miles: PROPLANE1 = 0.25 (unchanged). Step 4.1.2: Calculations for Non-Extrapolated Variables. Case 1 applies because there is only one variable of interest (ACCDENS). For the effect of access density on total crashes, Fig- ures 102 and 103 show the calculations of predicted total crashes per year for existing and pro- posed conditions, respectively, based on the coefficients in Table E-1. For the effect of the access density on turning crashes, Figures 104 and 105 show the calculations of predicted turning crashes per year for existing and proposed conditions, respectively, based on the coefficients in Table E-6. For the effect of access density on right-angle crashes, Figures 106 and 107 show

Predictive Method for Corridor-Level Analysis 97   the calculations of predicted right-angle crashes per year for existing and proposed conditions, respectively, based on the coefficients in Table E-11. Right-Angle Crashes: Predicted Right-Angle Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*14.0+0.2284*2.0) = 1.55 right-angle crashes/year Figure 106. Right-angle crashes: predicted right-angle crashes/year (existing). Total Crashes: Predicted Total Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.5187exp(0.0053*ACCDENS+0.1095*SIGDENS-0.5185*PROPLANE1) = (2.5)exp(-3.1845+0)(25,000)0.5187exp(0.0053*14.0+0.1095*2.0-0.5185*0.25) = 23.29 total crashes/year Figure 102. Total crashes: predicted total crashes/year (existing). Total Crashes: Predicted Total Crashes/Year (Proposed) = (length)exp(Intercept+Region)(AADT)0.5187exp(0.0053*ACCDENS+0.1095*SIGDENS-0.5185*PROPLANE1) = (2.5)exp(-3.1845+0)(25,000)0.5187exp(0.0053*16.4.0+0.1095*2.0-0.5185*0.25) = 23.59 total crashes/year Figure 103. Total crashes: predicted total crashes/year (proposed). Turning Crashes: Predicted Turning Crashes/Year (Existing) = (MVMT)exp(Intercept+Region)exp(0.0088*ACCDENS+0.1865*SIGDENS) = (2.5*25,000*365/1,000,000)exp(-2.1083+0)exp(0.0088*14.0+0.1865*2.0) = 4.55 turning crashes/year Figure 104. Turning crashes: predicted turning crashes/year (existing). Turning Crashes: Predicted Turning Crashes/Year (Proposed) = (MVMT)exp(Intercept+Region)exp(0.0088*ACCDENS+0.1865*SIGDENS) = (2.5*25,000*365/1,000,000)exp(-2.1083+0)exp(0.0088*16.4+0.1865*2.0) = 4.65 turning crashes/year Figure 105. Turning crashes: predicted turning crashes/year (proposed). Step 4.1.3: Calculations for Extrapolated Variables. There are no extrapolated variables, so this step is not applicable. Step 4.1.4: Estimated Safety Impacts. The estimated effect of increasing the number of drive- ways from 25 to 30 and the number of unsignalized intersections from 10 to 11 is as follows: • Total crashes: An increase of 0.30 total crashes/year (23.59 crashes/year – 23.29 crashes/year). • Turning crashes: An increase of 0.10 turning crashes/year (4.65 crashes/year – 4.55 crashes/year). • Right-angle crashes: An increase of 0.05 right-angle crashes/year (1.60 crashes/year – 1.55 crashes/ year). Right-Angle Crashes: Predicted Right-Angle Crashes/Year (Proposed) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*16.4+0.2284*2.0) = 1.60 right-angle crashes/year Figure 107. Right-angle crashes: predicted right-angle crashes/year (proposed).

98 Application of Crash Modification Factors for Access Management Sample Problem 8 Compare the expected crashes for two alternatives to select the most appropriate alternative. Problem Definition For a mixed-use corridor, a proposal has been made to increase the number of driveways by five and the number of unsignalized intersections by one. An alternate proposal will increase the number of driveways by three and the number of unsignalized intersections by one. Figure 108 shows the existing conditions (Do-Nothing Alternative A), Proposed Condition 1 (Alternative B), and Proposed Condition 2 (Alternative C). It is desired to estimate the impact of each proposed alternative in terms of the project cost and expected number of right-angle crashes per year. All other corridor characteristics, including the mainline AADT, are assumed to remain constant. This problem uses the same situation as Sample Problem 7 but incorporates the observed crash history. Step 1: Select Land Use and Region This is a mixed-use corridor. After reviewing the summary statistics for mixed land use in each of the four regions from which the models were developed and comparing them with the local data, it is determined that the corridor is most comparable to the data from Southern California. Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, it is desired to estimate the effect of the proposed changes on the expected number of right-angle crashes. In this case, the variable of interest is access density (ACCDENS), which is the number of driveways plus unsignalized intersections per mile. Step 3: Select Analysis Level of Interest It is desired to estimate the impact of each proposed alternative in terms of the project cost and expected number of right-angle crashes per year. A more precise estimate is required because Figure 108. Illustration of Sample Problem 8.

Predictive Method for Corridor-Level Analysis 99   the difference in expected crashes is to be compared with the difference in costs of the two alternatives. In this case, Analysis Level 2 is applicable because the objective is to estimate the expected crashes for the given alternatives. Step 4: Select Applicable Model(s) and Perform Analysis Table 69 presents the applicable models for mixed land use. The applicable model for right-angle crashes and ACCDENS is Mixed/Right-Angle Model 1 (Table E-11). Because the EB method is to be applied as part of Analysis Level 2, it is necessary to select a base model from the last column of Table 69. The applicable base model for applying the EB method is Mixed/Right- Angle Model 1 (Table E-11). In this case, the base model and the model for ACCDENS are the same. Note that extrapolated variables are not considered, and all variables are available to apply the models, so no default values are required. The model coefficients for right-angle crashes are given in Table E-11 as intercept (–5.8048), region (1.8390 if North Carolina or Minnesota, 0 otherwise), AADT (0.4656), ACCDENS (0.0112), and SIGDENS (0.2284). The equation in Figure 85 is applicable to this model and shown again here for ease of reference. ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn Step 4.2.1: Data for Conditions of Interest. The following are the data for the existing condition (Do-Nothing Alternative A): • Corridor length = 2.5 miles. • AADT = 25,000 vehicles per day. • 5 signalized intersections: SIGDENS = 5 signals/2.5 miles = 2.0 signals/mile. • 10 unsignalized intersections and 25 driveways: ACCDENS = (25 driveways + 10 unsignalized intersections)/2.5 miles = 14.0 access points/mile. • Length of roadway with 2 lanes is 0.625 miles: PROPLANE1 = 0.625/2.5 = 0.25. • Crash history includes 17 right-angle crashes in the most recent 4-year period. The following are the data for Proposed Condition 1 (Alternative B): • Corridor length = 2.5 miles. • AADT = 25,000 vehicles per day (unchanged). • 5 signalized intersections: SIGDENS = 2.0 signals/mile (unchanged). • 11 unsignalized intersections and 30 driveways: ACCDENS = (30 driveways + 11 unsignalized intersections)/2.5 miles = 16.4 access points/mile. • Length of roadway with two lanes is 0.625 miles: PROPLANE1 = 0.25 (unchanged). The following are the data for Proposed Condition 2 (Alternative C): • Corridor length = 2.5 miles. • AADT = 25,000 vehicles per day (unchanged). • 5 signalized intersections: SIGDENS = 2.0 signals/mile (unchanged). • 11 unsignalized intersections and 28 driveways: ACCDENS = (28 driveways + 11 unsignalized intersections)/2.5 miles = 15.6 access points/mile. • Length of roadway with two lanes is 0.625 miles: PROPLANE1 = 0.25 (unchanged). Step 4.2.2: Prediction for Existing Condition. Step 4.2.2a: Baseline Predicted Right-Angle Crashes/Year (Existing Alternative A). Figure 109 shows the calculation of the predicted right-angle crashes for the existing condition using the base model (Table E-11) with the values from Alternative A.

100 Application of Crash Modification Factors for Access Management Step 4.2.2b: Estimated EB Weight. Figure 110 shows the calculation of w. Note that k is given for each specific model in Table E-1 through Table E-41. For the base model for mixed-use, right-angle crashes (Table E-11), the value of k = 0.5585. Step 4.2.2c: Expected Right-Angle Crashes/Year (Existing Alternative A). Figure 111 shows the calculation of the annual expected crash frequency (EB estimate) for existing conditions. Step 4.2.2d: Estimated EB Correction Factor. The EB correction factor is calculated as the expected crashes for the existing condition (Step 4.2.2c) divided by the baseline predicted crashes for the existing condition (Step 4.2.2a). Figure 112 shows the calculation of the EB correction factor. This factor is used to adjust predictions for alternative scenarios and helps to account for several sources of potential bias, including variables that are omitted from the model. Step 4.2.3: Prediction for Proposed Conditions. Step 4.2.3a: Difference in Predicted Right-Angle Crashes/Year for Existing and Proposed Conditions. Apply Steps 4.1.2 through 4.1.4 from Analysis Level 1 using the existing and pro- posed conditions as inputs. The result is an estimate of the difference in predicted crash frequency for the existing and proposed conditions. Step 4.1.2 is Calculations for Non-Extrapolated Variables. Figure 113 shows the calculation of the predicted right-angle crashes per year for the existing conditions with the values from Alternative A. Figure 114 shows the calculation of the predicted right-angle crashes per year for the proposed condition with the values from Alternative B. Figure 115 shows the calculation of the predicted right-angle crashes per year for the proposed condition with the values from Alternative C. Baseline Predicted Right-Angle Crashes/Year (Existing Alternative A) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*14.0+0.2284*2.0) = 1.55 right-angle crashes/year Figure 109. Baseline predicted right-angle crashes/year (Existing Alternative A). EB Weight EB weight (w) = 1 / [1 + (k * years * Step 4.2.2a estimate)] EB weight (w) = 1/(1+0.5585*1*1.55) = 0.5356 Figure 110. Estimate of EB weight (w). Expected Right-Angle Crashes/Year (Existing Alternative A) EB Estimate = [w * (Step 4.2.2a estimate)] + [(1 – w) * (observed crashes/years of data)] EB Estimate = 0.5356*1.55 + (1 – 0.5356)*(17/4) = 2.81 right-angle crashes/year Figure 111. Expected right-angle crashes/year (Existing Alternative A). EB Correction Factor Expected Crashes (Existing) / Baseline Predicted Crashes (Existing) = 2.81/1.55 = 1.81 Figure 112. Estimated EB correction factor.

Predictive Method for Corridor-Level Analysis 101   Step 4.1.3 is Calculations for Extrapolated Variables. There are no extrapolated variables, so this step is not applicable. Step 4.1.4 is Estimated Difference in Crashes/Year for Different Alternatives. Comparing Alternative A and Alternative B (i.e., an increase in the number of driveways by five and an increase in the number of unsignalized intersections by one for a mixed-use corridor), the predicted change in right-angle crashes is an increase of 0.05 right-angle crashes/year (1.60 crashes/year – 1.55 crashes/year). Comparing Alternative A and Alternative C (i.e., an increase in the number of driveways by three and an increase in the number unsignalized intersections by one for a mixed-use corridor), the predicted change in right-angle crashes is an increase of 0.03 right-angle crashes/year (1.58 crashes/year – 1.55 crashes/year). Step 4.2.3b: Adjusted Predicted Right-Angle Crashes/Year for Existing Conditions. Add the difference in predicted crashes for existing and proposed conditions from Step 4.2.3a to the baseline predicted crashes for existing conditions from Step 4.2.2a, as shown in Figure 116. Predicted Right-Angle Crashes/Year (Existing Alternative A) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*14.0+0.2284*2.0) = 1.55 right-angle crashes/year Figure 113. Predicted right-angle crashes/year (Existing Alternative A). Predicted Right-Angle Crashes/Year (Proposed Alternative B) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*16.4+0.2284*2.0) = 1.60 right-angle crashes/year Figure 114. Predicted right-angle crashes/year (Proposed Alternative B). Predicted Right-Angle Crashes/Year (Proposed Alternative C) = (length)exp(Intercept+Region)(AADT)0.4656exp(0.0112*ACCDENS+0.2284*SIGDENS) = (2.5)exp(-5.8048+0)(25,000)0.4656exp(0.0112*15.6+0.2284*2.0) = 1.58 right-angle crashes/year Figure 115. Predicted right-angle crashes/year (Proposed Alternative C). Step 4.2.3c: Expected Right-Angle Crashes/Year for Proposed Conditions. Multiply the adjusted predicted crashes for the existing conditions from Step 4.2.3b by the EB correction factor from Step 4.2.2d, as shown in Figure 117. Figure 117. Expected right-angle crashes/year for proposed condition. Alternative B: 1.60 * 1.81 = 2.88 right-angle crashes/year Alternative C: 1.58 * 1.81 = 2.86 right-angle crashes/year Alternative B: 0.05 + 1.55 = 1.60 right-angle crashes Alternative C: 0.03 + 1.55 = 1.58 right-angle crashes Figure 116. Adjusted predicted right-angle crashes/year for existing conditions.

102 Application of Crash Modification Factors for Access Management Step 4.2.4: Estimated Safety Impacts. The results are provided as the expected crash fre- quencies per year for the crash types selected under both alternatives. The estimates for the existing conditions are from Step 4.2.2c, and the estimates for the following proposed conditions are from Step 4.2.3c: • Alternative B: The estimated effect of Alternative B compared with Alternative A (i.e., increasing the number of driveways from 25 to 30 and increasing the number of unsignalized intersections from 10 to 11) on right-angle crashes is an increase of 0.07 right-angle crashes/ year (2.88 crashes/year – 2.81 crashes/year). • Alternative C: The estimated effect of Alternative C compared with Alternative A (i.e., increasing the number of driveways from 25 to 28 and increasing the number of unsignalized intersections from 10 to 11) on right-angle crashes is an increase of 0.05 right-angle crashes/ year (2.86 crashes/year – 2.81 crashes/year). This sample problem included calculations for right-angle crashes only. A similar method would be applied to compute the EB correction factor for other crash types using the crash history for those specific crash types. The applicable correction factor would then be applied to the model predictions for alternative scenarios to estimate the expected crashes for other crash types of interest. Results from individual crash type models should not be summed to estimate total crashes. Sample Problem 9 Estimate the safety impact of variables that are available for a given crash type but not for the land use type of interest. In this case, it is necessary to use extrapolation. The extrapolation method first requires the use of a model from the land use and crash type of interest to predict crashes for existing conditions. Then, a model is selected from another land use to estimate the impacts of the variables of interest. Problem Definition For a commercial corridor, a proposal has been made to install a divided median for the entire length of the corridor. Presently, the corridor is partially divided. In the segment that is to be divided (currently undivided), a single new median opening would be provided. Figure 118 shows the existing conditions (A) and proposed conditions (B). It is desired to estimate the relative safety impact of the proposed changes on right-angle crashes. All other corridor char- acteristics, including the AADT, are assumed to remain constant. Figure 118. Illustration of Sample Problem 9.

Predictive Method for Corridor-Level Analysis 103   Step 1: Select Land Use and Region This is a commercial corridor. After reviewing the summary statistics for commercial use in each of the four regions from which the models were developed and comparing them to the local data, it is determined that the corridor is most comparable to the data from Minnesota. Step 2: Select Crash Types and Variables of Interest As noted in the problem definition, it is desired to estimate the relative effect of the proposed changes on right-angle crashes. In this case, the variables of interest include the proportion of corridor with divided median (PROPDIV) and density of median openings (MEDOPDENS). Step 3: Select Analysis Level of Interest It is desired to estimate the relative safety of two alternatives, one of which is the do-nothing alternative (i.e., existing conditions). In this case, Analysis Level 1 is applicable because the objective is to compare the relative safety impacts. Step 4: Select Applicable Model(s) and Perform Analysis Table 70 presents the applicable models for commercial land use. There are no directly appli- cable models for right-angle crashes and PROPDIV or MEDOPDENS, but the column titled “Variables Available Through Extrapolation” indicates that these variables may be considered through extrapolation. The applicable model for PROPDIV is Mixed/Right-Angle Model  2 (Table E-12). The applicable model for MEDOPDENS is Mixed/Right-Angle Model 2 (Table E-12). In this case, the applicable models are the same for the two variables of interest. It is also necessary to select a base model from the last column of Table 70 for use in the extrapolation process. The applicable base model for extrapolation is Commercial/Right-Angle Model 1 (Table E-24). Note that default values are required from Appendix D for use in the extrapolation process. The model coefficients to estimate the impact of the variables of interest on right-angle crashes are given in Table E-12 as PROPDIV (–0.4710) and MEDOPDENS (0.1901). Note that only the coefficients for the variables of interest are required from this model. The model coefficients for the base model are given in Table E-24 as intercept (–1.6746), region (1.4756 if North Carolina or Minnesota, 0 otherwise), AADT (0.1238), ACCDENS (0.0165), and SIGDENS (0.1532). The equation in Figure 85 is applicable to these models and shown again here for ease of reference: ( )= ∗ ∗ ( )( )+ ∗ + + ∗Crashes mile year exp AADT expintercept Region b c1 X1 . . . cn Xn Step 4.1.1: Data for Conditions of Interest. The following are the data for the existing con- dition (Alternative A): • Corridor length = 2.5 miles. • AADT = 46,000 vehicles per day. • 5 signalized intersections: SIGDENS = 5 signals/2.5 miles = 2.0 signals/mile. • 10 unsignalized intersections and 25 driveways: ACCDENS = (25 driveways + 10 unsignalized intersections)/2.5 miles = 14.0 access points/mile. • Length of roadway with divided median is 1.5 miles: PROPDIV = 1.5/2.5 = 0.6. • Number of median openings on divided section is three: MEDOPDENS = 3 median openings/ 1.5 miles = 2.0 median openings/mile. The following are the data for the proposed condition (Alternative B): • Corridor length = 2.5 miles. • AADT = 46,000 vehicles per day. • 5 signalized intersections: SIGDENS = 2.0 signals/mile (unchanged).

104 Application of Crash Modification Factors for Access Management • 10 unsignalized intersections and 25 driveways: ACCDENS = 14.0 access points/mile (unchanged). • Length of roadway with divided median is 2.5 miles: PROPDIV = 2.5/2.5 = 1.0. • Number of median openings on divided section is four: MEDOPDENS = 4 median openings/ 2.5 miles = 1.6 median openings/mile. Step 4.1.2: Calculations for Non-Extrapolated Variables. The effects are extrapolated from a model for a different land use, so this step is not applicable. Step 4.1.3: Calculations for Extrapolated Variables. For each of the two variables to be considered through extrapolation, the following steps are taken. Step 4.1.3a: Baseline Predicted Right-Angle Crashes/Year (Existing). Figure 119 shows the calculation of predicted right-angle crashes for the existing condition using the base model (Table E-24) with the values from the existing condition (Alternative A). Step 4.1.3b: Estimate the Impacts of the Variables of Interest for Existing Conditions. The effects of the variables of interest for the existing conditions are estimated using the equation in Figure 120 along with the coefficients in Table E-12 and the values from Alternative A: The coefficients for PROPDIV and MEDOPDENS are −0.4710 and 0.1901, respectively. The mean values of PROPDIV and MEDOPDENS are obtained from Appendix D for the land use and region from which the model was developed. In this example, the corridor of interest is similar to the data from Minnesota, and the model is based on data for mixed land use. From Appendix D, the mean values for PROPDIV and MEDOPDENS from mixed-use corridors in Minnesota are 0.61 and 1.47, respectively (Table D-2), and the multipliers are calculated as shown in Figure 121. Step 4.1.3c: Adjusted Predicted Right-Angle Crashes/Year (Existing Alternative A). The estimate from Step 4.1.3b is then multiplied by the estimate from Step 4.1.3a, as shown in Figure 122. Adjusted Predicted Right-Angle Crashes/Year (Existing Alternative A) = MultiplierPROPDIV * MultiplierMEDOPDENS * Existing Predicted Right-Angle Crashes/Year = 1.00 * 1.11 * 13.25 right-angle crashes/year = 14.72 right-angle crashes/year Figure 122. Adjusted predicted right-angle crashes/year (Existing Alternative A). Baseline Predicted Right-Angle Crashes/Year (Existing) = (length)exp(Intercept+Region)(AADT)0.1238exp(0.0165*ACCDENS+0.1532*SIGDENS) = (2.5)exp(-1.6746+1.4756)(46,000)0.1238exp(0.0165*14.0+0.1532*2.0) = 13.25 right-angle crashes/year Figure 119. Baseline predicted right-angle crashes/year (existing). Multiplier = exp(coefficient)*(Variable Actual Value – Variable Default Value) Figure 120. Estimate of the impacts of the variables of interest for existing conditions. MultiplierPROPDIV = exp-0.4710(PROPDIVexisting - PROPDIVmean) = exp-0.4710(0.60 – 0.61) = 1.00 MultiplierMEDOPDENS = exp0.1901(MEDOPDENSexisting - MEDOPDENSmean) = exp0.1901(2.00 – 1.47) = 1.11 Figure 121. Estimation of multipliers.

Predictive Method for Corridor-Level Analysis 105   Step 4.1.3d: Baseline Predicted Right-Angle Crashes/Year for Proposed Conditions. The baseline predicted crashes for the proposed conditions are estimated using the base model (Table E-24) with the values from the proposed conditions (Alternative B). In this case, there are no anticipated changes in the variables included in the base model; therefore, the estimate remains the same as the baseline predicted crashes for the existing conditions (13.25 right-angle crashes per year). Step 4.1.3e: Estimate the Impacts of the Variables of Interest for Proposed Conditions. The effects of the variables of interest for the proposed conditions are estimated using Figure 123 along with the coefficients in Table E-12 and the values from Alternative B: The coefficients for PROPDIV and MEDOPDENS are –0.4710 and 0.1901, respectively. The mean values of PROPDIV and MEDOPDENS are obtained from Appendix D for the land use and region from which the model was developed. In this example, the corridor of interest is similar to the data from Minnesota, and the model is based on data for a mixed land use. From Appendix D, the mean values for PROPDIV and MEDOPDENS from mixed-use corridors in Minnesota are 0.61 and 1.47, respectively (Table D-2), and the multipliers are calculated as shown in Figure 124. Step 4.1.3f: Adjusted Predicted Right-Angle Crashes/Year (Proposed Alternative B). Figure 125 shows the calculation of the adjusted predicted right-angle crashes per year for Alter- native B, which is the estimate from Step 4.1.3e multiplied by the estimate from Step 4.1.3d. Step 4.1.4: Estimated Safety Impacts. The adjusted predicted crash frequency for proposed conditions (Step 4.1.3f) is subtracted from the adjusted predicted crash frequency for existing conditions (Step 4.1.3c). The result is the difference in the predicted crash frequency for Alter- native B compared with Alternative A. The impact of the proposed conditions (i.e., installing a median along the remainder of the corridor with one additional median opening) is a reduction of 3.39 right-angle crashes/year (14.72 crashes/year – 11.33 crashes/year). Sample Problem 10 Estimate the effects when one or more variables of interest do not appear in any models for any crash type of interest or land use. In this case, it is not possible to quantify the effects of those variables in the manner shown in the previous sample problems. Instead, qualitative assessments could be made based on relationships identified from basic summary statistics. Adjusted Predicted Right-Angle Crashes/Year (Proposed Alternative B) = MultiplierPROPDIV * MultiplierMEDOPDENS * Predicted Right-Angle Crashes/Year (Proposed) = 0.83 * 1.03 * 13.25 right-angle crashes/year = 11.33 right-angle crashes/year Figure 125. Adjusted predicted right-angle crashes/year (Proposed Alternative B). MultiplierPROPDIV = exp-0.4710(PROPDIVproposed - PROPDIVmean) = exp-0.4710(1.00 – 0.61) = 0.83 MultiplierMEDOPDENS = exp0.1901(MEDOPDENSproposed - MEDOPDENSmean) = exp0.1901(1.60 – 1.47) = 1.03 Figure 124. Estimation of multipliers. Figure 123. Estimate of impacts of variables of interest for proposed conditions. Multiplier = exp(coefficient)*(Variable Proposed Value – Variable Default Value)

106 Application of Crash Modification Factors for Access Management To facilitate such an assessment, Appendix F provides coefficients from the correlation matrix between the variables of interest that do not appear in any models and the various crash types by land use. Correlation coefficients range between –1.0 and 1.0. A positive coefficient indicates that higher values of a variable are correlated with a higher crash frequency. A negative coefficient indicates that higher values of a variable are correlated with a lower crash frequency. The closer the coeffi- cient is to –1.0 or 1.0, the stronger the correlation. It is important to understand that correlation does not equal causality because no other vari- ables, including traffic volume, are accounted for in the correlation coefficients. This can result in completely erroneous relationships due to the potential for unaccounted confounding factors. As such, it is critical to employ caution and judgment when using correlation coefficients to assess the potential impact of a variable, and this is a last resort when the variable of interest does not appear in the more rigorous predictive models. To provide a point of reference, the parameter estimates and p-values are also provided with the correlation coefficients. The parameter estimates are based on a restricted model in which only traffic volume and the variable of interest are included. Where the correlation coefficient and the parameter estimate differ (i.e., opposite signs), it may be an indication that other factors are confounding the results or that the association is not statistically significant. The remainder of this section provides two examples to illustrate the interpretation of correlation coefficients and the associated parameter estimate and p-value to assess the potential safety relationship for the variable of interest. Example of Consistent and Logical Effects Several of the variables in Appendix F are related to the spacing of signalized and unsignal- ized access such as the minimum spacing of signalized intersections (MINSPCSIG). For all crash types in all three land use scenarios, the correlation coefficient is negative for MINSPCSIG, as shown in Table 72. This indicates that greater values for minimum signal spacing are corre- lated with fewer crashes. Again, traffic volume is not considered in the estimation of correlation coefficients. The model coefficients and associated p-values are also provided in Table 72 (shown in paren- theses below the respective correlation coefficients). The only other variable considered in the estimation of the model coefficients is AADT, so the results should be interpreted with caution because other important factors may be omitted. All of the model coefficients are negative, indicating that greater minimum signal spacing may reduce crashes for these crash types. This is consistent with the correlation coefficients. Further, many of the p-values are less than 0.10, particularly for commercial and residential land use, indicating that the effects are statistically significant at the 90-percent confidence level. Land Use Total Injury Turning Rear-End Right-Angle Mixed Use –0.1800 (–0.0001, 0.2200) –0.2100 (–0.0001, 0.2600) –0.1600 (–0.0001, 0.3600) –0.2000 (–0.0002, 0.1100) –0.2100 (–0.0002, 0.0700) Commercial –0.2100 (–0.0002, 0.0000) –0.2200 (–0.0002, 0.0000) –0.1600 (–0.0001, 0.0300) –0.2200 (–0.0003, 0.0000) –0.2300 (–0.0002, 0.0000) Residential –0.3400 (–0.0002, 0.0100) –0.3300 (–0.0002, 0.0000) –0.2200 (–0.0001, 0.1100) –0.3300 (–0.0003, 0.0000) –0.3100 (–0.0001, 0.3400) Table 72. Correlation coefficients for minimum signal spacing (model coefficient, p-value).

Predictive Method for Corridor-Level Analysis 107   Example of Inconsistent and Illogical Effects Several of the variables in Appendix F are related to the presence of left-turn lanes, such as the number of signalized intersections with a left-turn lane on the mainline (NOLTLSIG). For all crash types in all three land use scenarios, the correlation coefficient is positive for NOLTLSIG, as shown in Table 73. This indicates that the presence of left-turn lanes is correlated with higher numbers of crashes. Again, traffic volume is not considered in the estimation of correlation coefficients and left-turn lanes are often installed along corridors with higher traffic volumes, which typically experience more crashes because of the higher volumes. In this case, it appears that traffic volume could be a confounding factor. The model coefficients and associated p-values are also provided in Table 73 (shown in paren- theses below the respective correlation coefficients). The only other variable considered in the estimation of the model coefficients is AADT, so the results should be interpreted with caution because other important factors may be omitted. Some of the coefficients are negative, indi- cating that left-turn lanes may reduce crashes for these crash types. This is intuitive, but counter to the correlation coefficients. This indicates that the results may be unreliable, and there may be other factors that should be considered. In addition, all p-values are much greater than 0.10, indicating that the effects are not statistically significant at the 90-percent confidence level. Land Use Total Injury Turning Rear-End Right-Angle Mixed Use 0.790(0.009, 0.282) 0.860 (0.011, 0.192) 0.740 (0.010, 0.328) 0.590 (0.004, 0.690) 0.860 (0.014, 0.168) Commercial 0.730(0.011, 0.259) 0.800 (0.010, 0.282) 0.650 (0.006, 0.583) 0.460 (0.013, 0.355) 0.810 (0.017, 0.173) Residential 0.620(–0.003, 0.911) 0.670 (0.005, 0.811) 0.590 (0.008, 0.765) 0.500 (0.017, 0.604) 0.390 (–0.027, 0.351) Table 73. Correlation coefficients for number of left-turn lanes at signalized intersections (model coefficient, p-value).