Understanding and Communicating Reliability of Crash Prediction Models (2021) / Chapter Skim
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19 Chapter 3. Procedures for Quantifying the Reliability of Crash Prediction Model Estimates with a Focus on Mismatch Between CMFs and SPF Base Conditions Introduction The crash prediction models (CPMs)
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20 SPF base conditions. The motivation for type of application can vary (e.g., the analyst desires to evaluate the benefits of a new treatment that has yet to be deployed system-wide but for which a CMF has been developed from studies of its use at a few trial locations)
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21 Table 5. Summary of Applications Associated with Reliability Reduction in Predicted Value.
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22 kreported = reported overdispersion parameter for CPM; kp, true = predicted true overdispersion parameter; Np = predicted crash frequency from CPM, crashes/yr; and Np,true = predicted true crash frequency, crashes/yr; The reported overdispersion parameter is the value obtained from HSM Part C for the CPM that is used for the reliability evaluation. The predicted true overdispersion parameter is obtained from the equations provided in the procedure described in the next section (i.e., Procedural Steps)
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23 Procedural Steps This section describes the procedures for quantifying the bias and added uncertainty (i.e., variance) associated with each of the three application cases identified in Table 5.
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24 value ππππΉ would then be computed using this representative set of sites. If the treatment is discrete (e.g., "add beacon")
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25 Equation 19 π πΏπ πΆππΉ π πΏπ πΆππΉ ππ π where b = estimation coefficient; CMFD = HSM Part D CMF for geometric design element, or traffic control feature of interest; π = average independent variable value associated with CMF of interest at sites of interest; π = average independent variable value at sites used to estimate the SPF; CMFD(π) = HSM Part D CMF value associated with π; and CMFD(π )
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26 Equation 24 π π π , Β where e is the error in predicted crash frequency; and all other variables are as previously defined. Second, compute the absolute difference in the change in variance of the predicted value using the following equation.
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27 this regard, typical values of AADT, segment length, and variables in the CMFs (other than the external CMF) can be used to apply the CPM in Step 4.
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28 to all of the sites of interest, then π equals the value of X averaged for all sites. If the treatment is discrete (e.g., "add beacon")
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29 π , = variance of the independent variable at sites of interest; b = estimation coefficient; and ct = correction term.
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30 constants. In general, there is at least one empirically derived constant for each CMF used to develop the CPM plus 1 for the external CMF.
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31 coefficient of variation CVI and bias percent Bias computed in Steps 7 and 8, respectively, were derived to have the characteristic that they are insensitive to the value of the predicted crash frequency (NP)
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32 When Several Sites of Interest are Being Evaluated. The average of the independent variable value associated with the omitted CMF (π)
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33 with Equation 43 π 1.120 ππ π 0; 0.880 ππ‘βπππ€ππ π where fC = bias adjustment factor for Case C; π , = variance of the independent variable at sites of interest; b = estimation coefficient; and ct = correction term.
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34 The number of empirically derived constants p is determined by inspecting the CMFs in the CPM. Regression constants in the SPF (e.g., intercept, AADT coefficient, segment length coefficient)
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35 Case A CMF from Part D used with SPF (CMF is consistent with SPF base conditions)
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36 to estimate the SPF had an average lane width of 12 ft and a standard deviation of 2.0 ft. Thus, the average independent variable value π equals 12 ft and the standard deviation of lane width at these sites π , equals 2.0 ft.
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37 considered when the SPF was developed and its base conditions were established. An example of this application is when a Part D CMF is used with a Part C CPM (and the Part D CMF's variables are not included in the CPM's base conditions)
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38 by these researchers was obtained and the location of the intersections identified. A review of Google Earth historical aerial photos for each intersection indicated that a few of the intersections had a flashing beacon during the period for which data were collected to develop the CPM.
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39 Finally, the predicted value of Οe,I and the predicted true crash frequency Np,true are used in Equation 39 to compute the coefficient of variation for the increased root mean square error CVI. The predicted value of CVI is 0.15.
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40 Table 11. Required Data for Case C Example Application.
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41 Step 3. Compute Bias Adjustment Factor.
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