Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results (2021) / Chapter Skim
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From page 9... ...
9 Introduction The CPMs in HSM Part C include a SPF, one or more CMFs, and a local calibration factor (C)
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10 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Method 4 is not based on the use of an SPF. Rather, the observed crash frequency for the site is used to estimate the expected crash frequency.
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From page 11... ...
Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 11 In Scenario 1, Case A, the CMF obtained from HSM Part D or another source represents the "CMF of interest." It describes the safety effect of treatment of interest. The GOF measures that are computed describe the reliability of the estimated average crash frequency when the treatment is applied to one or more sites of interest.
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12 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results estimate the SPF. Finally, if this database is not available or it does not contain the variable of interest X, then it may be possible to identify the regions from which the data were obtained to develop the SPF and obtain values of the variable X at a representative set of sites.
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 13 2. Compute the value of the CMF of interest for the sites of interest [CMFD(X –)
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14 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results where Np = predicted average crash frequency, crashes/year NSPF,j-s = predicted crash frequency for site with base conditions that are in balance with the CMFs (jurisdiction-specific)
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 15 where σe,I = increased root mean square error σ2abs = absolute difference of the change in variance of the predicted value e = error in predicted crash frequency 4. Compute the CV using the following equation: = σ CV NI e I p true , , where CVI = coefficient of variation for the increased root mean square error σe,I = increased root mean square error Np,true = predicted true crash frequency, crashes/year Step 7.
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From page 16... ...
16 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Outline of Solution Step 1. Assemble the Data Needed to Apply the Procedure The data needed to apply the procedure are listed in Table 3.
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 17 3. These two CMF values are used in the following equation to compute the estimation coefficient: [ ]
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18 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results 4. To compute the CV for the increased root mean square error CVI, the predicted value σe,I and the predicted true crash frequency Np,true are used in the following equation: = σ =CV NI e I p true 0.17, , This CVI means that there is a relatively large amount of error-related variability in the predicted crash frequency.
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From page 19... ...
Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 19 Each step is described in terms of data needs, equations, variable estimation, selected GOF measures, and outcome related to the quantitative assessment of the degree of reliability.
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From page 20... ...
20 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results The practitioner may be seeking the reliability evaluation of one site of interest or a group of sites of interest: • When One Site of Interest Is Being Evaluated. The average of the independent variable value associated with the external CMF (X–)
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 21 3. Use the following equation to compute the estimation coefficient b.
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22 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Step 5. Compute the Unbiased Predicted Crash Frequency for Site of Interest The following equation is used to compute the unbiased predicted crash frequency for the site of interest.
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 23 where e = error in predicted crash frequency Np = predicted average crash frequency, crashes/year Np,true = predicted true crash frequency, crashes/year 2. Compute the absolute difference in the change in variance of the predicted value using the following equation: k N k Nabs reported p p true p true( )
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24 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Outline of Solution Step 1. Assemble the Data Needed to Apply the Procedure The data needed to apply the procedure are listed in Table 5.
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 25 Step 2. Compute Estimation Coefficient There are three sub-steps in this computation: 1.
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26 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Step 5. Compute the Unbiased Predicted Crash Frequency for Site of Interest To compute the predicted true crash frequency Np,true, the predicted crash frequency Np, CMFex(X – CPM)
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 27 This CVI means that there is a relatively large amount of error-related variability in the predicted crash frequency. As noted, values over 0.20 are considered to be unreliable for most applications.
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28 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results Step 1. Assemble the Data Needed to Apply the Procedure The data needed to apply the procedure are listed in Table 6.
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 29 (or has been treated)
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30 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results X– = average independent variable associated with CMF of interest at sites of interest X– CPM = average independent variable value at sites used to estimate the CPM CMFom(X –) = omitted CMF value associated with X– CMFom(X – CPM)
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Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 31 where Np,true = predicted true crash frequency, crashes/year Np = predicted average crash frequency, crashes/year fC = bias adjustment factor for Scenario 1, Case C CMFom(X –) = omitted CMF value associated with X– CMFom(X – CPM)
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From page 32... ...
32 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results 2. Compute the absolute difference in the change in variance of the predicted value using the following equation: 2 2 , , 2( )
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From page 33... ...
Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 33 Outline of Solution Step 1. Assemble the Data Needed to Apply the Procedure The data needed to apply the procedure are listed in Table 7.
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From page 34... ...
34 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results purposes of the reliability evaluation, typical AADT values can be used for the calculations. The typical intersection major road AADT is 10,000 vehicles/day and the typical minor road AADT is 2,000 vehicles/day.
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From page 35... ...
Quantifying the Reliability of CPM Estimates for Mismatches Between Crash Modification Factors and SPF Base Conditions 35 Step 5. Compute the Unbiased Predicted Crash Frequency for Site of Interest To compute the predicted true crash frequency Np,true, the predicted crash frequency Np, CMFom(X – CPM)
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From page 36... ...
36 Reliability of Crash Prediction Models: A Guide for Quantifying and Improving the Reliability of Model Results This CVI means that there is a relatively large amount of error-related variability in the predicted crash frequency. Values over 0.20 are considered to be unreliable for most applications.
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