Crash Modification Factors in the Highway Safety Manual: A Review (2023)

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32 Validation of SPF Adjustment Factors Each chapter in Part C of the HSM1 describes a safety prediction method for a specific facility type (e.g., rural two­lane two­way roads). Each method comprises several CPMs, each of which is associated with one site type (e.g., four­leg signal­controlled intersection). Each CPM typically consists of an SPF, one or more CMFs, a calibration factor, a severity distribution, and a crash type distribution. [Note: The plan for Part C of the HSM2 is to change the term “crash modifica­ tion factor,” or CMF, to “SPF adjustment factor (AF).”] In some chapters in Part C, some site types are associated with two or more crash­type­specific CPMs. NCHRP 17­62 developed crash­specific SPFs and severity­specific SPFs for inclusion in Part C of the HSM2. These SPFs were developed to replace the CPMs in the HSM1. They were estimated for specific base conditions, but NCHRP 17­62 did not develop CMFs for these SPFs. As dis­ cussed earlier, NCHRP 17­72 developed these CMFs from the high­quality CMFs documented in the FHWA CMF Clearinghouse. Since the CMFs and the SPFs were estimated independently, there is a need to validate these CMFs for the SPFs. 8.1 Approach for Validation In this effort, each adjustment factor was validated individually. The validation is a cross­ sectional comparison, so one approach is to compare two sets of data in which the only difference is in the variable of interest. The approach taken was to use sites that met all base conditions except for the variable to which the adjustment factor applied. For example, where the adjustment factor for lighting was of interest, all the sites used met the base conditions except for lighting; sites with and without lighting were used. The following three analysis approaches based on the nature of the adjustment factors were explored. 8.1.1 Approach 1 The first approach was to use the base condition model to compare the number of observed crashes with the predicted number of crashes at each level of the variable, for example, sites with lighting and those without. If that variable has an effect on safety, then the ratio of observed to predicted crashes will differ between the levels of the variable. The calibration factor, C, for each level, i, is the sum of observed crashes divided by the sum of predicted crashes, as shown in the following equation: observed crashes predicted crashes all sites all sites Ci ∑ ∑ = C H A P T E R 8

Validation of SPF Adjustment Factors 33 The steps in this approach are as follows: • Step 1: Apply the base condition models to a data set of sites that meet all base conditions except for the variables of interest. For this variable, site selection is not constrained. • Step 2: Calculate the calibration factor Ci for each level of the variable. • Step 3: Estimate adjustment factors for each level of the variable. Each factor is related to the base condition level by dividing the factor for level i by the factor for the base level. To illustrate, in Table 3, a variable has three levels, and an adjustment factor has been esti­ mated for each, ranging from 1.0 to 1.53. Level 1 is the base condition for the SPF. The adjustment factors for the other levels are estimated by dividing each factor Ci by the Ci for Level 1. Note that in this example, the Ci for Level 1 is not 1.0. This may occur if the sites used did not exactly match those used for calibrating the base condition models or because of rounding the numbers of predicted crashes. These adjustment factors were then compared with the recommended adjustment factors. 8.1.2 Approach 2 The second approach made use of the GLM method. In this approach, the expected number of crashes is modeled with the prediction from the base condition as an offset. The variable of interest is then included in the model to estimate the adjustment factor. The equations below illustrate this approach. crashes = (intercept)(years)(SPF)f (VAR) ln(crashes) − ln[(years)(SPF)] = ln[(intercept)( f (VAR)] where SPF = base model prediction, intercept = a constant term, and f (VAR) = function representing the relationship between crashes and the variable of interest. 8.1.3 Approach 3 For some variables, the recommended adjustment factor is not a single value or simple equation. In these cases, the approach to validation was to compare the sum of observed and predicted values for the base model and the base model plus adjustment factor when applied to sites that did not meet the base conditions for the variable of interest. Additionally, where the variable was a continuous variable with sufficient variation, plots of the cumulative residuals for the two predictions were compared to see whether the use of the adjustment factors improved the predictions at the non–base condition sites. Level of Variable Ci Adjustment Factor 1 0.98 1.00 2 1.20 1.22 3 1.50 1.53 Table 3. Illustration of Approach 1.

34 Crash Modification Factors in the Highway Safety Manual: A Review 8.2 Results Section 5 of Appendices K, L, and M provides a detailed discussion of the validation exercise for segments on rural two­lane roads, urban segments, and intersections, respectively. Generally, in most cases, sample sizes were too small to conclude with high confidence that the implied adjustment factors were statistically similar to the ones being validated. Instead, the best that can be said in general is that one cannot reject a hypothesis that the implied adjustment factors from the validation are statistically different from the HSM­recommended adjustment factors. That said, there can be more confidence in some adjustment factors because (1) there is relative consistency in the results from different approaches for validating the same adjustment factors and (2) there is relative consistency in the adjustment factor trends when the adjustment factors are in the form of a function, as was the case for roadside hazard rating.