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44 7.00 Removals per Mile-Year WVCs or Deer Carcass 6.00 5.00 WVCs 4.00 3.00 Deer Carcass Removals 2.00 1.00 0.00 0 20000 40000 60000 80000 100000 Average Annual Daily Traffic Figure 7. Multilane rural roadway volume-only model results. Cumulative residual (CURE) plots were used to assess how framework to provide good estimates of the long-term expected well the models (SPFs) performed for all values of AADT. To deer carcass removal frequency. The dispersion parameters of construct a CURE plot the data are sorted in ascending order the deer carcass removal models show that these data are much of the variable of interest and the cumulative residuals more overdispersed than the WVC data. This difference rein- (observed minus predicted frequencies) are plotted on the forces the need for deer carcass removal data at the site level. y-axis with the x-axis being the values of the variable of inter- Figure 9, on the other hand, shows that for multilane rural road- est. Also plotted are the 2 standard deviation limits. These ways, the recalibrated volume-only WVC model does not limits are calculated based on the assumption that the sum of perform well. The cumulative residuals show that the model residuals for the model is approximately normally distributed overpredicts for AADT less than approximately 15,000 vehicles with the mean equal to 0. If the plot of cumulative residuals is per day and then underpredicts for higher AADT. The CURE outside these limits then the SPF can be concluded to be pre- plot deviates well outside two standard deviations. dicting poorly within that range of the independent variable. Figure 8 indicates that for rural two-lane roadways the Interpretation, Appraisal, and Applications volume-only WVC model performed reasonably well for Aspect 1: Application of Reported WildlifeVehicle predicting the mean deer carcass removal frequency if it can be Collision Data recalibrated. The cumulative residual plotted is generally between the two standard deviation curves. For site-specific As they stand, the primary application of the models is for the estimates, it is still important to have a record of the number of safety management of existing roads as opposed to design or deer carcass removals to combine with the prediction in the EB planning applications for new or newly built roads. For existing 400.00 300.00 Cumulative Deer Carcass 200.00 Removal Residuals 100.00 WVC Recalc. 0.00 Minus 2 Std. Dev. 0 2000 4000 6000 8000 10000 12000 14000 -100.00 Plus 2 Std. Dev. -200.00 -300.00 -400.00 Average Annual Daily Traffic Figure 8. Cumulative residuals for two-lane rural roadway volume-only WVC model recalibrated and applied to deer carcass removals.

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45 400.00 200.00 Cumulative Deer Carcass 0.00 Removal Residuals 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 -200.00 -400.00 WVC Recalc. -600.00 Minus 2 Std. Dev. -800.00 Plus 2 Std. Dev. -1000.00 -1200.00 -1400.00 -1600.00 Annual Average Daily Traffic Figure 9. Cumulative residuals for multilane rural roadway volume-only WVC model recalibrated and applied to deer carcass removals. roads, WVC data are available and used, along with the model frequency with the frequency expected by applying the SPFs predictions in an empirical Bayes procedure to estimate the ex- described earlier. In this approach, overlapping segments of pected long-term mean collision frequency of a specific roadway equal length should be considered in what is often termed a segment. The following three types of model applications, which "sliding window" approach. A brief overview of the method would be most relevant to the development of the desired guide- is provided with an example calculation. When the SafetyAn- lines, are summarized and illustrated in the sections to follow: alyst ( software becomes available, there will be a facility to consider segments of different length Network screening to identify roadway segments that may using a sophisticated "peak searching" algorithm. be good candidates for WVC countermeasures, In the EB procedure, the SPF is used to first estimate the Evaluation of the effectiveness of implemented counter- number of collisions that would be expected at locations with measures, and traffic volumes and other characteristics similar to the ones Estimation of the cost effectiveness of potential counter- being analyzed. The estimate (P) is then combined with the measures. count of collisions (x) observed to obtain an estimate of the expected number of collisions (m). This estimate of m is: Network screening to identify roadway segments that m = w1(x) = w2(P), may be good candidates for wildlifevehicle collision coun- termeasures. Two fundamental methodologies are pre- where the weights (w1 and w2) are estimated from the mean sented and illustrated for this application: and variance of the SPF estimate as: w1 = P/(P + 1/k) Identifying and ranking sites based on a high expected w2 = 1/k/(P + 1/k), frequency of WVCs, and Identifying and ranking sites based on a high proportion of and where k is the dispersion parameter for a given model and WVCs is estimated from the SPF calibration process with the use of a maximum likelihood procedure. In this process, a negative SPFs are used in the first application. The second applies for binomial distributed error structure is assumed with k being situations where an SPF may not be available or applicable. the dispersion parameter of the distribution. For network Identifying and ranking sites based on a high long-term fre- screening purposes, each segment is then ranked in descend- quency of wildlifevehicle collisions. As noted earlier, the short- ing order by the expected number of collisions (m). term collision count at a location is not a good estimate of its As an illustration, suppose that the two-lane rural roads in safety. Thus, identifying and ranking collision-prone locations Utah are divided into 1-mi WVC segments that may or may based on short-term counts will be inaccurate. Longer term not overlap. Consider one such segment for which the fol- collision frequency data are now recognized as the best basis for lowing information applies: identifying and ranking these locations. The long-term frequency of WVC data at a site is obtained Length = 1 mi (1.6 km) by using the EB methodology that combines the site's WVC Years of data = 16

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46 WVCs observed = 40 Table 20. Comparison of alternative Average AADT = 2,066 ranking methods. Rank by EB Rank by Proportions First, the UT 1 model from Table 12 is used for this example Site Method Method to calculate the regression estimate (P). 11430 1 9 10194 2 6 P = (years)(length)(AADT)1 9463 3 3 10336 4 48 P = (16)(1)exp(-9.1135)(2, 066)1.0237 = 4.36 11546 5 11 9947 6 4 Next, the weights (w1 and w2) are calculated. 9154 7 2 10177 8 5 w1 = 4.36/(4.36 + 1/1.7610) = 0.88 6749 9 1 6716 10 35 w2 = 1/1.7610/(4.36 + 1/1.7610) = 0.12 11545 11 19 11554 12 12 Last, the regression estimate (P) and the observed collision 10195 13 7 count (x) are combined. 10197 14 8 11432 15 47 m = 0.88(40) + 0.12(4.36) = 35.72 6697 16 28 The EB estimate of the expected number of collisions dur- 9477 17 920 10673 18 18 ing the 16-year period is 35.72, lower than the observed count 6752 19 80 of 40. This EB estimate is used in ranking this location rela- 6694 20 86 tive to the other 1-mi segments. Identifying and ranking sites based on a high proportion alternative to ranking by the EB estimate of WVCs if the of wildlifevehicle collisions. Where traffic volume and required data or resources are not available for developing other characteristics necessary to estimate the expected colli- or applying SPFs. sion frequency at a site are unavailable, identifying sites with a high proportion of WVCs might be appropriate. This Evaluation of the safety effectiveness of implemented method uses the observed counts for WVCs and all collisions countermeasures, specifically the installation of animal at a site but adjusts for the "noise" in each of these counts. For crossings. The methodology for the conduct of a proper example, one is more certain that the proportion is high for observational before-after study is well documented in a a site with 20 WVCs out of 30 collisions than for a site with landmark book by Hauer.114 The statistically defendable 2 WVCs out of 3 collisions. The theory behind this method is before-after analysis methodology proposed overcomes the described in Appendix C. Of particular note is that the difficulties associated with simple before-after comparisons method only requires the counts of WVCs and all collisions of collision counts. The proposed methodology: at sites to be screened (i.e., SPFs are not required). This method is also being implemented in SafetyAnalyst. Properly accounts for regression-to-the-mean, By way of illustration, the Utah two-lane rural roadway Overcomes the difficulties of using collision rates in nor- dataset is used. The data were manipulated into 1-mi long malizing for traffic volume differences between the before segments, although any desired length could be considered. and after periods, All sites were ranked by the two methods. The top 20 sites Reduces the level of uncertainty in the estimates of safety ranked using the EB estimate of mean WVC frequency out- effects, lined earlier are presented in Table 20. Provides a foundation for developing guidelines for esti- The same segments were also screened based on the prob- mating the likely safety consequences of installing a cross- ability that their proportion of WVCs is greater than 20.7%, ing and fencing, and the mean proportion for all segments. The rankings from Properly accounts for differences in collision experience this "proportions" method are shown in the last column of and reporting practice in amalgamating data and results Table 20. As seen, seven of the top ten segments identified from diverse jurisdictions. by the EB method were also in the top ten ranked by the proportions method. Thirteen of the top twenty seg- The task is to estimate what was the effect on safety of ments identified by the EB method were also in the top installing wildlife crossing measures. In this, "safety" is the twenty ranked by the proportions method. It appears that expected number of WVCs per unit of time for a road seg- ranking by a high proportion of WVCs may be a reasonable ment of interest. This estimate requires three steps:

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47 1. Predict what safety would have been during the "after" pe- nomial distributed error structure is assumed with k being the riod, had the status quo been maintained, dispersion parameter of this distribution. 2. Estimate what safety was during the after period with The variance of the estimate (m) is: crossing measures in place, and Var(m) = ((x + 1/k)P2)/(1/k + P)2 3. Compare the two. A factor f is then applied to m to account for the length of the The following approach to Step 1 (predicting what safety after period and differences in traffic volumes between the would have been during the after period had the status quo before and after periods. This factor is the value of the SPF been maintained) is suggested: prediction for the after period divided by P: f = sum of SPF predictions post treatment/P Account explicitly for the effect of changes in traffic flow by using an SPF; The result, after applying this factor, is an estimate of . The Account for the effect of weather, demography, and other procedure also produces an estimate of the variance of . variables by using a comparison group to recalibrate the Var() = (f/P)2Var(m) SPFs to be used; and Account for possible selection bias (regression-to-the-mean The estimate of is then summed over all locations in a treat- effects) and improve estimation accuracy by the EB method ment group of interest (to obtain sum) and compared with using the best available methodology.114 the count of collisions during the after period in that group (sum). The variance of is also summed over all sections in In the EB approach, the change in safety for a given colli- the treatment group. sion type is given by: The Index of Effectiveness () is estimated as: - = (sum/sum) / {1 +[Var(sum)/(sum2]} where is the expected number of collisions that would have The standard deviation of is given by: occurred during the after period without the crossing measures Stddev() = [2{[Var(sum)/sum2] + and is the number of reported collisions during the after [Var(sum)/(sum2]}/[1 + Var(sum)/sum2]2]0.5 period. In estimating , the effects of regression to the mean and changes in traffic volume are explicitly accounted for by The percent change in collisions is in fact 100(1 - ); thus, a using SPFs relating collisions of different types and severities to value of = 0.7 with a standard deviation of 0.12 indicates a traffic flow and other relevant factors for each jurisdiction 30% reduction in collisions with a standard deviation of 12%. based on locations without crossing measures. The exposure of As an illustration of the method, Table 21 presents the re- animals to the roadway is not accounted for. sults of an analysis for two sites located in Utah (U.S. Hwy 40 In the EB procedure, the SPF is used to first estimate the between mileposts 4.0 and 8.0, and Utah Route 248 between number of collisions that would be expected during the mileposts 3.3 and 13.5). Each site involved the construction before period at locations with traffic volumes and other of one or more at-grade wildlife crossings and continuous characteristics similar to the one being analyzed. The esti- exclusion fencing that extended beyond the limits of the mate (P) is then combined with the count of collisions (x) crossings themselves. Note that the roadway inventory data during the before period at a treatment site to obtain an es- has divided these sections of the road into multiple subseg- timate of the expected number of collisions (m) before the ments due to differences in number of lanes, AADT, and crossing measures were installed. This process is identical to other variables. that presented earlier, but is repeated here for completeness. The results for the demonstrative case indicate a WVC This estimate of m is: reduction of: m = w1(x) + w2(P) (1 - 0.702) * 100 = 29.8% with a standard error of 9.1% where the weights (w1 and w2) are estimated from the mean Note that this result is based on only two sites in one state and and variance of the SPF estimate as: thus should not be used as conclusive evidence of the safety benefits of installing wildlife crossings and fencing. w1 = P/(P + 1/k) w2 = 1/k/(P + 1/k) Estimation of the cost effectiveness of a potential coun- and where k is the dispersion parameter for a given model and termeasure, such as a crossing. The objective is to pro- is estimated from the SPF calibration process with the use of a vide designers and planners with a guide to estimate the maximum likelihood procedure. In that process, a negative bi- change in WVC frequency expected with the installation of

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48 Table 21. Illustration of EB before-after study for U.S. Highway 40 and Utah Route 248 in Utah. Sum of SPF No. of Years Years AADT AADT Crashes Crashes Length Predictions k w1 w2 m Var (m) Var ( ) Site Lanes Before After Before After Before (x) After ( ) After 1 4 2.04 9 6 7654 13227 39 18 18.85 1.53 0.97 0.03 38.52 32.69 37.42 26.96 1 4 1.96 9 6 7450 13227 45 47 18.11 1.53 0.97 0.03 44.28 38.04 42.96 31.69 2 2 0.05 4 6 2630 7493 1 1 0.36 1.76 0.13 0.87 0.20 0.87 0.03 0.48 2 2 0.19 4 6 2630 7493 0 0 1.37 1.76 0.36 0.64 0.20 0.88 0.07 1.38 2 2 0.58 4 6 2630 7493 2 5 4.19 1.76 0.63 0.37 1.61 7.06 1.01 19.39 2 3 0.18 4 6 2630 7493 0 2 1.30 1.76 0.34 0.66 0.19 0.85 0.07 1.28 2 4 0.21 4 6 2630 7493 3 2 1.24 1.53 0.44 0.56 1.62 3.86 0.72 4.07 2 4 0.12 4 6 2553 7493 3 2 0.71 1.53 0.31 0.69 1.13 2.73 0.35 2.04 2 4 1.40 4 6 1707 3375 3 6 5.80 1.53 0.81 0.19 2.97 6.03 2.42 9.95 2 4 0.07 4 6 1707 3375 0 0 0.29 1.53 0.18 0.82 0.12 0.24 0.02 0.09 2 4 0.42 4 6 1707 3375 4 2 1.74 1.53 0.57 0.43 2.64 5.36 1.50 6.17 2 3 2.70 4 6 1707 3375 16 17 8.62 1.76 0.83 0.17 13.82 41.66 11.53 104.77 2 4 0.34 4 6 1707 3375 8 2 1.41 1.53 0.52 0.48 4.47 9.05 2.30 9.46 2 4 0.08 4 6 1707 3375 0 1 0.33 1.53 0.20 0.80 0.13 0.26 0.03 0.11 2 3 3.09 4 6 1707 3375 10 21 9.86 1.76 0.85 0.15 9.00 27.14 7.67 69.71 2 2 0.77 4 6 1707 3375 0 0 2.46 1.76 0.59 0.41 0.33 1.01 0.20 1.79 SUM 126 121.26 177.74 289.36 0.702 VAR( ) 0.008 S.E.( ) 0.091

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49 wildlife crossings and fencing at a segment of roadway period. The average AADT was observed to be 5,000 and is under consideration. assumed to increase by 5% following the proposed construc- For the approach, an SPF representative of the existing tion, although this anticipated increase in traffic is not related road segment is required. Therefore, an SPF must already to the contemplated construction. The SPF to be used is: exist for the jurisdiction or data must be available to enable a P = (years)(length)exp(-9.1135)(AADT)1.0237 ; k = 1.6098 recalibration of a model calibrated for another jurisdiction. The SPF would be used, along with the segment's collision Use the EB procedure to estimate the expected annual num- history, in the EB procedure to estimate the expected collision ber of WVCs that would occur without construction of the frequency with the status quo in place; that estimate of colli- crossing and fencing. sion frequency would then be compared to the expected frequency if a crossing and fencing were constructed in order P = (5)(2)exp(-9.1135)(5, 000)1.0237 = 6.74 to estimate their benefits. w1 = 6.74/(6.74 + 1/1.6098) = 0.92 This model application requires four steps: w2 = 1/1.6098/(6.74 + 1/1.6098) = 0.08 1. Assemble data and collision prediction models for road Last, the regression estimate (P) and the observed collision segments: count (x) are combined. a. Obtain the count of WVCs; b. For each year, obtain or estimate the average AADT; m = 0.92(18) + 0.08(6.74) = 17.1, or 3.4/year and The combination of a high dispersion parameter (k) and rel- c. Estimate the AADT that would prevail for the period atively long length of the segment leads to a relatively high immediately after construction. weight being given to the SPF estimate (P). 2. Use the EB procedure documented earlier, with the data Because traffic is expected to increase 5% in the period from Step 1, and the road segment model to estimate the ex- after the contemplated construction the estimate (m) is pected annual number of WVCs that would occur without adjusted by the ratio of the AADT term in the model: construction of the crossing and fencing. 3. Apply a Collision Modification Factor (CMF) to the ex- m* = 3.4*(5000 * 1.05)1.0237/(5000)1.0237 = 3.57/year pected collision frequency with the status quo in place to An appropriate CMF is applied to the estimate (m* ) to esti- get the expected benefit in terms of the number of annual mate the expected benefit in terms of the number of annual WVC expected to be reduced. A CMF is an adjustment to WVCs expected to be reduced. For this illustration assume the estimate based on the expected reduction in WVCs. that the expected reduction is 20% (i.e., that the CMF is Until a reliable CMF can be determined from properly (100-20)/100 = 0.8). conducted before-after studies, an interim CMF could be Annual Benefit = 0.20(3.57) = 0.71 wildlifevehicle collisions developed through an expert panel as has been done for other roadway safety countermeasures. 113 Apply the estimated cost per collision to the previously esti- 4. Compare against the cost, considering other impacts if mated annual WVC benefit to estimate the dollar value benefit desired, and using conventional economic analysis guides. per year. Compare this benefit against the annualized cost of The results of the analysis above may indicate that crossings construction, maintenance, and other relevant considerations. are justified based on a consideration of safety benefits. This justification should not be taken to mean that crossings Aspect 2: Comparison of WildlifeVehicle Collision should be constructed, because: and Carcass Removal Data a. Other measures may have higher priority in terms of cost effectiveness, The primary objective of this aspect of the safety data analy- b. The safety benefits may need to be assessed in the light sis was to investigate the hypothesis that the choice and appli- of other impacts, and cation of reported WVC and carcass removal data (as they c. Other locations may be more deserving of a crossing. In might exist and could be plotted at a DOT) could result in other words, the results of the above analysis should be varying policies or WVC countermeasure-related roadway de- fed into the safety resource allocation process. velopment decisions. One or both of these two databases have been used in the past to describe the magnitude of the WVC As an illustration, suppose a 2-mi long section of road, problem and to propose and evaluate the effectiveness of with data from 1998 to 2002, is being considered for the con- WVC countermeasures. Overall, the visual and quantitative struction of a wildlife crossing and fencing along the entire findings of the reported WVC and deer carcass removal com- section. This section experienced 18 WVCs during this time parison activities revealed that both their magnitudes and