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161 APPENDIX F GLM Analysis Results for Safety Effectiveness of Shoulder Rumble Strips This appendix presents the generalized linear model (GLM) Each regression model is represented by the following results to investigate the effect of treatment with shoulder equation: rumble strips on the four crash types of interest: Expected crashes mi yr = exp ( a + blnADT + cRHR Out + dIRS ) TOT crashes FI crashes where a (i.e., intercept), b, c, and d are the coefficients whose SVROR crashes estimates are shown in Tables F-1 through F-8. The coeffi- SVROR FI crashes cient d only applies to treatment sites since IRS is a 0,1 variable where 0 indicates absence and 1 presence of shoulder rumble Two groups of tables are presented in this appendix: strips. For states that treat both sides of a divided highway as separate sites (i.e., Missouri and Pennsylvania), the RHR vari- Tables F-1 through F-4: GLM results based on all site ables in the models represent the values for a single side of the types (i.e., all nontreatment and treatment sites in the divided highway. When both sides of a divided highway are study) treated as a single site (i.e., Minnesota sites), the RHR variables Tables F-5 through F-8: GLM results based on all before-after in the model represent average values for both directions sites and nontreatment cross-sectional sites (i.e., same sites as of travel. Similarly, the RHR variable in the model for rural in Tables G-1 through G-4 but without treatment cross- two-lane roads represents the average RHR for both sides of sectional sites). These results should be most comparable to the roadway. the SPF results since both approaches use the same types of Tables F-1 through F-8 are the companion tables to Tables 29 sites. through 36. Number of sites and number of site-years for each model are provided in those tables. To obtain the percent The statistics shown for each crash type, roadway type, and change due to rumble strip treatment shown in Tables 29 state (individually or combined) are: through 36, use the rumble strip coefficient, d, shown in Tables F-1 through F-8 and calculate: Intercept: estimate and standard error ADT (on natural log scale): estimate, standard error, and Percent change = 100 [ exp ( d ) - 1] p-value (i.e., significance level) Outside RHR: estimate, standard error, and p-value Lower and upper 95-percent confidence intervals for the Rumble strip effect: estimate, standard error, and p-value. percent change are calculated in a similar fashion based on Rumble strip statistics are bolded whenever the effect is lower and upper 95-percent confidence intervals of the esti- statistically significant at the 0.10 level mates in Tables F-1 through F-8 (confidence limits calculated Overdispersion parameter: estimate and standard error but not shown in these tables).

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Table F-1. GLM estimates for TOT crashes based on all site types. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 9.53 1.04 1.00 0.10 <.0001 0.15 0.10 0.111 0.04 0.06 0.496 0.22 0.03 Combined 9.22 1.46 1.04 0.15 <.0001 0.01 0.07 0.890 0.23 0.03 Rural freeways MO 6.55 2.11 0.79 0.21 0.000 0.08 0.07 0.227 0.19 0.03 PA 4.27 1.85 0.50 0.19 0.008 0.08 0.11 0.480 0.21 0.05 Combined 5.90 1.10 0.64 0.12 <.0001 0.26 0.06 <.0001 0.18 0.08 0.021 0.24 0.03 Rural multilane MN 8.03 1.07 0.88 0.12 <.0001 0.15 0.06 0.010 0.15 0.08 0.053 0.11 0.02 divided highways (nonfreeways) MO 6.53 2.96 0.81 0.31 0.009 0.25 0.11 0.027 0.42 0.08 PA 0.97 4.23 0.20 0.46 0.653 0.21 0.24 0.374 0.23 0.12 Combined 6.27 0.87 0.66 0.10 <.0001 0.26 0.04 <.0001 0.15 0.11 0.178 0.54 0.04 Rural two-lane MN 5.72 1.11 0.56 0.14 <.0001 0.31 0.05 <.0001 0.04 0.07 0.594 0.27 0.04 roads MO 4.71 2.01 0.64 0.23 0.006 0.18 0.88 0.836 0.99 0.11 PA 4.55 0.80 0.57 0.10 <.0001 0.28 0.19 0.145 0.36 0.06 a Statistics are bolded when p 0.10. Table F-2. GLM estimates for FI crashes based on all site types. Intercept lnADT Outside RHR Rumble strips a Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 11.19 1.27 1.08 0.12 <.0001 0.20 0.12 0.086 0.10 0.08 0.222 0.28 0.05 Combined 10.55 1.26 1.08 0.13 <.0001 0.08 0.07 0.284 0.10 0.03 Rural freeways MO 9.95 1.67 1.02 0.17 <.0001 0.03 0.09 0.758 0.12 0.04 PA 10.16 2.32 1.04 0.24 <.0001 0.12 0.12 0.316 0.06 0.07 Rural multilane Combined 7.71 1.24 0.72 0.13 <.0001 0.23 0.07 0.001 0.01 0.11 0.956 0.22 0.04 divided MN 9.18 1.27 0.90 0.14 <.0001 0.11 0.07 0.131 0.07 0.09 0.474 0.09 0.04 highways MO 14.93 3.71 1.59 0.40 <.0001 0.05 0.20 0.799 0.38 0.12 (nonfreeways) PA 0.28 0.24 0.54 0.27 0.045 0.40 0.22 Combined 7.16 0.77 0.65 0.09 <.0001 0.31 0.05 <.0001 0.32 0.12 0.006 0.50 0.06 Rural two-lane MN 6.45 1.10 0.53 0.14 0.0002 0.31 0.06 <.0001 0.14 0.10 0.155 0.24 0.08 roads MO 8.37 1.95 0.61 0.25 0.013 0.71 0.19 0.0002 0.51 0.75 0.501 0.51 0.11 PA 5.44 0.86 0.61 0.10 <.0001 0.18 0.22 0.415 0.37 0.08 a Statistics are bolded when p 0.10.

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Table F-3. GLM estimates for SVROR crashes based on all site types. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 6.79 0.90 0.72 0.09 <.0001 0.04 0.08 0.625 0.19 0.04 Combined 5.94 1.57 0.65 0.16 <.0001 0.10 0.07 0.175 0.25 0.04 Rural freeways MO 5.41 2.31 0.61 0.23 0.009 0.07 0.07 0.357 0.23 0.04 PA 3.42 2.40 0.29 0.25 0.256 0.26 0.14 0.057 0.02 0.13 0.875 0.26 0.07 Combined 7.11 1.08 0.62 0.11 <.0001 0.39 0.08 <.0001 0.35 0.12 0.004 0.39 0.05 Rural multilane MN 8.74 1.21 0.83 0.13 <.0001 0.17 0.08 0.035 0.33 0.12 0.006 0.24 0.05 divided highways (nonfreeways) MO 12.64 2.98 1.26 0.32 <.0001 0.34 0.22 0.128 0.53 0.16 0.001 0.45 0.12 PA 0.59 6.16 0.12 0.65 0.855 0.27 0.17 0.117 0.17 0.14 Combined 5.24 0.83 0.37 0.10 0.0002 0.42 0.05 <.0001 0.35 0.17 0.037 0.72 0.07 Rural two-lane MN 3.82 0.83 0.10 0.10 0.353 0.50 0.08 <.0001 0.18 0.13 0.180 0.51 0.13 roads MO 0.33 0.18 0.09 0.79 0.906 1.23 0.18 PA 2.64 0.89 0.28 0.11 0.008 0.60 0.22 0.008 0.49 0.09 a Statistics are bolded when p 0.10. Table F-4. GLM estimates for SVROR FI crashes based on all site types. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 6.92 1.15 0.67 0.11 <.0001 0.02 0.10 0.862 0.20 0.07 Combined 8.53 1.48 0.76 0.15 <.0001 0.22 0.11 0.042 0.15 0.08 0.078 0.19 0.06 Rural freeways MO 6.75 1.85 0.65 0.19 0.001 0.13 0.10 0.173 0.20 0.07 PA 9.99 2.78 0.89 0.29 0.002 0.29 0.16 0.076 0.14 0.16 0.383 0.17 0.10 Combined 7.19 1.48 0.58 0.16 0.0004 0.32 0.10 0.001 0.05 0.14 0.738 0.45 0.09 Rural multilane MN 9.50 1.49 0.88 0.15 <.0001 0.12 0.14 0.398 0.22 0.08 divided highways (nonfreeways) MO 15.15 3.96 1.56 0.42 0.000 0.17 0.21 0.422 0.59 0.20 PA 0.07 0.28 0.40 0.28 0.156 0.58 0.32 Combined 5.46 0.77 0.32 0.10 0.001 0.41 0.06 <.0001 0.47 0.16 0.004 0.85 0.13 Rural two-lane MN 4.50 1.19 0.26 0.15 0.084 0.04 0.17 0.840 1.16 0.33 roads MO 8.46 2.18 0.40 0.24 0.094 0.95 0.15 <.0001 0.90 1.38 0.515 0.19 0.14 PA 2.96 0.94 0.25 0.12 0.035 0.47 0.24 0.054 0.57 0.14 a Statistics are bolded when p 0.10.

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Table F-5. GLM estimates for TOT crashes based on before and after sites and nontreatment cross-sectional sites. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 9.30 1.23 1.03 0.12 <.0001 0.05 0.06 0.372 0.22 0.03 Combined 8.83 1.75 1.01 0.18 <.0001 0.07 0.07 0.363 0.21 0.03 Rural freeways MO 5.38 2.63 0.68 0.26 0.010 0.11 0.07 0.113 0.19 0.03 PA 1.03 2.32 0.17 0.24 0.492 0.06 0.15 0.677 0.14 0.05 Combined 5.46 1.30 0.60 0.14 <.0001 0.24 0.08 0.003 0.25 0.08 0.004 0.29 0.03 Rural multilane MN 7.44 1.46 0.82 0.17 <.0001 0.14 0.08 0.086 0.15 0.12 0.185 0.12 0.03 divided highways (nonfreeways) MO 6.59 3.18 0.82 0.34 0.014 0.24 0.11 0.028 0.42 0.08 PA 1.11 4.54 0.22 0.49 0.656 0.30 0.31 0.337 0.26 0.13 Combined 5.96 0.87 0.64 0.10 <.0001 0.23 0.04 <.0001 0.06 0.14 0.680 0.59 0.04 Rural two-lane MN 5.16 1.09 0.49 0.13 0.000 0.34 0.05 <.0001 0.16 0.09 0.058 0.31 0.06 roads MO 4.79 2.05 0.65 0.24 0.007 0.17 0.93 0.858 0.99 0.12 PA 4.55 0.80 0.57 0.10 <.0001 0.28 0.19 0.145 0.36 0.06 a Statistics are bolded when p 0.10. Table F-6. GLM estimates for FI crashes based on before and after sites and nontreatment cross-sectional sites. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 10.24 1.50 1.05 0.14 <.0001 0.23 0.10 0.019 0.29 0.05 Combined 9.51 1.58 0.97 0.16 <.0001 0.04 0.09 0.631 0.12 0.04 Rural freeways MO 9.70 2.26 0.99 0.23 <.0001 0.01 0.10 0.888 0.13 0.04 PA 5.19 3.37 0.52 0.35 0.134 0.09 0.15 0.555 0.08 0.08 Combined 7.49 1.52 0.70 0.17 <.0001 0.23 0.09 0.007 0.05 0.17 0.766 0.29 0.06 Rural multilane MN 8.70 1.48 0.87 0.15 <.0001 0.20 0.18 0.278 0.08 0.05 divided highways (nonfreeways) MO 15.91 3.83 1.70 0.41 <.0001 0.02 0.21 0.929 0.38 0.12 PA 1.02 9.61 0.14 1.03 0.893 0.58 0.29 0.045 0.41 0.22 Combined 6.86 0.75 0.63 0.09 <.0001 0.28 0.05 <.0001 0.16 0.13 0.244 0.54 0.06 Rural two-lane MN 5.99 1.06 0.47 0.13 0.000 0.31 0.06 <.0001 0.07 0.15 0.648 0.28 0.10 roads MO 8.46 1.91 0.63 0.24 0.010 0.70 0.19 0.000 0.44 0.76 0.567 0.50 0.11 PA 5.44 0.86 0.61 0.10 <.0001 0.18 0.22 0.415 0.37 0.08 a Statistics are bolded when p 0.10.

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Table F-7. GLM estimates for SVROR crashes based on before and after sites and nontreatment cross-sectional sites. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 7.26 1.11 0.77 0.11 <.0001 0.10 0.11 0.339 0.19 0.05 Combined 5.16 2.02 0.58 0.21 0.005 0.10 0.08 0.214 0.26 0.04 Rural freeways MO 5.15 3.12 0.58 0.31 0.063 0.06 0.08 0.453 0.26 0.05 PA 0.18 0.08 0.14 0.18 0.450 0.16 0.08 Rural multilane Combined 7.12 1.25 0.64 0.13 <.0001 0.33 0.09 0.0003 0.51 0.14 0.0002 0.42 0.06 divided MN 8.58 1.41 0.86 0.14 <.0001 0.30 0.10 0.002 0.20 0.06 highways MO 13.09 3.08 1.31 0.34 <.0001 0.33 0.22 0.137 0.51 0.16 0.002 0.46 0.12 (nonfreeways) PA 0.46 6.31 0.11 0.67 0.874 0.26 0.17 0.141 0.18 0.14 Combined 5.23 0.83 0.38 0.10 0.0002 0.41 0.05 <.0001 0.30 0.22 0.177 0.73 0.08 Rural two-lane MN 3.60 0.85 0.06 0.11 0.578 0.52 0.08 <.0001 0.11 0.18 0.523 0.46 0.16 roads MO 0.32 0.18 0.06 0.79 0.940 1.21 0.17 PA 2.64 0.89 0.28 0.11 0.008 0.60 0.22 0.008 0.49 0.09 a Statistics are bolded when p 0.10. Table F-8. GLM estimates for SVROR FI crashes based on before and after sites and nontreatment cross-sectional sites. a Intercept lnADT Outside RHR Rumble strips Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA 6.95 1.39 0.67 0.13 <.0001 0.10 0.13 0.43 0.18 0.08 Combined 6.61 1.89 0.63 0.19 0.001 0.19 0.10 0.05 0.21 0.07 Rural freeways MO 8.20 2.37 0.79 0.24 0.001 0.15 0.11 0.18 0.22 0.08 PA 1.86 3.25 0.14 0.34 0.680 0.25 0.20 0.21 0.17 0.13 Combined 7.07 1.79 0.57 0.20 0.004 0.30 0.12 0.014 0.14 0.20 0.50 0.52 0.11 Rural multilane MN 8.15 1.71 0.74 0.18 <.0001 0.16 0.19 0.40 0.16 0.09 divided highways (nonfreeways) MO 16.48 3.99 1.70 0.43 <.0001 0.11 0.21 0.60 0.60 0.21 PA 0.04 0.29 0.24 0.20 0.23 0.59 0.32 Combined 5.39 0.80 0.31 0.10 0.003 0.41 0.06 <.0001 0.50 0.20 0.01 0.86 0.14 MN 3.83 1.22 0.17 0.16 0.286 0.26 0.25 0.30 1.26 0.47 Rural two-lane roads MO 8.49 2.16 0.41 0.24 0.087 0.94 0.15 <.0001 0.84 1.43 0.56 0.19 0.14 PA 2.96 0.94 0.25 0.12 0.035 0.47 0.24 0.05 0.57 0.14 a Statistics are bolded when p 0.10.