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166
APPENDIX G
GLM Analysis Results for Effect
of Shoulder Rumble Strip Offset
and Recovery Area on Safety
This appendix presents the companion tables to the four where a (i.e., intercept), b, and c are the coefficients whose
cross-sectional generalized linear model (GLM) analyses inves- estimates are shown in Table G-1. The companion coefficients
tigating the effect of shoulder rumble strip offset. for rumble strip placement, d, at two levels (edgeline vs. non-
edgeline) as compared to no RS, are shown in Table 42.
· Table G-1 presents the GLM results to investigate the effect Table G-2: The statistics shown for all sites and states
of shoulder rumble strip placement (edgeline vs. non-edge- combined include the estimate for:
line) on SVROR FI crashes based on all site types; it is the
· Intercept
companion table to Table 42.
· ADT (on natural log scale)
· Table G-2 presents the GLM results to investigate the overall
· Outside RHR
effect of shoulder rumble strip placement on SVROR FI
· Overdispersion parameter
crashes across all sites in all states; it is the companion table
to Table 43. The single regression model is represented by the following
· Table G-3 presents the GLM results to investigate the effect equation:
of shoulder rumble strip offset (at three levels) on SVROR
Expected total crashes mi yr =
FI crashes based on all site types; it is the companion table
to Table 44. exp {( a + b × lnADT + c × RHR Out + d × RS Placement )
· Table G-4 presents the GLM results to investigate the com-
× IRoadway type×State }
bined effect of shoulder rumble strip offset and recovery
area on SVROR FI crashes based on all site types; it is the where a (i.e., intercept), b, and c are the coefficients whose
companion table to Table 45. estimates are shown in Table G-2. The variable IRoadway type×State
is an indicator variable with value 1 for a particular roadway
Number of sites, number of site-years, offset, and offset × type × state combination in the table, and zero otherwise. The
recovery area statistics for each model are provided in the companion coefficients for rumble strip placement, d, at two
corresponding Tables 42 through 45. levels (edgeline vs. non-edgeline) as compared to no RS, are
Table G-1: The statistics shown for each roadway type and shown in Table 43.
state (combined or single) include: Table G-3: The statistics shown for each roadway type and
state (combined or single) include:
· Intercept: estimate and standard error
· Intercept: estimate and standard error
· ADT (on natural log scale): estimate, standard error, and
· ADT (on natural log scale): estimate, standard error, and
p-value (i.e., significance level)
· Outside RHR: estimate, standard error, and p-value
p-value (i.e., significance level)
· Outside RHR: estimate, standard error, and p-value
· Overdispersion parameter: estimate and standard error
· Overdispersion parameter: estimate and standard error
Each regression model is represented by the following Each regression model is represented by the following
equation: equation:
Expected total crashes mi yr = Expected total crashes mi yr =
exp ( a + b × lnADT + c × RHR Out + d × RS Placement ) exp ( a + b × lnADT + c × RHR Out + d × Offset )

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Table G-1. GLM estimates for SVROR FI crashes based on all sites--rumble strip placement analysis.
Intercept lnADT Outside RHR Overdispersion
Roadway type State Estimate SE Estimate SE pvalue Estimate SE pvalue Estimate SE
Urban freeways PA 6.92 1.15 0.67 0.11 <.0001 0.20 0.07
Combined 8.76 1.46 0.79 0.15 <.0001 0.21 0.11 0.0622 0.19 0.06
Rural freeways MO 7.02 1.79 0.67 0.18 0.0002 0.20 0.07
a
PA
Combined 7.25 1.47 0.59 0.16 0.0003 0.30 0.10 0.0024 0.44 0.09
Rural multilane
MN 9.73 1.47 0.90 0.15 <.0001 0.20 0.07
divided highways
(nonfreeways) MO 15.06 3.93 1.55 0.42 0.0002 0.58 0.20
PA 0.05 0.28 0.57 0.32
Combined 5.46 0.77 0.31 0.10 0.0014 0.41 0.06 <.0001 0.84 0.13
MN 4.49 1.20 0.25 0.15 0.09 1.15 0.33
Rural twolane roads a
MO
a
PA
b Combined 5.38 0.79 0.31 0.10 0.003 0.41 0.06 <.0001 0.86 0.14
Rural two-lane roads
MN 3.83 1.20 0.17 0.15 0.28 1.21 0.46
a
LM algorithm did not converge.
b
Excludes 53 Minnesota nontreatment cross-sectional sites.

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168
Table G-2. GLM estimates for SVROR FI crashes based on all sites--
overall rumble strip placement analysis.
Intercept
Roadway type State (or state effect) lnADT Outside RHR Overdispersion
Urban freeways PA 3.70 0.62 0.07
MO 4.29 0.66 0.12
Rural freeways
PA 6.82 0.87 0.27
Rural multilane MN 6.00 0.82 0.07
divided highways MO 11.11 1.42 0.13 0.29
(nonfreeways)
PA 2.14 0.38 0.39
MN 0.93 0.06 0.43
Rural twolane roads MO 6.01 0.45 0.98
PA 3.01 0.25 0.0008
where a (i.e., intercept), b, and c are the coefficients whose where a (i.e., intercept), b, and c are the coefficients whose
estimates are shown in Table G-3. The companion coefficients estimates are shown in Table G-4. The companion coeffi-
of offset distance, d, at three levels as compared to no RS, are cients, d, for the combination offset × recovery area, at five
shown in Table 44. levels as compared to no RS with narrow shoulders, are
Table G-4: The statistics shown for each roadway type and shown in Table 45.
state (combined or single) include: Tables G-1 through G-4: For states that treat both sides
of a divided highway as separate sites (i.e., Missouri and
· Intercept: estimate and standard error Pennsylvania), the RHR variables in the models represent the
· ADT (on natural log scale): estimate, standard error, and values for a single side of the divided highway. When both sides
p-value (i.e., significance level) of a divided highway are treated as a single site (i.e., Minnesota
· Outside RHR: estimate, standard error, and p-value sites), the RHR variables in the model represent average values
· Overdispersion parameter: estimate and standard error
for both directions of travel. Similarly, the RHR variable in
the models for rural two-lane roads represents the average
RHR for both sides of the roadway.
Each regression model is represented by the following
No GLM results are shown in those cases where the algo-
equation:
rithm did not converge. Empty cells in those cases where the
GLM algorithm did converge indicate that the corresponding
Expected total crashes mi yr =
coefficient estimate is not statistically significant at the 0.15
exp ( a + b × lnADT + c × RHR Out + d × Offset × RA ) level or that the coefficient's sign is not in the expected direction.

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Table G-3. GLM estimates for SVROR FI crashes based on all sites--offset analysis.
Intercept lnADT Outside RHR Overdispersion
Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE
Urban freeways PA 6.92 1.15 0.67 0.11 < .0001 0.20 0.07
Combined 8.73 1.51 0.78 0.16 < .0001 0.21 0.12 0.068 0.19 0.06
Rural freeways MO 6.74 1.77 0.65 0.18 0.0004 0.20 0.07
a
PA
Combined 7.36 1.56 0.60 0.17 0.001 0.29 0.10 0.003 0.43 0.09
Rural multilane
MN 8.90 1.47 0.82 0.15 < .0001 0.19 0.07
divided highways
(nonfreeways) MO 15.06 3.93 1.55 0.42 0.0002 0.58 0.20
a
PA
Combined 5.48 0.77 0.31 0.10 0.001 0.42 0.06 <.0001 0.84 0.13
MN 4.32 1.20 0.23 0.15 0.123 1.13 0.33
Rural two-lane roads a
MO
a
PA
a
GLM algorithm did not converge.
Table G-4. GLM estimates for SVROR FI crashes based on all sites--combined rumble strip offset and recovery area.
Intercept lnADT Outside RHR Overdispersion
Roadway type State Estimate SE Estimate SE pvalue Estimate SE pvalue Estimate SE
Urban freeways PA 5.85 1.21 0.60 0.11 <.0001 0.18 0.07
Combined 0.54 0.26 0.07
Rural freeways MO 7.02 1.79 0.67 0.18 0.0002 0.20 0.07
PA 0.54 0.24 0.11
Combined 6.59 1.49 0.60 0.16 0.0003 0.29 0.10 0.004 0.43 0.09
Rural multilane
MN 9.73 1.47 0.90 0.15 <.0001 0.20 0.07
divided highways
(nonfreeways) MO 15.11 3.91 1.55 0.42 0.0002 0.58 0.20
PA 0.81 0.00 0.48 0.30
Combined 5.45 0.78 0.34 0.11 0.0021 0.39 0.07 <.0001 0.81 0.12
MN 4.50 1.33 0.25 0.19 0.1774 1.14 0.33
Rural twolane roads
MO 0.65 0.75 0.23
PA 0.89 0.59 0.15