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Currently, there are two methods that can be used for esti- its coefficients. The linear equation is given by the following
mating AMFs using regression models. The first method equation:
consists of estimating AMFs directly from the coefficients of
statistical models. This method has been used by Lord and Yi - i = 1 X1 + . . . + m X m (3)
Bonneson (42) for estimating AMFs for rural frontage roads
in Texas. Washington et al. (41) used a similar approach in where
their study. The AMFs are estimated the following way: µi = the predicted number of crashes for Site i per year
estimated by the baseline model;
AMFj = e ( × [ x
j j - y j ])
(2) Yi = observed number of crashes for Site i per year;
Xm = a vector of the baseline variables (each site not meeting
where one or more of these variables); and
xj = range of values or a specific value investigated (e.g., lane m = a vector of coefficients to be estimated.
width, shoulder width, etc.) for AMF j;
yj = baseline conditions or average conditions for the vari- The AMFs are estimated using the following relationship
able xj (when needed or available); and when the coefficients are found to be statistically significant
j = regression coefficient associated for the variable j. (e.g., at the 5% or 10% level):
i=1Yi n
n
This method provides a simple way to estimate the effects
of changes in geometric design features. However, although AMFm = (4)
Yi
i=1
n
the variables are supposed to be independent, they may be - m
n
correlated, which could affect the coefficients of the model.
The Variance Inflation Factor (VIF) can be used for detecting where
correlated variables, but this procedure usually flags only AMFm = AMF for Coefficient m, and
extreme cases of correlation among variables (43). n = the number of observations in the sample.
The second method consists of estimating the AMF using
baseline models and applying them to data that do not meet
Data Base
the nominal conditions (41). These models are developed
using data that reflect nominal conditions commonly used by As noted above, the initial approach was to evaluate the
design engineers or could also reflect the average values for safety implications from specific changes to values of design
some input variables. Such models usually include only traffic elements though a review and analysis of cases where such
flow as the input variable. Examples of nominal conditions flexibility changes were implemented. The meeting with the
for rural four-lane undivided highways may include 12-ft NCHRP project panel at the end of Phase I resulted in a sig-
lane and 8-ft shoulder widths, straight sections, and so forth. nificant change of the scope of the work and the type of data
It is anticipated that by controlling the input variables, the to be acquired. The discussion during the meeting focused on
models will more accurately estimate the safety performance the potential problems and issues identified from the original
of the facility for the given input conditions. However, an approach. That approach was centered on the identification
important drawback to developing baseline models is associ- of cases where design flexibility was used and was documented
ated with the smaller sample size. Because the input data only by a comparison of the safety performance of each case to
include data meeting the nominal conditions, the sample size control sites where no flexibility was required. A variety of
can be significantly reduced. This reduction can (1) affect the issues were identified that led to the need for another approach
model stability, especially if the sample mean value is low (44); to produce the most beneficial research. This research must
(2) increase the model error (variance); and (3) decrease the be useful in the ongoing HSM efforts, and that required this
statistical power of the model. Baseline models are currently revised approach. The project panel recommended that the
used for the HSM (45). research be concentrated on multilane rural roads and that it
The second method was proposed by Washington et al. (41), should be limited to specific design elements: lane width,
who have re-calibrated models for estimating the safety per- shoulder width, and median type and width. The possibility of
formance of rural signalized and unsignalized intersections. examining the contribution of clear zones was also discussed,
For this method, the baseline model is first applied to sites not but this decision was made contingent on a determination of
meeting all of the baseline conditions; then, the predicted and data availability and potential feasibility.
observed values per year are compared, and a linear relation- The first task in Phase II of the research was to identify
ship between these two values is estimated via a regression candidate states with crash data suitable for analysis. The plan
model to determine whether AMFs can be produced from was to retrieve crash data from the states participating in the
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HSIS database in a manner that would achieve a broad geo- evaluated the databases for these two states. The Kentucky
graphic distribution to ensure consideration of terrain, climate, data were also evaluated by the research team to provide
and other key factors. compatibility among the three data sets and to see that all
The states in the FHWA HSIS database include California, variables to be examined provided the same information
Illinois, Maine, Michigan, Minnesota, North Carolina, Utah, and values.
and Washington. Data availability varies among these states An effort was made to augment the Kentucky data with the
with respect to time periods (some have fewer years than others) available clear zone width for all segments included in the
as well as the type of information available (not all include database. Site visits were conducted at all 437 rural multilane
roadway geometry data in the crash records). Therefore, data segments in the database. The intent of these visits was to
from these states were evaluated with respect to the availability review the available information included in the state's High-
of the following data types and classes: (1) multilane rural way Information System and to determine its accuracy. Past
roads; (2) geometric elements including lane and shoulder work with this data indicated occasional inaccuracies regard-
width and median type and width; (3) crash severity level; and ing the geometric elements used. Kentucky is conducting a
(4) possibly, crash type. In addition, in order to stratify the similar review, but their results were not available at the
data and the potential crash models, the number of lanes and time of this research work. For each site, the lane, shoulder,
functional classification were needed. and median widths were measured, the shoulder and median
A review of the data available through HSIS for each state types were recorded, and an estimate was made of the available
found that only Ohio and Washington have data available for clear zone. The data were then used to update the geometry
horizontal and vertical curves. At the end of Phase I in 2005, file, which was in turn used to develop the crash database
2004 data were available from Minnesota and were being for analysis.
processed for the other states. In addition, data were available The final data base was developed by aggregating the
from Kentucky that had been used satisfactorily by the research individual state databases into one. For each state, a 12-year
team in the past. To achieve the objective of identifying period was used with examination of data covering 2,387 miles.
possible geographic differences among the states and, thus, to A further evaluation of the data to determine presence of
achieve a national perspective, the databases from California, all common available variables and values indicated that the
Kentucky, and Minnesota were selected for the Phase II majority of the segments (more than 95%) were four-lane
analysis. This allows for a reasonable geographic distribution facilities and most (more than 90%) had lane widths of 12 ft.
that should adequately cover roadways found throughout the These data indicate that there may be some concerns regarding
nation. A final element discussed at the project panel meeting the distribution of certain variables since a significant mileage
was the exclusion of intersections to create a database with was at specific values, which may not allow for the development
midblock sections only. of complete models. For example, it was envisioned to create
An understanding of the safety consequences for both the separate models for four- and six-lane facilities. However, the
total number and specific types of crashes is of interest in available data indicate that there are only 35 segments for
evaluating design element trade-offs. The change in the crash six-lane facilities accounting for 205.45 miles (8.6%) of the
rate will provide an understanding of the overall safety risks total mileage. Therefore, the decision was made to develop
of the applied trade-off. There are also specific crash types that models only for four-lane, 12-ft lane width segments. This
would be expected to occur due to a trade-off on a specific approach resulted in a new data set that had a total extent of
geometric element--for example, if the decision involved the 1,433.7 miles with 35,694 crashes of which 9,024 were injury
use of medians, the number of head-on crashes would be of crashes. The ADT ranged from 241 to 77,250 vehicles/day, and
particular interest. The analysis of such specific types of the total miles for divided highways was 1,241.4. All segments
crashes would provide an understanding of the effect of certain were classified as non-freeway, even though these facilities
types of decisions. Therefore, the number of all crashes and could qualify as rural multilane roadways and all have a
the number of specific crash types for each case would be col- length greater than 0.10 miles. An average of the left and right
lected for evaluating the safety trade-offs from varying values shoulder widths was used as the shoulder width since this
of design elements. An additional evaluation would focus on approach resulted in models with more reasonable and intu-
the severity of the crashes. It is possible that trade-offs for a itive coefficients. The average shoulder width is computed as
design element may not show significant impacts on roadway the mean of the left and shoulder width in the same direction
safety expressed in total crashes, but might affect the severity for divided highways and as the mean for the right shoulders in
of the crashes. undivided segments. Moreover, the shoulder type was checked
The California and Minnesota data used for this research to ensure that both shoulders used in the calculation are of
were provided by NCHRP Project 17-29, which was also the same type. All segments included in the final data set had
working on a similar issue and had already developed and the same type of left and right shoulders. Finally, all injury
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levels (ABC injuries) and fatalities (K) are included in the of the variables considered and the number of segments in
injury crashes. the final database by each state (as described above). In all
These state databases exhibited various values for commonly cases, the term "injury crash" denotes both injury and fatality
named variables. For example, the California database codes crashes.
median barrier types differently than do Minnesota and The data in Table 10 indicate that most segments are divided
Kentucky. It was important to decipher these differences and highways without median barriers, with shoulder widths
to determine the common categories and groups among all between 6 and 8 ft, and with traffic volumes between 5,000 and
three state databases. It became apparent that the commonality 15,000 vehicles/day. All are four-lane rural highways with
of data coding among these databases should be evaluated in 12-ft lanes. There are differences among the states for certain
order to avoid misinterpretation of the results. variables--for example, most of the roads with higher ADT
The unit of analysis in the model development process is a are in California, and they account for approximately one-third
highway segment that has homogenous geometry and traffic of the segments within the state. California and Minnesota
conditions. The database developed herein used this approach also had large numbers of segments with wide medians (greater
and, thus, allows for the development of models that will than 60 ft), while most median widths for Kentucky were
have the segment as a unit. Table 10 presents a summary narrower (more than one-half of the segments were less than
Table 10. Extent of variables in database.
Divided Undivided
Variable Categories CA KY MN CA KY MN
All 16,951 8,035 5,106 3,495 1,037 1,068
Crashes
Injury 4,045 2,765 681 995 405 133
Yes 571 539 615 164 73 84
Principal arterial
No 183 71 46 125 8 31
95 3 NA NA
Median barrier Yes 6 NA
659 607 NA NA
No 655 NA
Yes 624 530 595 243 68 47
Paved right shoulder
No 130 80 66 46 13 68
0 1 10 6 2 49
0
49 27 1 20 7 2
02
102 32 14 124 1 9
Average shoulder 24
width (ft) 87 218 99 36 19 13
46
412 329 536 75 31 18
68
104 3 1 28 21 24
8+
65 61 91 103 4 34
<5
116 172 268 80 31 38
510
181 239 178 53 23 32
ADT 1015
(vehicles/day; 000s) 131 89 92 34 12 10
1520
89 30 26 12 8
2025
172 19 6 7 3 1
>25
55 101 27 NA NA NA
<10
177 188 12 NA NA NA
1020
116 159 20 NA NA NA
2030
Median width (ft) 59 108 37 NA NA NA
3040
149 37 142 NA NA NA
4050
32 14 185 NA NA NA
5060
>60 166 3 238 NA NA NA
