Semisequicentennial Transportation Conference Proceedings

May 1996, Iowa State University, Ames, Iowa

# Determination of a Discriminant Function as a Prediction Model for Effectiveness of Speed Zoning in Urban Areas

Fred Coleman and William C. Taylor

F. Coleman III,

Department of Civil Engineering,

University of Illinois at Urbana-Champaign Urbana,

Illinois 61801. W.C. Taylor,

Department of Civil and Environmental Engineering,

Michigan State University,

East Lansing, Michigan 48824.

Speed zoning is the application of a different speed limit to a section of roadway than is applicable to adjoining highway segments. Speed zoning traditionally has been based on one of two similar procedures, one relying primarily on the 85th percentile speed and engineering judgment and the second, which includes 85th percentile speed, with some form of quantification of environmental and geometric variables to reduce the speed limit below the 85th percentile speed. Three problems exist with the current practice of establishing speed zones. First is that traffic engineers have no way of predicting if their speed zoning actions will result in better compliance with the speed limit. Second it is unclear whether the section will make the driving environment safer resulting in fewer accidents. The third problem is that where states have procedures which quantify and use environmental and geometric variables, the empirical basis for their exclusion or inclusion has not been validated. This study was conducted using discriminant analysis to determine if a quantifiable relationship between accident parameters, speed parameters, roadside friction, and environmental/geometric variables can be used to predict the effectiveness of proposed speed zoning actions. The findings are that the most significant variables identified by the discriminant functions for effective zones were: skewness index (negatively skewed), signalization, driveway frequency, and 85th percentile speed.

Speed zoning has traditionally been based on one of two similar procedures, one relying primarily on the 85th percentile speed and engineering judgment, and the second, utilizing the 85th percentile speed, with some form of quantification of environmental and geometric variables to reduce the speed limit below the 85th percentile speed.

The results of prior research conducted in speed zoning effectiveness
indicate the results are mixed in regards to the relationship
between setting speed limits at the 85th percentile speed and
accident improvement. In a study by Parker (*1*) of speed
zones in Michigan he reported that 46 of the zones resulted in
an increase in accidents while 19 resulted in a decrease. Taylor
and Coleman (*2*) report similar results for a study of speed
zones in Muskegon County, Michigan. They found that 16 sites exhibited
an increase in accidents following implementation of a speed limit,
while 16 exhibited a reduction in accidents.

In a 1985 Federal Highway Administration (*3*) survey of
state and local transportation officials four factors received
the highest frequency response as part of their speed zoning procedure.
In descending order they are: 85th percentile speed, accidents
and pace speed tied for second, type and amount of roadside development
was fourth. These four factors are measurable in quantitative
units and are utilized by a number of states as part of a procedure
to adjust the speed limit.

The purpose of this research is to identify additional factors which can be used to determine where speed zoning will be effective and to clarify their relationship to raising or lowering the speed limits. The hypothesis is that a quantifiable relationship exists between accident parameters, speed parameters, roadside friction, and environmental/geometric variables such that it is possible to predict the effectiveness of speed zoning in urban areas. It is hypothesized that specific variables exists which can serve as predictors of the effectiveness of proposed speed zoning actions.

The premise of this analysis is that it is possible to discriminate between effective speed zones and noneffective speed zones based on identifying significant variables and characteristics of these road segments.

**METHODOLOGY**

**Experimental Design**

The research methodology used is a multi-stage process to create and compare comparable groups of speed zones distinguished by their effectiveness or noneffectiveness as measured by accident reduction. The first stage is to determine effective versus noneffective speed zones using the Before and After with comparison groups experimental design. Speed zones studies which resulted in a change in the speed limit were considered treatment zones and those road segments studied where the decision was made not to change the speed limit were used as control zones. Zone matching of treatment and control zones for comparability was based on the criteria of speed limits (prior to change), volume, laneage, type (i.e. urban or transition), and length. The number and type of zones by zoning action are presented in Table 1.

**Individual Zone Effectiveness Leading to Effective and Noneffective Group Formation**

Each speed zone was analyzed for its effectiveness in reducing
accidents after treatment, in this case a speed zoning change
of raising or lowering the speed limit. The primary focus of this
effort was to determine which zones were individually effective
in comparison to their matched control zone in reducing accident
frequency. The methodology was to use the treatment and control
zones before and after accident frequencies, along with the number
of years in the treatment after period to produce an expected
accident frequency for the treatment zones. A percentage improvement
was derived based on the difference between the expected and actual
accident frequency. Poisson curves (*4*) based on expected
after accident frequencies without treatment and percentage improvement
were used to determine a significance level. This procedure was
applied to each zone and groups of zones based on speed zoning
action and type of zone. Table 2 presents the results of this
procedure stratified by zoning action and accident categories.

Table 3 is the summary of the number of zones determined to be effective at the 85 percent level of significance. Normally, a 95 percent level of significance would be utilized; however, since the total number of zones in the study was small (26) and the majority of effective sites were greater than 95 percent level of significance, and only two sites would be affected by this change it was concluded this would not jeopardize the results. The results in Table 3 determine the mutually exclusive groups which is the primary methodological requirement for using discriminant analysis.

**Discriminant Analysis**

Discriminant analysis is a multivariate statistical procedure
which analyzes differences between mutually exclusive groups through
linear relationships between variables to create the largest distance
between the groups. This procedure was used to determine how the
effective groups differ from the noneffective. The key measures
of effectiveness used to determine the best discriminant function
are eigenvalue, Wilks' lambda and percent correctly classified.
Wilks' lambda has a range between "1.0" and "0.0",
with values close to zero indicating a function providing the
best separation between groups. Wilks' lambda was selected over
alternative measures due to its close underpinnings to Analysis
of Variance, using the ratio of the within-groups sum of squares
to the total groups sum of squares. This yields the proportion
of the total variance in the discriminant scores not explained
by differences among groups. Norusis (*5*) indicates "Small
values of lambda are associated with discriminant functions that
have much variability between groups and little variability within
groups."

**Variable Selection**

There were approximately 200 variables in the initial data set. Correlation analysis and crosstabulation analysis reduced this to 32 variables. Forward stepwise variable selection was used to identify an initial set of variables which minimized Wilks' lambda. Further analysis allowed identification of a smaller number of variables which contributed approximately 80-85 percent of the total reduction in Wilks' lambda.

**Analysis Categories**

Four group comparisons were formulated for analysis. These are as follows:

- Before Period Raised and Lowered Effective vs Before Period Raised and Lowered Non-Effective (BP2 RAISLOW EFF ALL vs BP2 RAISLOW NON-EFF ALL)
- Before Period Raised and Lowered Effective {Rear Ends} vs Before Period Raised and Lowered Non-Effective {Rear Ends} (BP2 RAISLOW EFF ALL vs BP2 RAISLOW NON-EFF ALL—REAR END ACCIDENTS ONLY)
- After Period Raised and Lowered Effective vs After Period Raised and Lowered Non-Effective (AP2 RAISLOW EFF ALL vs AP2 RAISLOW NON-EFF ALL)
- After Period Raised and Lowered Effective {Rear Ends} vs After Period Raised and Lowered Non-Effective {Rear Ends} (AP2 RAISLOW EFF ALL vs AP2 RAISLOW NON-EFF ALL—REAR END ACCIDENTS ONLY).

The before period effective versus noneffective comparisons were used to identify those variables which separate effective and noneffective groups based on variable values existing prior to changing the speed limit. The utilization of the combined speed raised and lowered effective groups in comparison with control counterparts was to determine what variables (regardless of speed zoning action) distinguish effective zones from noneffective zones. These are the variables that can be used to predict the performance of a proposed change in the speed limit. Analysis by all and rear end accident types were conducted to determine whether variables change based on the accident type investigated.

The after period analysis allows comparison of the variables differentiating the effective versus noneffective speed zones based on variable values measured after the speed limit change. This would allow the analyst to predict the success (or lack of success) in reducing accidents based on measured changes in the traffic characteristics resulting from the implementation of the speed limit.

**Before Period Discriminant Analysis Findings**

Results from the discriminant analysis for the before period comparison are shown in Table 4. The before period comparison for all accident types combined and rear end accidents only indicated similar discriminant analysis statistics. The findings indicate that for both accident groupings inclusion of speed variables improves all the measures of effectiveness with the exception of Correct Classification for Group 1, which is the effective zones grouping. The significance of this finding is that: 1) The importance of speed variables in distinguishing between effective and noneffective zones is confirmed, and 2) Even without speed variables, the models correctly classify a high percentage of the cases as effective and noneffective zones.

The variables found to be good predictors of the effectiveness of speed zoning in the before period were signalization, driveways, and negative skewness index. The noneffective zones for all accidents and rear end accidents had 62 percent and 63 percent of their accidents respectively near signalized intersections, while effective zones had 25 percent and 23 percent of their accidents respectively near signalized intersections.

The noneffective zones had over two-thirds of their accidents at locations where no driveways were in the immediate vicinity. The mean number of driveways per tenth of a mile for effective zones were 3.1 and 3.2 for all and rear ends respectively, while for noneffective zones the values were 1.0 and .80 respectively.

The mean skewness index for effective zones was found to be negatively skewed with values of .56 and .52 for all and rear ends respectively. A negatively skewed distribution indicates the majority of drivers are traveling above the mean and grouped close to the 85th percentile. A normal distribution would have a skewness value of 1.0. The value for noneffective zones was found to be 1.03 and 1.02 for all and rear ends respectively. This finding for effective zones further substantiates the axiom that safety is enhanced when the majority of drivers are traveling at or near the same speed.

85th percentile speeds were also identified as a significant variable in this data set, however since it contained both speed raised and lowered effective and noneffective zones, the overlap in ranges in 85th percentile speed was not considered here to be a good predictor of success in speed zoning. However, where only speed raised or lowered was analyzed in this same manner, 85th percentile speed was determined to be a good predictor of success.

**After Period Discriminant Analysis Findings**

The after period analysis allows comparison of the variables differentiating the effective versus noneffective speed zones after the speed limit change. The limitation of no speed data for zones in the after period prevents the direct comparison of speed variables in the discriminant analysis between the before and after periods. The results of the discriminant analysis is indicated in Table 5.

The comparison of measures of effectiveness (MOEs) between the after period and the before period indicate they compare favorably with those in Table 4. Eigenvalues and Wilks' lambda are comparable and the percentage of cases correctly classified is similar.

The absence of speed variables limits the variables to land use, geometric, and environmental variables. The specific findings are that driveway frequency, specific laneage types, and a mixture of retail and residential land uses were found to provide the environment where speed zoning is effective. Noneffective zones accidents are characterized by a majority of the accidents being non-drive related (73 percent for all accidents and 74 percent for rear end accidents). The after period distribution for effective zones was found to have the same type of distribution as the before period. The specific laneage types in effective zones was five lane highways, as oppose to four lane highways in noneffective zones.

Although five lane highways were not a statistically significant variable in the before period discriminant function, a majority of the effective zones were on five lane highways. Driveways in the after period were found to have the same 3:1 ratio between effective and noneffective zones as in the before period.

**CONCLUSIONS**

The findings from the discriminant analysis performed on the combined raised and lowered data sets with all and rear end accidents have identified factors or characteristics from the mutually exclusive effective and noneffective data sets. These factors which distinguished effective and noneffective speed zones were driveway frequency (density), signalization, a negative skewness index, and to a lesser degree 85th percentile speed. The speed variables were seen to be highly significant in improving the overall performance of the discriminant function, indicating their value as predictive factors of effectiveness for candidate zones. When speed variables were not part of the discriminant function in the before period analysis on the same data set, a mixed land use of retail and single family residential were seen to be good predictors of success in speed zoning. This finding supports the driveway frequency finding since these land uses would have a higher driveway density. Signalization also remained a significant indicator of success in the absence of speed variables in the before period.

When the after period is analyzed for the combined raised and lowered data sets with all and rear end accidents, driveways and land uses were found to remain essentially unchanged in their ability to distinguish between effective and noneffective data sets. The finding of five lane highways suggests that this laneage configuration is an attribute that can be used to characterize sites where speed zoning will be effective.

From the combined raised and lowered data sets with all and rear end accidents, the findings of this research are that there is a quantifiable basis for including variables related to roadside, geometric, and environmental variables in speed zoning procedures. These variables in addition to the speed variables of a negative skewness index and the 85th percentile speed are good predictors of speed zoning effectiveness for candidate zones.

**REFERENCES**

- M.R. Parker.
*Comparison of Speed Zoning Procedures and Their Effectiveness.**Final Report.*Michigan Department of Transportation, Traffic and Safety Division, Lansing, Michigan, 1992. - W.C. Taylor, C. William, and F. Coleman, III.
*Analysis of Speed Zoning Effectiveness.*FHWA-MI-RD-88-01. College of Engineering, Michigan State University, East Lansing, Michigan, 1988. - U.S. Department of Transportation, Federal Highway Administration.
*Synthesis of Speed Zoning Practices.*Report No. FHWA/RD-85/096, Washington, D.C., 1985. - P.C. Box and J.C. Oppenlander.
*Manual of Traffic Engineering Studies.*4th ed. Institute of Transportation Engineers. Arlington, Virginia, 1976. - M.J. Norusis.
*SPSS Advanced Statistics User's Guide.*SPSS, Inc., Chicago, Illinois, 1990.