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Prediction of the Expected Safety Performance of Rural Two-Lane Highways

The base models for the accident prediction algorithm were developed as part of the preparation of two FHWA reports, Accident Models for Two-Lane Rural Roads: Segments and Intersections, and Accident Models for Rural Intersections: 4-Lane by 2-Lane Stop-Controlled and 2-Lane by 2-Lane Signalized.^(3,5) This appendix describes the data base development, the base model for roadway segments, and the base models for at-grade intersections.

Data Base Development

The base models were developed with geometric design, traffic control, traffic volume, and accident data on roadway sections and intersections on rural two-lane highways in California, Michigan, Minnesota, and Washington. These data were obtained from the FHWA Highway Safety Information System (HSIS). The geometric design data in the HSIS files, from databases maintained by the States identified above, were supplemented with additional data obtained by Vogt and Bared from field measurements and photolog review. These efforts are described more fully in two FHWA reports and a published paper.^(3,4,5)

Base Model for Roadway Segments

In the modeling of roadway segment accidents, the dependent variable included five years of accident data (1985-1989) for 619 rural two-lane roadway segments in Minnesota and 3 years of accident data (1993-1995) for 712 roadway segments in Washington. The model development excluded roadway segments within 76 m (250 ft) of an at-grade intersection and excluded the (relatively few) accidents that occurred more than 76 m (250 ft) from an intersections but were identified by the investigating officer as related to an intersection.

The independent variables representing geometric, design traffic control. and traffic volume used in modeling included:

• Exposure (million vehicle-miles of travel).
• State in which the roadway section is located (Minnesota/Washington).
• Lane width.
• Shoulder width.
• Roadside hazard rating.
• Driveway density.
• Horizontal curvature.
• Grade rate for crest vertical curves.
• Percent grade for straight grades.

All of these independent variables were found to have a statistically significant relationship to roadway section accidents.

The base model for roadway segments was developed from the HSIS roadway segment data for rural two-lane highways in Minnesota and Washington. The base model is presented below:

where:

The model was developed with extended negative binomial regression analysis. This extension of the standard negative binomial regression analysis technique was devised by Miaou.⁽³⁾ In negative binomial models for roadway segments, the mean number of accidents in a specified time period is typically represented in the form:

EXPO exp(aX + bY + ...)

which is equivalent to:

EXPO exp(aX) exp(bY) ...

where EXPO is a measure of exposure, X and Y are measures of roadway segment characteristics, and a and b are appropriate regression coefficients.

The extended negative binomial regression analysis technique devised by Miaou replaces some of the factors exp(aX) by expressions of the form:

w₁ exp(aX₁) + w₂ exp(aX₂) + ... +w_m exp (aX_m)

where X₁, X₂, ..., X_m are local variables along the roadway segment, characterizing for subsegments what X attempts to measure for the entire segment. For example, X₁, ..., X_m might represent the degree of curvature for individual horizontal curves while X is the average degree of curvature for the roadway segment as a whole.Thus, X is a composite variable, while the X_is represent variation within the segment. Such variation occurs for many variables used in accident modeling of roadway segments, even on supposedly homogeneous segments. Notable examples are degree of curvature, grade, and change of grade per unit length. The variable w_i is the proportion of the segment length to which the value X_i applies. (The default value for X_i is assumed to be zero if there is no horizontal or vertical curve or if the grade is level, and an artificial subsegment with this value is added, if necessary, so that the weights, w_i, always sum to 1.0.)⁽³⁾

The extended negative binomial regression model decomposes the roadway segment into subsegments within which the roadway characteristic measured by X is constant. If this is done for two or more variables (e.g., X, Y, ...), the method assumes that the variables are independent of one another, so that the value Y_j occurs with a particular value of X_i. Although such independence cannot be assured, the extended negative binomial regression model attempts to capture the effect of variation within a segment in an additive manner consistent with the basic form of the model.⁽³⁾

Table 29 summarizes the model presented in equation (42) with the coefficient, standard deviation, and significance level (p) for each independent variable and the overdispersion parameter (k). The goodness-of-fit measures for the roadway segment base model include R², the traditional measure of the percentage of variation in accident frequency explained by the independent variables in the model, as well as R_k², defined as:

Where:

This latter measure of goodness of fit, R_k², has been proposed by Miaou.⁽⁹⁾ For the roadway segment base model in equation (42), the values of the goodness-of-fit measures are R² = 0.6547 and R_k² = 0.8291.

Table 29. Model Parameters and Goodness of Fit for Equation (42).

Note: The values of the goodness-of-fit measures are R² = 0.6547 and R_k² = 0.8291

Table 30 presents descriptive statistics for the variables in the roadway segment model.

Table 30. Descriptive Statistics for Roadway Segments Used in Modeling.

Conversion: 1 ft = 0.305 m; 1 mi = 1.61 km

The exposure variable, EXPO, was treated as a scale factor in the development of the model. Therefore, even though multiple years of accident data were used in developing the model, the expected annual accident frequency can be determined from the model if EXPO is determined as (ADT)(365)(L)(10^-6).

Other variables investigated in the development of the roadway segment base models included posted speed limit, truck percentage, and intersection density (i.e., number of intersections per mile). Posted speed limit was found to be negatively correlated with accident frequency, while truck percentage and intersection density were positively correlated with accident frequency. However, none of these three variables was statistically significant in regression models that included the variables listed above. Grade change per unit length of roadway was also considered for sag vertical curves and for all vertical curves (i.e. both sags and crests), but the version of the variable for crest vertical curves (V_j) had the greatest statistical significance and was, therefore, retained in the final model. Two weather-related variables were also investigated in the modeling for the Minnesota roadway segments—number of rain days and number of snow days per year. These variables were based on the climate district in which each roadway segment was located. These variables were found to be negatively correlated with accident frequency. Because these variables were not sufficiently local (i.e., they represented climate districts rather than the climate of individual roadway segments) and because they were only marginally statistically significant, they were not collected for the Washington data and were omitted from the final model.

Base Models for At-Grade Intersections

Base models have been developed for three types of at-grade intersections on rural two-lane highways. These are:

• Three-leg intersections with STOP control on the minor-road approach.
• Four-leg intersections with STOP control on the minor-road approach.
• Four-leg signalized intersections.

Models for each of these intersection types were developed using three different modeling approaches, described below. The available database used in modeling included 5 years of accident data (1985-89) for selected STOP-controlled intersections in Minnesota and 3 years of accident data (1993-1995) for selected signalized intersections in California and Michigan. Following the description of the modeling approaches, the models developed for each intersection type are presented.

The available accident data for at-grade intersections generally included accidents within 76 m (250 ft) of the intersection on the major road, typically a State highway. For minor roads that are also State highways, data were generally available for all accidents that occur within 76 m (250 ft) of the intersection. For minor roads that are not State highways, accidents on the minor road that are classified as intersection-related are typically assigned the milepost of the intersection on the major road and are therefore included in the available data. In Michigan, all minor-road accidents within 31 m (100 ft) of the intersection and, in California, all accidents within 76 m (250 ft) of the intersection are included in the available data. In Minnesota, all accidents that occurred on minor-road approaches and were identified as related to the intersection are included in the available data.

Modeling Approaches

Three different modeling approaches were employed to develop candidate base models for each intersection type. The approaches are:

• The dependent variable (number of accidents in a 5-year period) included only accidents that occurred within the curbline limits of a particular intersection or within 76 m (250 ft) of that intersection and were identified by the investigating officer as being related to the intersection.
• The dependent variable included only accidents that occurred within the curbline limits of a particular intersection or within 76 m (250 ft) of that intersection and were of accident types that are generally related to intersection operations.
• The dependent variable included all accidents that occurred within the curbline limits of a particular intersection or within 76 m (250 ft) of that intersection, whether those accidents were related to the intersection or not. However, the modeling technique used an offset to the observed accident frequency applied iteratively to account for the frequency of roadway section accidents that would be expected to occur on 152 m (500 ft) of the major roadway (76 m or 250 ft on either side of the intersection), as predicted by equation (37).

Each of these modeling techniques is described in greater detail in the following discussion. A fourth modeling technique that was considered but not used is explained at the end of this appendix.

The research reports by Vogt and Bared from the FHWA project that developed the base models and the related paper include only the models based on accidents that were identified by the investigating officer as being intersection related.^(3,4,5) The models based on accident types that are generally related to intersection operations and on the iterative offset approach were developed as part of the same project but are documented only in this report.

Limitation of the Analysis to Intersection-Related Accidents

The first modeling approach used to develop base models for at-grade intersections was to limit the dependent variable to those accidents that occurred within the curbline limits of the intersection or within 76 m (250 ft) of the intersection on any approach and were identified by the investigating officer as related to the intersection. This definition is generally reasonable because the vast majority of intersection-related accidents on a rural two-lane highway would be expected to occur within 76 m (250 ft) of the intersection to which they are related. For example, traffic queues that extend more than 76 m (250 ft) from an intersection and which might lead to rear-end collisions remote from the intersection are much less common in rural than in urban areas.

Not all accidents within 76 m (250 ft) of an intersection would be expected to be related to the operation of that intersection. For example, collisions between motor vehicles and animals and collisions involving vehicles entering or leaving a driveway may occur within 76 m (250 ft) of an intersection but may have no particular relationship to the presence of that intersection. In other words, some accidents would be expected to occur on the roadway near the intersection whether the intersection were present or not. the first approach to modeling distinguishes between intersection-related and non-intersection-related accidents based on judgments made by the investigating officer or by an accident coder and recorded in the State’s computerized accident record system. Nominally, such judgments make exactly the distinction that is desired, but there is concern that investigating officers and accident coders may not make such judgments consistently.

Once the dependent variable was defined, as described above, predictive models were developed using extended negative binomial regression in a manner similar to the development of the roadway segment model in equation (42).

Limitation of the Analysis to Selected Accident Types

The second modeling approach used was to limit the dependent variable to accidents that occurred within the curbline limits of the intersection and are of accident types that are generally related to intersection operations. The accident types classified as related to the intersection were:

• Rear-end collisions.
• Right-angle collisions.
• Left-turn collisions.
• Right-turn collisions.
• Sideswipe, same-direction collisions.

All other accidents types were classified as unrelated to the intersection.

The list of accident types classified as intersection-related and non-intersection-related were established through two special studies that involved a review of hard copy police accident reports and classification of accidents as intersection-related or non-intersection-related based on the judgment of safety experts.

This approach to modeling eliminates the concern raised in the first modeling approach about the potential misjudgment in classifying accidents made by investigating officers or accident coders. However, the approach based on classification of particular accident types as intersection-related has a similar concern since not every accident of the types identified above is actually related to an intersection and some accidents of other types are, in fact, intersection-related. For example, the proposed classification scheme based on accident types would classify all reported right-turn accidents within 76 m (250 ft) of the intersection as intersection-related, including accidents that are, in fact, related to turning movements at nearby driveways. The effectiveness of this classification could be improved by an agency by utilizing other fields of the accident record such as a driveway involvement indicator, if available, in classifying accidents.

Once the dependent variable was defined, as described above, predictive models were developed using extended negative binomial regression in a manner similar to the development of the roadway segment model in equation (42).

Use of All Accidents with an Offset for Expected Roadway-Segment Accidents

The third modeling technique uses as the dependent variable all accidents that occur within the curbline limits of a particular intersection and all accidents that occur within 76 m (250 ft) of that intersection, regardless of the accident type and regardless of the judgment made by the investigating officer or accident coder concerning the relationship of the accident to the intersection. Since this dependent variable includes some accidents that are clearly unrelated to the intersection, the expected frequency of roadway segment accidents, as predicted by equation (42), is used as an offset factor in the model development. This modeling used an iterative technique that makes successive approximations to the model coefficients.

The iterative offset modeling approach was performed as follows. Let:

denote an equation with integer subscript i estimating the mean number of intersection-related accidents per unit time, Zⁱ, in terms of intersection characteristics (X, Y, ...). Let N denote the mean number of non-intersection-related accidents on a 152 m (500 ft) section of roadway containing the intersection (i.e., 76 m or 250 ft on either side of the intersection), as predicted by a roadway section model such as equation (42), as applied to Minnesota (STATE=0).

Let A be the mean number of accidents of all kinds per unit time within 76 m (250 ft) of the intersection. Let:

The modeling approach used is iterative. Equation (44) implies that the following relationship must be valid for iteration i+1:

A negative binomial model for A is sought of the form:

which can be expressed as:

The initial negative binomial model for intersection-related accidents is represented by an equation for Z₀ in the form of equation (44). The offset technique represented by equations (47) through (50) is applied repeatedly to obtain a sequence of new models for Z₁, Z₂, Z₃, ... . This process is continued until the coefficients k_n, a_n, b_n, ... cease to change appreciably; i.e., until Zn+1 is approximately the same as Z_n. The appropriate model for the mean number of intersection-related accidents is then:

In principle, A = N + Z, or Z = A - N. Thus from, the model for roadway segment accidents used to estimate N and the initial model for intersection-related accidents Z₀, the offset technique yields a final model for intersection-related accidents, Z. This final model depends on the choice of the model for N, but should not generally depend on the initial model for Z₀. Thus, initial estimates or starting values of the regression coefficients k₀, a₀, b₀, ... can be selected through engineering judgment or an alternative preliminary model.

Models Developed

The following discussion presents the candidate base models developed for three-leg STOP-controlled intersections, four-leg STOP-controlled intersections, and four-leg signalized intersections.

Three-Leg STOP-Controlled Intersections

Candidate base models were developed for three-leg intersections with STOP control on the minor-road approach. The dependent variables used in these models have been described above in the discussion of modeling techniques. All of the models for three-leg STOP-controlled intersections used a data sets of approximately 382 intersections in Minnesota including 5 years of accident data (1985-1989). There were minor variations in sample size from one model to the next because of small amounts of missing data. The candidate independent variables considered in predicting accidents at three-leg STOP-controlled intersections were:

• Average daily traffic volume on the major road.
• Average daily traffic volume on the minor road.
• Intersection skew angle.
• Posted speed limit on major road.
• Presence of a right-turn lane on the major road.
• Number of driveways on the major road within 76 m (250 ft) of the intersection.
• Grade rate for crest vertical curves on the major road within 76 m (250 ft) of the intersection.
• Radius of horizontal curves on the major road within 76 m (250 ft) of the intersection.
• Roadside hazard rating along the major road within 76 m (250 ft) of the intersection.

Table 31 presents descriptive statistics for these variables.

A candidate model for three-leg STOP-controlled intersections developed using the intersection-related accident definition based on the investigating officer’s assessment of each accident is:

where:

Table 31. Descriptive Statistics for 382 Three-Leg STOP Controlled Intersections in Minnesota Used Modeling.

Conversion: 1 ft = 0.305 m

Equation (52) includes all of the candidate independent variables except the number of driveways which was dropped because its coefficient was not statistically significant (p=0.5405) and because coefficient had a negative sign, which is opposite to the direction expected. Table 32 summarizes the model parameters and goodness of fit for the model in equation (52). Goodness of fit for models like equation (52) is measured by R² and R_k², as noted earlier for equation (42), as well as by R_PD². This last goodness-of-fit measure, R_PD², has been proposed by Fridstrøm for use with negative binomial models.⁽⁴³⁾ A description of this goodness-of-fit measure is also provided by Vogt and Bared.⁽³⁾

Table 32. Model Parameters and Goodness of Fit for Equation (52).

Note: The values of the goodness-of-fit measures are R² = 0.4409, R_k² = 0.7805, and R_PD² = 0.6279

The model in equation (52) was reevaluated including only those variables that were statistically significant with a significance level (p) of 0.150 or less. This model is presented below:

Table 33 summarizes the model parameters and goodness of fit for the model in equation (53).

A candidate model developed for three-leg STOP-controlled intersections using only those accident types generally related to intersection operations is:

Equation (54) includes all of the candidate independent variables except speed limit (p=0.41), number of driveways (p=0.56), horizontal curvature (p=0.62), and vertical curvature (p=0.40) which were dropped because their coefficients were not statistically significant. Table 34 summarizes the model parameters and goodness of fit for the model in equation (54).

Table 33. Model Parameters and Goodness of Fit for Equation (53).

Note: The values of the goodness-of-fit measures are R² = 0.3955, R_k² = 0.7546, and R _PD² = 0.6109.

Table 34. Model Parameters and Goodness of Fit for Equation (54).

Note: The values of the goodness-of-fit measures are R² = 0.4181, R_k² = 0.8070, and R _PD² = 0.7228.

The model in equation (54) was reevaluated including only those variables that were statistically significant with a significance level of 0.150 or less. This model is presented below:

Table 35 summarizes the model parameters and goodness of fit for the model in equation (55).

Table 35. Model Parameters and Goodness of Fit for Equation (55).

Note: The values of the goodness-of-fit measures are R² = 0.4008, R _k² = 0.7953, and R _PD² = 0.7162

A candidate model for three-leg STOP-controlled intersections developed with the iterative offset technique is:

Equation (56) includes all of the candidate independent variables except number of driveways (p=0.35), presence of right-turn lane (p=0.47), and horizontal curvature (p=0.50) which were dropped because their coefficients were not statistically significant. Table 36 summarizes the model parameters and goodness of fit for the model in equation (56). It should be noted that the goodness-of-fit measure, R_PD², is not directly applicable to models developed with the iterative offset technique and, therefore, is not presented in Table 36. Moreover, R² must be interpreted with caution since it measures the goodness-of-fit for the combined roadway segment and intersection model for all accidents with 76 m (250 ft) of the intersection. Since most of these accidents are intersection-related, R² at least roughly measures the goodness of fit for intersection-related accidents

Table 36. Model Parameters and Goodness of Fit for Equation (56)

Note: The values of the goodness-of-fit measures are R² = 0.4163, and R k² = 0.5809.

The model in equation (56) was reevaluated including only those variables that were statistically significant with a significance level of 0.150 or less. This model is presented below:

Table 37 summarizes the model parameters and goodness of fit for the model in equation (57).

A decision was made to use in the accident prediction algorithm the models containing only those independent variables that are statistically significant at a significance level of 0.15 or less, like equations (53), (55), and (57).

Table 37. Model Parameters and Goodness of Fit for Equation (57).

Note: The value of goodness-of-fit measures are R² = 0.4069 and R_k² = 0.5765.

Four-Leg STOP-Controlled Intersections

Candidate base models were developed for four-leg intersections with STOP control on the minor-road approaches. The dependent variables used in these models have been described above in the discussion of modeling techniques. All of the models for four-leg STOP-controlled intersections used a data sets of approximately 324 intersections in Minnesota including 5 years of accident data (1985-1989). There were minor variations in sample size from one model to the next because of small amounts of missing data. The candidate independent variables considered in predicting accidents at four-leg STOP-controlled intersections were:

• Average daily traffic volume on the major road.
• Average daily traffic volume on the minor road.
• Intersection skew angle.
• Posted speed limit on major road.
• Presence of right-turn lanes on the major road.
• Number of driveways within 76 m (250 ft) of the intersection.
• Grade rate for crest vertical curves within 76 m (250 ft) of the intersection.
• Radius of horizontal curves within 76 m (250 ft) of the intersection.
• Roadside hazard rating.

Table 38 presents descriptive statistics for these variables.

A candidate model for four-leg STOP-controlled intersections developed using the intersection-related accident definition is:

where:

Table 38. Descriptive Statistics for 324 Four-Leg STOP-Controlled Intersections in Minnesota.

Conversion: 1 ft = 0.305 m; 1 mi = 1.61 km

Equation (58) includes all of the candidate independent variables except roadside hazard rating (p=0.28) and presence of right-turn lanes (p=0.66) which were not statistically significant. Table 39 summarizes the model parameters and goodness of fit for the model in equation (58).

Table 39. Model Parameters and Goodness of Fit for Equation (58).

Note: The values of goodness-of-fit are R² = 0.5944, R _k² = 0.8336, and R _PD² = 0.7364

The model in equation (58) was reevaluated including only those variables that were statistically significant with a significance level of 0.150 or less. This model is presented below:

Table 40 summarizes the model parameters and goodness of fit for the model in equation (59).

Table 40. Model Parametere and Goodness of Fit for Equation (59).

Note: The values of goodness-of-fit measures are R² = 0.5662, R _k² = 0.8081, and R _PD² = 0.7326

A candidate model developed using only those accident types generally related to intersection operations is:

Equation (60) includes all of the candidate independent variables except speed limit (p=0.25 to 0.50), presence of right-turn lane (p=0.59), and horizontal curvature (p=0.48) which were not statistically significant, and roadside hazard rating (p=0.12) which was marginally statistically significant but whose coefficient was negative, which is opposite to the direction expected. Table 41 summarizes the model parameters and goodness of fit for the model in equation (60).

The model in equation (60) was reevaluated including only those variables that were statistically significant with a significance level of 0.150 or less. This model is presented below:

Table 41. Model Parameters and Goodness of Fit for Equation (60).

Note: The values of goodness-of-fit measures are R² = 0.5495, R _k² = 0.8131, and R _PD² = 0.7183

Table 42. Model Parameters and Goodness of Fit for Equation (61).

Note: The values of goodness-of-fit measures are R²= 0.5020, R k²= 0.7835, and R _PD²= 0.7047

Table 42 summarizes the model parameters and goodness of fit for the model in equation (61).

A candidate model for four-leg STOP-controlled intersections developed with the iterative offset technique is:

Equation (62) includes all of the candidate independent variables except horizontal curvature (p=0.51) and vertical curvature (p=0.30 to 0.41) which were not statistically significant, and roadside hazard rating (p=0.11) which was marginally statistically significant but whose coefficient was negative, which is opposite to the direction expected. Table 43 summarizes the model parameters and goodness of fit for the model in Equation (62). No value of R _PD² is computed for equation (62) because this goodness-of-fit measure is not directly applicable to iterative offset technique.

Table 43. Model Parameters and Goodness of Fit for Equation (62).

Note: The values of goodness-of-fit measures are R² = 0.5563, and Rk² = 0.7984

All of the variables in equation (62) are statistically significant at the 0.15 significance level. Therefore, no alternative version of equation (62) was developed.

Four-Leg Signalized Intersections

Candidate base models were developed for four-leg signalized intersections. The dependent variables used in these models were those described above for the intersection-related and selected-accident-type modeling techniques. All of the models for four-leg signalized intersections used a data sets of 49 intersections, 18 in California and 31 in Michigan, with 3 years of accident data (1993-1995) for each intersection. The candidate independent variables considered in predicting accidents at four-leg signalized intersections on rural two-lane highways were:

• Average daily traffic volume on the major road.
• Average daily traffic volume on the minor road.
• Presence of protected left-turn signal phase on the major road.
• Grade rate for all vertical curves (including both crests and sags) within 244 m (800 ft) of the intersection along the major and minor roads.
• Percentage of minor-road traffic turning left at the signal for the morning and evening peak hours combined.
• Percentage of trucks (vehicles with more than four wheels) in the traffic stream entering the intersection from all approaches for morning and evening peak hours combined.
• Number of driveways within 76 m (250 ft) of the intersection on the major-road leg.

Table 44 presents descriptive statistics for these variables.

Table 44. Descriptive Statistics for 49 Four-Leg Signalized Intersections in California and Michigan Used in Modeling.

Note: The values of goodness-of-fit measures are R² = 0.4327, R _k² = 0.6094, and R _PD² = 0.1816

Assessment of Alternative Base Models

A careful examination and comparison was made of the alternative base models presented above to select the most suitable models for use in the accident prediction algorithm. The final selections were made based on a sensitivity analysis and an assessment of the combined roadway segment and intersection models to predict total accidents within 76 m (250 ft) of the set of study intersections as a whole, including both intersection-related and non-intersection-related accidents.

Equation (42) was the only candidate roadway segment model and that model was found to be satisfactory for use as the base model for roadway segments. This model also appears as equation (5) in the main text of the report.

Six candidate models were developed for three-leg STOP-controlled intersections. Of these six models, the models developed using the officer’s assessment of intersection-related accidents were found, together with the roadway segment model, to provide the best estimate of total accidents with in 76 m (250 ft) of the 382 study intersections. In choosing between equations (52) and (53), preference was given to equation (53) which includes only those variables found to be statistically significant with a significance level (p) of 0.015 or less. Therefore, equation (53) was selected as the base model for three-leg STOP-controlled intersections and it also appears as equation (7) in the main text of this report.

Similar logic was used to select equation (59) as the base model for four-leg STOP-controlled intersections. Equation (59) also appears as equation (9) in the main text of this report.

The assessment of the candidate models for four-leg signalized intersections was difficult because all seven candidate models were based on a relatively small sample size (49 intersections) and none of the models was found to be completely satisfactory. Equation (69) was appealing because it contains the same independent variables for which AMFs have been provided in the accident prediction algorithm. However, the functional form selected for equation (69) is such that the predicted accident frequency begins to decrease when the major-road ADT exceeds approximately 10,000 veh/day. This does not appear reasonable, so equation (69) was eliminated from consideration. The best of the remaining candidate models was equation (68), which also appears in the main text of the report as equation (11).

Another Alternative Approach for Future Consideration

The accident prediction algorithm for two-lane highways is based on the concept that accidents in the vicinity of an intersection can be predicted by separate models for intersection-related accidents and roadway-segment-related (or non-intersection-related) accidents. The models used to predict roadway segment and intersection accidents are independent; this is based on the assumption that there is a certain “background” level of roadway segment accidents that would occur on the major-road legs of the intersection whether the intersection was present or not. The accident prediction algorithm does not consider the possibility that the presence of the intersection could affect the frequency, severity, or collision types for accidents that are classified as non-intersection-related.

An alternative concept for considering the interaction described above was proposed during the development of the accident prediction algorithm. While this approach was, in the end, judged to have sufficient conceptual problems to be unworkable, this alternative approach is documented here for future reference in case a workable variation can be developed in the future.

The proposed concept was that a 152 m (500 ft) roadway segment along the major road (76 m or 250 ft on either side of the intersection) operates as an intersection approach during the time when traffic is present on the minor-road approach and operates as a roadway segment the rest of the time. Thus, if one could estimate the proportions of time when the segment operated as a roadway segment and as an intersection, its safety performance could be predicted as:

where:

Values for N_rs and N_int would could be determined from the accident prediction algorithm as shown in Equations (13) and (14). Furthermore, it was proposed that the proportion p could be estimated as follows:

where:

The average time each minor-road vehicle is present at or near the intersection, t_minor, could be estimated as some representatives value, such as 10 to 20 sec. The constant value of 86,400 in the denominator of equation (66) represents the number of seconds in a 24-hour day.

The approach represented by equations (70) and (71) has substantial conceptual appeal because it incorporates a direct proportionality to the minor-road ADT. The approach could be strengthened conceptually by accounting for traffic turning from the major road onto the minor road and by adjusting for time periods when more than one minor-road vehicle is present at the intersection at the same time. Furthermore, the concept might also be adapted to the prediction of driveway accidents by assuming very low values of ADT₂ for driveways. This could allow the accident prediction algorithm to address driveway accidents much more explicitly than is permitted by the driveway density AMF shown in equation (22).

The approach represented by equations (70) and (71) has conceptual disadvantages as well. First, it is based on a presumption that when a minor-road vehicle is present at the intersection there is no risk of an accident occurring elsewhere on the adjacent 152 m (500 ft) roadway segment. This presumption appears unrealistic. There must be some risk of an accident elsewhere on the major road when a minor-road vehicle is present at the intersection. Indeed, there is simply no evidence as to whether the presence of a minor-road vehicle at an intersection affects the risk of accidents elsewhere on the major road at all. Second, the form of equation (71) is such that, depending on the value of t_minor that is selected, there is some level at which p becomes equal to 1.0. At and above that ADT level, equation (70) implies that there would be no roadway-section-related accidents within 152 m (500 ft) of the intersection. Such a proposition is also unrealistic.

^{On balance, this approach to intersection accident prediction discussed above was found to be unworkable and was abandoned. The concept has been presented here to document that it was considered and to suggest an alternative that might be adapted for use in the future.}

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