Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges (2021)

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319 CHAPTER 8: SEVERITY DISTRIBUTION FUNCTIONS This chapter describes the activities undertaken to calibrate severity distribution functions (SDFs) for various components of the freeway system. A SDF is a discrete choice model that includes variables describing a site’s geometric design, traffic control features, traffic characteristics, and a calibration factor. It is used to predict for each site the proportion of crashes associated with each of the following severity levels. ● Fatal (K). ● Incapacitating injury (A). ● Non-incapacitating injury (B). ● Possible injury (C). The SDFs were developed to be used with a predictive model to estimate the expected crash frequency for each severity level. They were calibrated using a highway safety database that combines crash data with road inventory data. The procedure used to assemble the highway safety database is described in Chapter 4. The application of SDFs is described in Appendices C and D. This chapter consists of four parts. The first part gives a brief background on SDFs used in highway safety evaluation. The second part describes the development of a SDF for freeway segments. The third part describes the development of a SDF for ramp and C-D road segments. The fourth part describes the development of a SDF for crossroad ramp terminals. LITERATURE REVIEW Previous studies have documented models for estimating crash frequency for each severity level by jointly modeling the frequency of crashes by severity level using multivariate Poisson and mixed-Poisson models (Ma and Kockelman, 2006; Park and Lord, 2007). In contrast, a recent study used a two-stage frequency-severity model that linked the SDF with a SPFs to estimate the frequency of crashes by severity level (Wang et al., 2011). Several statistical models are available to develop SDFs. The models that are more commonly used by safety analysts include the ordered logit or probit, partially-ordered logit, ordered mixed logit, multinomial logit, nested logit, and random parameters (mixed) logit. Each of these statistical models is briefly described in the following paragraphs. Due to the ordinal nature of crash severities, an ordered logit or probit model is the logical choice for SDF development. This kind of model recognizes the natural order of increasing severity among the response alternatives (i.e., C, B, A, K) by fitting one function for all severity levels, with a unique cut-off value for each severity level. In this manner, the ordinal structure is well suited to modeling factors that have the same effect across all severity levels. The ordered logit and ordered probit models have been extensively used for crash severity analysis (Kweon and Kockelman, 2003; Donnell and Mason, 2004; Wang and Abdel-Aty, 2008). Two important limitations exist when an ordinal model is used (Savolainen and Mannering, 2007). The first limitation relates to under-reporting issues associated with PDO and

320 C severity crashes. When under-reporting occurs, the ordered probability model yields biased and inconsistent coefficient estimates (Ye and Lord, 2011). The second limitation of the ordinal model corresponds to the implied influence of each model variable. Ordered models constrain each variable’s effect such that a variable that increases the probability of the most severe outcome decreases the probability of the less severe outcomes. Similarly, a variable that increases the probability of the least severe outcome decreases the probability of the more-severe outcomes. This limitation is problematic when the influence of a variable does not follow this trend. For example, an increase in barrier offset is likely to decrease both fatal crash frequency and PDO crash frequency. The partially-ordered logit model can be used to overcome the aforementioned disadvantage of the ordered logit model. This model allows the coefficient of some variables to vary across severity levels, while the effect of other variables will be fixed across severity levels. Wang and Abdel-Aty (2008) used this model to examine the severity of left-turn-related crashes. They found that partial proportional odds models consistently perform better than ordered probability models. Wang et al. (2009) used this model to evaluate the effect of geometric and environmental conditions on crash severity in freeway diverge areas. An ordered mixed (i.e., random effects) logit model represents an extension of the ordered logit. It quantifies that portion of the response variability that represents unobserved heterogeneity among sites (i.e., variation among sites that is likely explainable by missing variables). The response variability is reduced by this technique, with the result being more efficient regression coefficient estimates. Srinivasan (2002) used this model structure to evaluate the driver and vehicle factors that influence crash severity on highways. The multinomial logit model (MNL) has also been used to analyze crash severities (Shankar and Mannering, 1996). It offers flexibility of constraining some variables to have the same effect on each severity level, while allowing the effect of other variables to vary among severity levels. As a result, the MNL model has the advantage of greater flexibility in modeling variable influence. The MNL model was derived assuming that the error components are extreme value distributed (i.e., Gumbel). Though this assumption simplifies the probability equation, it adds the “independence from irrelevant alternatives” (IIA) property in the MNL model. The IIA property of the MNL restricts the ratio of probabilities for any pair of crash severities to be independent of the existence and characteristics of other crash severities in the set of severities considered in the model. This restriction implies that the introduction of a new crash severity level in the set will affect all other severities proportionately (Koppelman and Bhat, 2006). The nested logit overcomes the IIA limitation of MNL model. The nested logit model groups crash severities that share unobserved attributes at different levels of a nest. This technique allows error terms within a nest to be correlated. Several studies have used the nested logit model for crash severity analysis (Shankar et al., 1996; Savolainen and Mannering, 2007).

321 The (multinomial) random parameters logit model (i.e., mixed logit model) represents a more generalized version of the ordered mixed logit model. This type of model has also been used by researchers to examine crash severity (Milton et al., 2008; Anastasopoulos and Mannering, 2011). This model overcomes the aforementioned disadvantage of the ordered logit structure by allowing a more flexible formulation that calibrates separate functions to each severity level. The “random parameters” element of this model quantifies for each model variable the portion of the response variability that is due to site-to-site variation. One disadvantage of this model structure is that it requires simulation-based methods to estimate the model regression coefficients, which leads to an increase in model development time. Another disadvantage is that it does not consider the hierarchy of severity levels (Savolainen et al., 2011). FREEWAY SEGMENTS This part of the chapter consists of four sections. The first section describes the data used to calibrate the SDF for freeway segments. The second section describes the methodology used for calibrating the models. The third section presents the modeling results. The last section describes the procedure for local calibration of a SDF. Highway Safety Database The HSIS was used as the primary source of data for model calibration. The “HSIS” states California, Maine, and Washington were identified as including ramp volume data, which is of fundamental importance to all aspects of this project. These data were not available from the other HSIS states. Hence, the database assembly focused on these three states. They are called the “study states” in this report. The data acquired from the HSIS is summarized in Table 29. As discussed in Appendix B, several of the geometry and lane use variables in the study state databases were of unknown accuracy. Also, several variables often had subtly different definitions among states. Moreover, the study state databases often did not include variables that describe road-related factors known to be associated with crash severity. To overcome these limitations, the study-state databases were enhanced using data from other sources. The data collected include the width of various cross section elements, barrier presence and location, horizontal curvature, ramp configuration, ramp entrance location, and median type. A complete list of the supplemental data is provided in Table 30. Methodology This section describes the methodology used to calibrate the SDF for freeway segments. The first subsection describes the discrete choice model used for SDF development. The second subsection describes the approach used to develop the SDF model form. Discrete Choice Model Based on a review of the literature, it was concluded that the prediction of crash frequency by severity level can be accomplished by using a SDF with a safety prediction model. For freeway safety evaluation, the SDF would be used with the safety prediction models in

322 Chapter 5. This approach is intended to minimize the frequency-severity indeterminacy problem described by Hauer (2006). The SDF model considers all severity levels together and, therefore, can be used to predict the shift in crashes among levels due to a change in roadway conditions. The discrete choice model includes only infrastructure-specific variables (such as geometric design, traffic control, and traffic characteristic data). It ignores post-crash variables (such as driver behavior and environmental data). This approach results in some loss in forecasting accuracy, relative to models that include these variables (Anastasopoulos and Mannering, 2011), but is appropriate for the intended application. The MNL model was selected as the basis for SDF development. Nested logit models were developed to evaluate the IIA limitation of the MNL model for this application. A test comparing the two models showed that the inclusive value parameters (for nesting) for these models were not significantly different from 1.0. For an acceptable nesting structure, the inclusive values need to be between 0.0 and 1.0. An inclusive value parameter equal to 1.0 indicates that there is no correlation in the unobserved factors within the nest and, therefore, the nested logit model is not different from the standard MNL model. A linear function was used to relate the crash severity with the geometric design features, traffic control features, and traffic characteristics. Modeling Approach For highway safety applications, the MNL model is used to predict the probability of each crash severity level. An individual crash’s severity among the given severities was considered to be predicted if the crash severity likelihood function was maximum for that particular severity. The MNL model was derived assuming that the error components are extreme value distributed (McFadden, 1981). The probability of outcome j is defined by the following equation.  = = J i V V j i j e eP 1 (320) where, Pj = probability of the outcome j; Vj = deterministic component of outcome j; and J = total number of possible outcomes modeled. When applied to crash severity, the outcomes for severe crashes can be represented by three severity levels (i.e., K, A, and B), with severity level C used as the base scenario. This application is shown in the following equations. BAK K VVV V K eee C eP +++ = 0.1 (321)

323 BAK A VVV V A eee C eP +++ = 0.1 (322) BAK B VVV V B eee C eP +++ = 0.1 (323) ( )BAKC PPPP ++−= 0.1 (324) where, PK = probability of severity level K (fatal); PA = probability of severity level A (incapacitating injury); PB = probability of severity level B (non-incapacitating injury); PC = probability of severity level C (possible injury); and C = local calibration factor. The likelihood function for the MNL model is considered to have a deterministic component and a random error component. While the deterministic part is assumed to contain variables that can be measured; the random part corresponds to the unaccounted factors that impact crash severity. The deterministic part of the crash severity model was designated as a linear function of roadway conditions. The following equation is used to describe the deterministic component.  = += N n njnjj XbASCV 1 , (325) where, Vj = deterministic component for severity level j ( j = K, A, B); ASCj = alternative specific constant for crash severity level j; bn, j = calibration coefficient for crash severity level j and variable n; Xn = independent variable n, n = 1, 2, ..., N; and N = total number of independent variables included in the model. The SAS (2009) nonlinear mixed modeling procedure (NLMIXED) was used for model calibration. Modeling Results This section describes the modeling results. It is divided into four subsections. The first subsection describes the calibration data. The second subsection describes the formulation of the calibration model. The third subsection describes the calibrated model and estimation results. The last subsection examines the sensitivity of the model prediction to selected variable values.

324 Calibration Data The database assembled for calibration included crash severity level as the dependent variable. Geometric design features, traffic control features, and traffic characteristics were included as independent variables. The highway safety database required modification to be used for SDF calibration. Each observation in the highway safety database represents one site with known geometric features, traffic control features, traffic characteristics, and crash frequency (by severity level). To convert this database to the form needed for SDF calibration, each observation is repeated once for each fatal or injury crash associated with it. An attribute indicating the severity of the crash is added to the newly-created SDF database. In this manner, sites that experience only PDO crashes are excluded from the SDF database. The total sample size of the SDF database is equal to total number of injury and fatal crashes in the highway safety database. During the model calibration, the “possible injury” level is set as the base scenario with coefficients restricted to 0.0. Table 102 presents a brief summary of the variables used for SDF development. The variables listed were those found to have an important influence on the crash severity level. A complete list of all variables in the database is given in Chapter 5. TABLE 102. Summary statistics for freeway SDF development Variable Type Mean Standard Deviation Minimum Maximum Crash Count Proportion of segment with barrier 0.58 0.24 0.00 1.00 8,249 Proportion of AADT during high-volume hours 0.49 0.35 0.00 0.93 8,249 Proportion of segment with rumble strips 0.20 0.38 0.00 1.00 8,249 Proportion of segment with horizontal curve 0.28 0.33 0.00 1.00 8,249 Lane width, ft 11.99 0.59 10.1 14.9 8,249 Area type Rural 2,417 Urban 5,832 Severity level K 171 A 445 B 2,550 C 5,083 Model Development The following model form was used for the deterministic component of the SDF during the regression analysis. ( ) ( ) ( ) ( ) ( ) ( )ruralKrurallKlcKhcorirKrs hvKhvobibKbarKK IbWbPbPPb PbPPbASCV ×+×+×++××+ ×++××+= ,,,, ,, ][5.0 ][5.0 (326)

325 ( ) ( ) ( ) ( ) ( )ruralAruralcAhcorirArs hvAhvobibAbarAA IbPbPPb PbPPbASCV ×+×++××+ ×++××+= ,,, ,, ][5.0 ][5.0 (327) ( ) ( ) ( ) ( ) ( ) ( )ruralBrurallBlcBhcorirBrs hvBhvobibBbarBB IbWbPbPPb PbPPbASCV ×+×+×++××+ ×++××+= ,,,, ,, ][5.0 ][5.0 (328) caca IbeC = (329) where, Pib = proportion of segment length with a barrier present in the median (i.e., inside); Pob = proportion of segment length with a barrier present on the roadside (i.e., outside); Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; Pir = proportion of segment length with rumble strips present on the inside shoulders; Por = proportion of segment length with rumble strips present on the outside shoulders; Pc = proportion of the segment length with curvature; Wl = lane width, ft; Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); and Ica = California indicator variable (= 1.0 if segment in California, 0.0 otherwise). The final form of the regression model is described by the preceding equations. This form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. Model Calibration Table 103 summarizes the estimation results of model calibration. An examination of the coefficient values and their implication on the corresponding crash severity levels are documented in a subsequent section. In general, the sign and magnitude of the regression coefficients in Table 103 are logical and consistent with previous research findings. The t-statistic for each coefficient in Table 103 indicates a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database).

326 TABLE 103. Parameter estimation for freeway SDF Variable Inferred Effect of... Fatal (K) Incapacitating Injury (A) Non-Incapacitating Injury (B) Value t-statistic Value t-statistic Value t-statistic ASC Alternative specific constant -0.1705 -0.09 -2.3929 -13.49 0.0732 0.13 bbar Proportion of barrier -0.3883 -1.06 -0.3253 -1.41 -0.2499 -2.08 bhv Proportion volume during high-volume hours -0.9239 -3.03 -0.8528 -4.42 -0.8720 -8.96 brs Proportion of rumble strips 0.3868 1.67 0.3906 2.63 0.1347 1.63 bhc Proportion of horiz. curves 0.2079 0.88 0.2427 1.62 0.1312 1.75 bl Lane width -0.2608 -1.72 -0.0464 -1.03 brural Added effect of rural area type 0.4919 2.47 0.4302 3.42 0.2079 3.14 bca Location in California 0.3490 6.45 0.3490 6.45 0.3490 6.45 Indicator variables were included for the states of California and Maine. However, only the coefficient for California was statistically significant. The coefficient for this variable is shown in the last row of Table 103. Its value indicates that a crash on a freeway in California is likely to be more severe than a crash on a freeway in Maine and Washington. The trend could not be explained by differences in road design among the states. A more detailed discussion of this variable is given in the subsequent section. The coefficients in Table 103 were combined with Equations 326 to 328 to obtain the deterministic component of each crash severity level for freeway crashes. The form of each model is described by the following equations. ( ) ( ) ( ) ( ) ( ) ( )rurallcorir hvobibK IWPPP PPPV ×+×−×++××+ ×−+××−−= 4919.02608.02079.0][5.03868.0 9239.0][5.03883.01705.0 (330) ( ) ( ) ( ) ( ) ( )ruralcorir hvobibA IPPP PPPV ×+×++××+ ×−+××−−= 4302.02427.0][5.03906.0 8528.0][5.03253.03929.2 (331) ( ) ( ) ( ) ( ) ( ) ( )rurallcorir hvobibB IWPPP PPPV ×+×−×++××+ ×−+××−= 2079.00464.01312.0][5.01347.0 8720.0][5.02499.00732.0 (332) The probability of each severity level is obtained by combining Equations 321 to 324 with Equations 330 to 332. The procedure for estimating the local calibration factor is described in the next section. Predicted Probabilities Barrier Presence. Two variables that define the existence of barrier include the proportion of segment length with a barrier present in the median Pib, and the proportion of segment length with a barrier present on the roadside Pob. These variables are calculated using

327 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 Proportion of Segment with Barrier D is tri bu tio n of C ra sh es b y Se ve rit y, % C B A K Equations 68 and 71 (in Chapter 5), respectively. The proportion-of-median-barrier and proportion-of-roadside-barrier variables were considered separately during the model calibration. However, both variables showed similar effect and, thus, the average of these two variables is represented in the final model. Barrier is defined herein to be any combination of cable barrier, concrete barrier, guardrail, or bridge rail. The relationship between the proportion-of-segment-with-barrier variable and severity level is shown in Figure 138. The negative value of the associated coefficient (in Table 103) indicates that, as the proportion of barrier increases, the likelihood of severity levels K, A, and B decreases. The trends in Figure 138 indicate that the fatal crash percentage changes from 7.1 percent without a barrier, to 5.7 percent with a continuous barrier. A similar trend is shown for severity levels A and B. Figure 138. Freeway severity distribution based on the proportion of segment with barrier. The trends shown in Figure 138 are consistent with the findings of other researchers. For example, Bligh et al. (2006) found that locations where barrier was not present had cross-median and other median-related crashes that were more likely to be of the K, A, or B severity, relative to locations with longitudinal barrier. Donnell and Mason (2006) found that the installation of median barriers decreases the probability of FI crashes. In another study, Tarko et al. (2008) noted that installing a concrete barrier decreased the most severe head-on crashes but increased the other non-severe crash types. High-Volume. This variable indicates the proportion of AADT during hours where volume exceeds 1,000 veh/h/ln. It is computed using the average hourly volume distribution associated with the subject segment. This distribution will typically be computed using the data obtained from the nearest continuous traffic counting station (on a freeway of similar character). The variable is positively correlated with the volume to-capacity ratio experienced by the

328 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 Proportion of AADT During High-Volume Hours D is tri bu tio n of C ra sh es b y Se ve rit y, % C B A K segment on an hourly basis. A more detailed explanation of this variable is provided in Chapter 5. The relationship between the proportion of AADT during high-volume hours and severity level is shown in Figure 139. The negative value of the associated coefficient (in Table 103) indicates that, as the proportion of high-volume hours increases, the likelihood of severity levels K, A, and B decreases. The trends in Figure 139 indicate that the fatal crash percentage changes from 7.1 percent when the proportion equals 0.0, to 4.4 percent when the proportion equals 1.0. A similar trend is shown for severity levels A and B. Figure 139. Freeway severity distribution based on the proportion of AADT during high-volume hours. It is rationalized that the trends in Figure 139 are due to the correlation between the proportion variable and speed. During high-volume conditions, the running speed of the vehicles decreases and, thus, the chance to be involved in a severe crash decreases. Martin (2002) investigated the relationship of traffic flow and crash severity on French motorways and concluded that lower traffic flow is associated with an increase in crash severity. In a study of London highways, Noland and Quddus (2005) found that congestion is less likely to be associated with severe crashes in urban conditions. The authors stated that the mobility benefits of reduced traffic congestion might be offset by the occurrence of more-severe crashes. In another study, Quddus et al. (2010) explored the relationship between crash severity and congestion. They found that the level of traffic congestion does not affect crash severity, which contradicts the 2005 study. Rumble Strips. The presence of shoulder rumble strips was found to have some association with the crash severity distribution. This presence is quantified as the proportion of the segment with rumble strips. It is computed separately for the outside shoulders and the inside shoulders. For the inside shoulders, this proportion is computed by summing the length of roadway with rumble strips on the inside shoulder in both travel directions and dividing by twice

329 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 Proportion of Segment with Rumble Strips D is tri bu tio n of C ra sh es b y Se ve rit y, % C B A K the segment length. For the outside shoulders, this proportion is computed by summing the length of roadway with rumble strips on the outside shoulder in both travel directions and dividing by twice the segment length. An initial regression model form contained both the inside and outside rumble strip proportions. However, the two variables yielded a similar relationship with crash severity level and, thus, the average of these two variables is represented in the final model. The relationship between the proportion-of-segment-with-rumble-strips variable and severity level is shown in Figure 140. The positive value of the associated coefficient (in Table 103) indicates that, as the proportion of rumble strips increases, the likelihood of severity levels K, A, and B also increases. The trends in Figure 140 indicate that the fatal crash percentage changes from 7.1 percent when the proportion equals 0.0, to 9.2 percent when the proportion equals 1.0. A similar trend is shown for severity levels A and B. Figure 140. Freeway severity distribution based on the proportion of segment with rumble strips. The trends shown in Figure 140 are consistent with the findings of other researchers. For example, Griffith (1999) found this trend in his before-after study of the effect of continuous shoulder rumble strips on freeways. He concluded that, for impaired drivers, there could be a possible transfer from single-vehicle run-off-the-road crashes to multiple-vehicle crashes, the latter crash type being more severe. Hu and Donnell (2010) concluded that an increase in severity could be caused by over-steering, which results in the driver leaving the traveled way in order to avoid possible multi-vehicle rear-end or sideswipe crashes with vehicles in adjacent lanes. It is possible that some drivers who encounter rumble strips on curves may respond by over-steering. Marvin and Clark (2003) conducted a before-after study to evaluate the safety effectiveness of shoulder rumble strips. They concluded that, in certain situations, rumble strips increased the severity of roll-over crashes. They hypothesized that the increase could be through

330 rumble strip deployment or other undefined factors. Smith and Ivan (2005) observed an increase in the proportion of multiple-vehicle crashes with the addition of rumble strips. They stated that a possible reason for the increase in the multiple-vehicle crashes is because of a driver hitting the rumble strip and subsequently panicking, which causes the driver to swerve and hit another vehicle. In contrast, Sayed et al. (2010) reported a reduction in crash severity after the installation of shoulder rumble strips. The association of rumble strip treatment with increased crash severity could be the result of confounding variables. That is, it is possible that rumble strips are being installed at locations where crash severity is relatively high. However, the application of rumble strips on freeways is a fairly routine practice among state transportation agencies, such that rumble strips tend to be installed as a matter of policy rather than as a problem-site treatment. Moreover, at least two of the studies cited in the previous paragraphs used a before-after design, which would control for some confounding elements. Horizontal Curve. The “proportion of segment with horizontal curve” variable Pc is computed as the ratio of the length of all curves on the segment to the length of the segment. For example, consider a segment that is 0.5 mi long and has only one curve that is 0.2 mi long. If one-half of the curve is on the segment, then Pc = 0.20 (= 0.1/0.5). In fact, this proportion is the same regardless of the curve’s length (provided that it is 0.1 mi or longer and 0.1 mi of this curve is located on the segment). In addition to Pc, different combinations of curve radius and length were considered during model calibration. However, the proportion-of-segment-with-curve variable was the only one found to be correlated with crash severity. The relationship between the proportion-of-segment-with-horizontal-curve and severity level is shown in Figure 141. The positive value of the associated coefficient (in Table 103) indicates that, as the proportion of the segment with horizontal curvature increases, the likelihood of severity levels K, A, and B also increases. The trends in Figure 141 indicate that the fatal crash percentage increases from 7.1 percent for a segment with no curve to 8.0 percent for a segment located fully on a horizontal curve. A similar trend is shown for severity levels A and B. Hu and Donnell (2010) found a similar result when analyzing median barrier crashes on curved and uncurved freeway segments. They concluded that the trend is likely due to the fact that vehicles on horizontal curves impact longitudinal barriers at higher impact angles, relative to those on tangent segments. Shankar et al. (1996) found that road sections with frequent horizontal curves tend to have a larger proportion of injury crashes, relative to road sections with infrequent curves. Abdel-Aty (2003) also found that roadway curves contribute to higher probability of injuries on roadway sections. Donnell and Mason (2006) analyzed the effect of curved sections on crash severity. They found the likelihood that a crash is designated as fatal or injury is higher for curved sections than for tangent sections.

331 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 Proportion of Segment with Horizontal Curve D is tri bu tio n of C ra sh es b y Se ve rit y, % C B A K Figure 141. Freeway severity distribution based on the proportion of segment with horizontal curve. Lane Width. The lane width used in this research is an average for all through lanes on the segment. Shoulder width was also considered during model calibration, but it was not found to have a correlation with crash severity. The relationship between lane width and severity level is shown in Figure 142. The negative value of the associated coefficient (in Table 103) indicates that, as the lane width increases, the likelihood of severity levels K, A, and B decreases. The trends in Figure 142 indicate that the fatal crash percentage decreases from 5.7 percent at 10-ft lane width, to 2.3 percent for a 14-ft lane width. A similar trend is shown for severity levels A and B. Previous studies have shown that an increase in lane width decreases head-on collisions, which are typically severe (Al-Senan et al., 1987; Zegeer et al., 1981). Geedipally et al. (2010) found that if a crash occurs on rural two-lane highways with a wider lane width, it is less likely to be classified as a rear-end collision. With wider lane widths, it is possible that drivers have more opportunity to avoid rear-end and head-on collisions, which in turn reduces the likelihood of high crash severity. Area Type. The relationship between area type and crash severity level was also considered during model calibration. Previous studies have documented differences in crash severity between urban and rural roadways (Lee and Mannering, 2002; Khorashadi et al., 2005). It is generally recognized that probabilistic models should be developed separately for urban and rural crashes. However, separate models were not developed in this project due to the limited sample size.

332 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 10 11 12 13 14 Lane Width, ft D is tri bu tio n of C ra sh es b y Se ve rit y, % C B A K Figure 142. Freeway severity distribution based on lane width. The relationship between area type and severity level is shown in Table 104. The positive value of the associated coefficient (in Table 103) indicates that a crash in a rural area is likely to be more severe than a crash in an urban area, when all other variables are controlled. The percentages in Table 104 indicate that the fatal crash percentage on a rural freeway is 7.1 percent, and it is 5.1 percent on an urban freeway. A similar trend is shown for severity levels A and B. TABLE 104. Freeway severity distribution based on area type and state Variable Type Severity Level Distribution, percent Fatal (K) Incapacitating Injury (A) Non-Incapacitating Injury (B) Possible Injury (C) Area type Rural 7.1 7.6 47.2 38.1 Urban 5.1 5.8 44.7 44.5 State Calif. 7.1 7.6 47.2 38.1 Other 6.1 6.5 40.7 46.6 The trend with area type in Table 104 can be attributed to higher operating speeds on rural freeways. A crash that occurs at higher speed typically has higher severity than a crash at lower speed. State. In addition to the roadway variables, an indicator variable for each state was included in the calibrated model to account for differences between states that could not be explained with the other variables in the model. Indicator variables for the states of California and Maine were initially included in the regression model. However, the coefficient for Maine

333 was very small and not statistically significant. This finding suggests that the state effect is very similar between Maine and Washington. The Maine indicator variable was removed as a result. The coefficient for California is relatively large and statistically significant. Its positive sign indicates that a crash on freeways in California is more severe than a crash on freeways in Washington or Maine, when all other variables are controlled. This difference may be explained by different crash reporting practices, highway design practices (e.g., use of different roadside design features, etc.), terrain, and weather for the various states. The severity distribution for California is compared with that of the other states in Table 104. Local Calibration Procedure This section describes the procedure for calibrating the SDF to local conditions. At least 30 sites should be randomly selected as calibration sites. They should have geometric design and traffic control features that are representative of facilities in the region, and similar to those to which the calibrated SDF will be applied. If the calibration site is a segment (as opposed to an intersection), then it should be between 0.1 and 1.0 mi in length to ensure statistical validity and site homogeneity. The calibration data should represent reported crashes for each calibration site for a period of at least one year, and no more than three years. Each year represented in the calibration period should have a duration of 12 consecutive months to avoid seasonal effects in the data. The calibration database should include at least 300 fatal or injury crashes for the calibration period. If this minimum is not realized for the sites selected, then (1) additional sites should be added to the database or (2) the calibration period should be expanded to include more years (but no more than three years). The procedure consists of three steps. During the first step, the count of injury or fatal crashes during the calibration period No, K+A+B+C is determined for each site. Also, the count of crashes with a severity level of K, A, or B during the calibration period No, K+A+B is also determined for each site. These two counts are then separately summed for all sites and used to compute the observed probability of a K, A, or B crash Po, K+A+B (= No, K+A+B /No, K+A+B+C), given that the crash involves an injury or fatality. In this manner, one average observed probability is obtained for all sites combined. In the second step, the uncalibrated SDF model (i.e., C = 1.0) is used with the predictive method described in a previous chapter to estimate the predicted number of FI crashes during the calibration period Np, K+A+B+C is determined for each site. Also, the predicted number of crashes with a severity level of K, A, or B during the calibration period Np, K+A+B is also determined for each site. These two estimates are then separately summed for all sites and used to compute the predicted probability of a K, A, or B crash Pp, K+A+B (= Np, K+A+B /Np, K+A+B+C), given that the crash involves an injury or fatality. In this manner, one average predicted probability is obtained for all sites combined.

334 In the third step, Equation 333 is used to estimate the local calibration factor using the probabilities computed in steps 1 and 2. BAKp BAKp BAKo BAKo P P P P C ++ ++ ++ ++ −× − = , , , , 0.1 0.1 (333) where, C = local calibration factor; Po, K+A+B = probability of a crash having a K, A, or B severity, given that it is an injury or fatal crash, and based on reported crash data; and Pp, K+A+B = probability of a crash having a K, A, or B severity, given that it is an injury or fatal crash, and based on predicted crashes. Table 105 illustrates the local calibration procedure using sample data from 50 freeway segments. The reported crash data are listed in columns 2 through 5 and the predicted crashes are listed in columns 6 through 9. The value of Po, K+A+B is computed as 0.431 (= [8 + 15 + 95]/[8 + 15 + 95 + 156]). In a similar manner, the value of Pp, K+A+B is computed as 0.373 using the predicted crash data. Substitution of these two proportions in Equation 333 yields a calibration factor of 1.27. TABLE 105. Example application of SDF local calibration procedure Site Number Reported Crashes by Severity Level (No) Predicted Crashes by Severity Level (Np) K A B C K A B C 1 1 3 17 25 1.1 2.4 16.0 26.6 2 1 2 6 7 0.2 0.7 4.5 10.6 3 0 0 1 1 0.0 0.1 0.5 1.4 : : : : : : : : : 50 0 1 3 18 0.2 0.6 4.4 16.7 Total: 8 15 95 156 5.8 15.0 81.3 171.8 RAMP SEGMENTS This part of the chapter describes the activities undertaken to calibrate a SDF for ramp and C-D road segments. It consists of three sections. The first section describes the data used to calibrate the SDF. The second section provides an overview of the approach used to develop the SDF model form. The third section presents the modeling results. Highway Safety Database The HSIS was used as the primary source of data for model calibration. The “HSIS” states California, Maine, and Washington were identified as including ramp volume data, which is of fundamental importance to all aspects of this project. These data were not available from the other HSIS states. Hence, the database assembly focused on these three states. They are called the “study states” in this report. The data acquired from the HSIS is summarized in Table 45.

335 As discussed in Appendix B, several of the geometry and lane use variables in the study state databases were of unknown accuracy. Also, several variables often had subtly different definitions among states. Moreover, the study state databases often did not include variables that describe road-related factors known to be associated with crash severity. To overcome these limitations, the study-state databases were enhanced using data from other sources. The data collected include the width of various cross section elements, barrier presence and location, horizontal curvature, and ramp entrance location. A complete list of the supplemental data is provided in Table 46. Modeling Approach For highway safety applications, the multinomial logit (MNL) model is used to predict the probability of each crash severity level. A brief description of the MNL model and other discrete choice models was given in the part titled Literature Review. This model is shown in Equations 320 to 325. The deterministic component of the model is used to relate the crash severity with the site’s geometric design features, traffic control features, and traffic characteristics. The SAS (2009) nonlinear mixed modeling procedure (NLMIXED) was used for the evaluation of MNL model. Initially, the SDF was developed to predict the proportion of crashes in each severity level. However, the model was not able to quantify statistically significant coefficients for most variables due to a small number of reported fatal crashes. Thus, the fatal and incapacitating injury crashes are combined into one level for model calibration. The probability for each crash severity level is given by the following equations. BAK AK VV V AK ee C eP ++ = + + + 0.1 (334) BK B VAV V B ee C eP ++ = +0.1 (335) ( )BAKC PPP +−= +0.1 (336) where PK+A is the probability of severity level K or A (fatal or incapacitating injury) and the other variables are defined previously. Modeling Results This section describes the modeling results. It is divided into four subsections. The first subsection describes the calibration data. The second subsection describes the formulation of the calibration model. The third subsection describes the calibrated model and estimation results. The last subsection examines the sensitivity of the model prediction to selected variable values.

336 Calibration Data The database assembled for calibration included crash severity level as the dependent variable. Geometric design features, traffic control features, and traffic characteristics were included as independent variables. The highway safety database required modification to be used for SDF calibration. Each observation in the highway safety database represents one site with known geometric features, traffic control features, traffic characteristics, and crash frequency (by severity level). To convert this database to the form needed for SDF calibration, each observation is repeated once for each fatal or injury crash associated with it. An attribute indicating the severity of the crash is added to the newly-created SDF database. The total sample size of the SDF database is equal to total number of injury and fatal crashes in the highway safety database. During the model calibration, the “possible injury” level is set as the base scenario with coefficients restricted to 0.0. Table 106 presents a brief summary of the variables used for SDF development. The variables listed were those found to have an important influence on the crash severity level. A complete list of all variables in the database is given in Chapter 6. TABLE 106. Summary statistics for ramp SDF development Variable Type Mean Standard Deviation Minimum Maximum Crash Count Proportion of segment with barrier 0.34 0.34 0.00 1.00 1,034 Number of lanes 1.31 0.16 1 2 1,034 Area type Rural 109 Urban 925 Ramp type 1 Exit 502 Other 532 Severity level K 27 A 81 B 415 C 511 Note: 1 - “Other” includes entrance ramps, connector ramps at system interchanges, and C-D roads. Model Development The following model form was used for the deterministic component of the SDF during the regression analysis. ( ) ( ) ( ) ( )exrAKexrruralAKrural AKnrblbAKbarAKAK IbIb nbPPbASCV ×+×+ ×++××+= ++ ++++ ,, ,, ][5.0 (337)

337 ( ) ( ) ( )ruralBrural BnrblbBbarBB Ib nbPPbASCV ×+ ×++××+= , ,, ][5.0 (338) caca IbeC = (339) where, Plb = proportion of segment length with a barrier present on the left side; Prb = proportion of segment length with a barrier present on the right side; n = number of through lanes on segment; Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); Iexr = exit ramp indicator variable (= 1.0 if segment is an exit ramp, 0.0 otherwise); and Ica = California indicator variable (= 1.0 if segment in California, 0.0 otherwise). The final form of the regression model is described by the preceding equations. This form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. Model Calibration Table 107 summarizes the estimation results of model calibration. An examination of the coefficient values and their implication on the corresponding crash severity levels are documented in a subsequent section. In general, the sign and magnitude of the regression coefficients in Table 107 are logical and consistent with previous research findings. TABLE 107. Parameter estimation for ramp SDF Variable Inferred Effect of... Fatal (K) or Incapacitating Injury (A) Non-Incapacitating Injury (B) Value t-statistic Value t-statistic ASC Alternative specific constant -1.5373 -3.85 0.2355 0.92 bbar Proportion of barrier -0.4813 -1.34 -0.4312 -1.92 bn Number of lanes -0.2280 -0.87 -0.4350 -2.68 brural Added effect of rural area type 0.6681 1.93 0.6963 2.91 bexr Added effect of exit ramp 0.4260 1.92 bca Location in California 0.4487 3.04 0.4487 3.04 The t-statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the

338 variable was important to the model and its trend was found to be consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). Indicator variables were included for the states of California and Maine. However, only the coefficient for California was statistically significant. The coefficient for this variable is shown in the last row of Table 107. Its value indicates that a crash on a ramp in California is likely to be more severe than a crash on a ramp in Maine and Washington. The difference may be explained by different crash reporting practices, highway design practices, terrain, and weather for the various states. The coefficients in Table 107 were combined with Equations 337 and 338 to obtain the deterministic component of each crash severity level for ramp and C-D road crashes. The form of each model is described by the following equations. ( ) ( ) ( ) ( )exrrural rblbAK II nPPV ×+×+ ×−+××−−=+ 4260.06681.0 2280.0][5.04813.05373.1 (340) ( ) ( ) ( )rural rblbB I nPPV ×+ ×−+××−= 6963.0 4350.0][5.04312.02355.0 (341) The probability of each severity level is obtained by combining Equations 334 to 336 with Equations 340 and 341. A procedure for local calibration was described previously in the discussion associated with Table 105. Predicted Probabilities Barrier Presence. Two variables that define the existence of barrier include the proportion of segment length with a barrier present on the right side Prb, and the proportion of segment length with a barrier present on the left side Plb. These variables are calculated using Equations 188 and 190 (in Chapter 6), respectively. The proportion of right side barrier and left side barrier variables were considered separately during the model calibration. However, both variables showed similar effect and, thus, the average of these two variables is represented in the final model. Barrier is defined herein to be any combination of cable barrier, concrete barrier, guardrail, or bridge rail. The relationship between the proportion-of-segment-with-barrier variable and severity level is shown in Figure 143. The negative value of the associated coefficient (in Table 107) indicates that, as the proportion of barrier increases, the likelihood of severity levels K+A and B decreases. The trends in Figure 143 indicate that the K+A crash percentage changes from 17.8 percent without a barrier, to 13.8 percent with a continuous barrier. A similar trend is shown for severity level B.

339 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.2 0.4 0.6 0.8 1 Proportion of Segment with Barrier D is tri bu tio n of C ra sh es b y Se ve rit y, % C B K+A Figure 143. Ramp severity distribution based on the proportion of segment with barrier. Barriers are installed on the sides of a ramp to prevent a vehicle from leaving the roadway and striking a fixed object or rolling over. For some ramp configurations, a barrier is installed along the left side of the ramp to prevent crashes with vehicles traveling on an adjacent ramp or the main lanes. Previous studies have shown that a significant percentage of severe crashes involve a vehicle that has run off the road and either struck a fixed object or rolled over (Zegeer et al., 1981; Neuman et al., 2003). Roll-over crashes are more likely to be severe than other crashes (Viano and Parenteau, 2004). Number of Lanes. This variable represents the count of through lanes at the start of the ramp or C-D road segment, relative to the direction of travel. It does not include speed-change lanes or the auxiliary lane in a C-D road weaving section. The relationship between number of lanes and severity level is shown in Table 108. The negative value of the associated coefficient (in Table 107) indicates that a crash on a one-lane segment is likely to be more severe than a crash on a two-lane segment, when all other variables are controlled. The percentages in Table 108 indicate that the K+A crash percentage on a one- lane segment is 16.4 percent, and it is 15.6 percent on a two-lane segment. The trends in Table 108 for number of lanes may be partly explained by the fact that segments with more lanes have increased likelihood of less severe same direction sideswipe crashes and reduced likelihood of more-severe rear-end crashes (Jonsson et al., 2007). Also, two- lane ramps are more common in urban areas and, thus, are more likely to be associated with lower speed than ramps in rural areas. Abdel-Aty and Keller (2005) analyzed crash severity at signalized intersections and found that intersections with more lanes on the major road have less severe crashes.

340 TABLE 108. Ramp severity distribution based on lanes, area type, and ramp type Variable Type Severity Level Distribution, percent Fatal (K) or Incapacitating Injury (A) Non-Incapacitating Injury (B) Possible Injury (C) Number of lanes 1 16.4 36.4 47.2 2 15.6 28.1 56.3 Area type Rural 21.1 47.9 31.0 Urban 16.4 36.4 47.2 Ramp type 1 Exit 16.4 36.4 47.2 Other 11.8 36.6 51.7 Note: 1 - “Other” includes entrance ramps, connector ramps at system interchanges, and C-D roads. Area Type. The relationship between area type and crash severity level was also considered during model calibration. It is generally recognized that probabilistic models should be developed separately for urban and rural crashes. However, separate models were not developed in this project due to the limited sample size. The relationship between area type and severity level is shown in Table 108. The positive value of the associated coefficient (in Table 107) indicates that a crash in a rural area is likely to be more severe than a crash in an urban area, when all other variables are controlled. The percentages in Table 108 indicate that the K+A crash percentage on a rural ramp is 21.1 percent, and it is 16.4 percent on an urban ramp. The trend with area type in Table 108 can be attributed to higher operating speeds on rural freeways and associated ramps. A crash that occurs at higher speed typically has higher severity than a crash at lower speed. Ramp Type. The relationship between ramp type and severity level is shown in Table 108. The positive value of the associated coefficient (in Table 107) indicates that a crash on an exit ramp is likely to be more severe than a crash on another type of ramp or on a C-D road, when all other variables are controlled. The percentages in Table 108 indicate that the K+A crash percentage on an exit ramp is 16.4 percent, and it is 11.8 percent on other ramp types. The increased likelihood of severe crashes on exit ramps can be attributed to driver speed adaption. Drivers on exit ramps tend to have difficulty reducing speed and complying with ramp advisory speeds after a long period of driving on a freeway (Highway, 2010). Jason et al. (1998) found that rear-end crashes involving trucks are more likely to occur in freeway sections with exit ramps than in sections with entrance ramps. CROSSROAD RAMP TERMINALS This part of the chapter describes the activities undertaken to calibrate a SDF for crossroad ramp terminals. It consists of three sections. The first section describes the data used to

341 calibrate the SDFs. The second section provides an overview of the approach used to develop the SDF model form. The third section presents the modeling results. Highway Safety Database The HSIS was used as the primary source of data for model calibration. The “HSIS” states California, Maine, and Washington were identified as including ramp volume data, which is of fundamental importance to all aspects of this project. These data were not available from the other HSIS states. Hence, the database assembly focused on these three states. They are called the “study states” in this report. The data acquired from the HSIS is summarized in Table 60. As discussed in Appendix B, several of the geometry and lane use variables in the study state databases were of unknown accuracy. Also, several variables often had subtly different definitions among states. Moreover, the study state databases often did not include variables that describe road-related factors known to be associated with crash severity. To overcome these limitations, the study-state databases were enhanced using data from other sources. The data collected include the ramp terminal configuration, number of lanes, bay presence, type of control, and median width. A complete list of the supplemental data is provided in Table 61. Modeling Approach For highway safety applications, the multinomial logit (MNL) model is used to predict the probability of each crash severity level. A brief description of the MNL model and other discrete choice models was given in the part titled Literature Review. This model is shown in Equations 320 to 325. The deterministic component of the model is used to relate the crash severity with the site’s geometric design features, traffic control features, and traffic characteristics. The SAS (2009) nonlinear mixed modeling procedure (NLMIXED) was used for the evaluation of MNL model. Initially, the SDF was developed to predict the proportion of crashes in each severity level. However, the model was not able to quantify statistically significant coefficients for most variables due to a small number of reported fatal crashes. Thus, the fatal and incapacitating injury crashes are combined into one level for model calibration. The probability for each crash severity level is given by Equations 334 to 336, as shown in the part of this chapter addressing ramp segments. Modeling Results This section describes the modeling results. It is divided into five subsections. The first subsection describes the calibration data. The second subsection describes the formulation of the calibration model. The third subsection describes the calibrated model and estimation results. The fourth subsection examines the sensitivity of the model for signalized crossroad ramp terminals. The last subsection examines the sensitivity of the model for unsignalized crossroad ramp terminals.

342 Calibration Data The database assembled for calibration included crash severity level as a dependent variable. Geometric design features, traffic control features, and traffic characteristics were included as independent variables. The highway safety database required modification to be used for SDF calibration. Each observation in the highway safety database represents one site with known geometric features, traffic control features, traffic characteristics, and crash frequency (by severity level). To convert this database to the form needed for SDF calibration, each observation is repeated once for each fatal or injury crash associated with it. An attribute indicating the severity of the crash is added to the newly-created SDF database. The total sample size of the SDF database is equal to total number of injury and fatal crashes in the highway safety database. During the model calibration, the “possible injury” level is set as the base scenario with coefficients restricted to 0.0. Table 109 presents a brief summary of the data variables used for SDF development. The variables listed were those found to have an important influence on crash severity level. A complete list of all variables in the database is given in Chapter 7. Model Development The following model form was used for the deterministic component of the SDF during the regression analysis. ( ) ( ) ( ) ( )ruralAKruralpsAKps psdwAKndltpAKpAKAK IbIb nnbIbASCV ×+×+ +×+×+= ++ ++++ ,, ,,, ][ (342) ( ) ( ) ( ) ( )ruralBruralpsBps psdwBndltpBpBB IbIb nnbIbASCV ×+×+ +×+×+= ,, ,,, ][ (343) memecaca IbIbeC += (344) where, Ip, lt = protected left-turn operation indicator variable for crossroad (= 1.0 if protected operation exists, 0.0 otherwise); ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; Ips = non-ramp public street leg indicator variable (= 1.0 if leg is present, 0.0 otherwise); Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); Ime = Maine indicator variable (= 1.0 if segment in Maine, 0.0 otherwise); and Ica = California indicator variable (= 1.0 if segment in California, 0.0 otherwise).

343 TABLE 109. Summary statistics for crossroad ramp terminal SDF development Control Type Variable Type Mean Standard Deviation Minimum Maximum Crash Count Signalized Driveway + public street approach freq. 0.63 0.99 0 4 1,708 Left-turn operation Protected 908 Other 800 Non-ramp public street leg Present 1,679 Not present 29 Area type Rural 69 Urban 1,639 Severity level K 2 A 50 B 316 C 1,340 Unsig- nalized Area type Rural 176 Urban 189 Severity level K 4 A 21 B 88 C 252 The final form of the regression model is described by the preceding equations. This form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. Model Calibration Table 110 summarizes the estimation results of model calibration. An examination of the coefficient values and their implication on the corresponding crash severity levels are documented in a subsequent section. In general, the sign and magnitude of the regression coefficients in Table 110 are logical and consistent with previous research findings. The t-statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database).

344 TABLE 110. Parameter estimation for crossroad ramp terminal SDF Control Type Variable Inferred Effect of... Fatal (K) or Incapacitating Injury (A) Non-Incapacitating Injury (B) Value t-statistic Value t-statistic Signalized ASC Alternative specific constant -3.2571 -14.78 -1.5107 -14.79 bp Protected left-turn operation -0.2884 -0.99 -0.1933 -1.5 bnd Driveways or pub. st. approaches 0.09905 0.71 0.1487 2.44 bps Public street leg at ramp terminal 1.171 1.48 0.7410 1.74 brural Added effect of area type 0.6191 0.99 0.4160 1.36 bme Location in Maine 0.5248 2.24 0.5248 2.24 Unsig- nalized ASC Alternative specific constant -3.167 -7.96 -1.476 -7.22 brural Added effect of area type 0.8907 1.91 0.2207 0.86 bca Location in California 0.7327 3.11 0.7327 3.11 Indicator variables were included for the states of California and Maine. For signalized terminals, only the coefficient for Maine was statistically significant. The coefficient for this variable is shown in row 6 of Table 110. Its value indicates that a crash at a signalized terminal in Maine is likely to be more severe than a crash at a signalized terminal in California and Washington. For unsignalized terminals, only the coefficient for California was significant. Its value indicates that a crash at an unsignalized terminal in California is likely to be more severe than a crash at an unsignalized terminal in Maine or Washington. The difference may be explained by different crash reporting practices, highway design practices, terrain, and weather for the various states. The coefficients in Table 110 were combined with Equations 342 and 343 to obtain the deterministic component of each crash severity level for crossroad ramp terminal crashes. The form of each model for signalized ramp terminals is described by the following equations. ( ) ( ) ( ) ( )ruralps psdwltpAK II nnIV ×+×+ +×+×−−=+ 6191.0171.1 ][09905.02884.02571.3 , (345) ( ) ( ) ( ) ( )ruralps psdwltpB II nnIV ×+×+ +×+×−−= 4160.07410.0 ][1487.01933.05107.1 , (346) The probability of each severity level is obtained by combining Equations 334 to 336 with Equations 345 and 346. A procedure for local calibration was described previously in the discussion associated with Table 105. Although several variables are considered during the calibration of the SDF for unsignalized terminal, only the rural indicator variable was found to be significant. The insignificance of other variables is partially attributed to small sample size. The form of each model for unsignalized ramp terminals is described by the following equations.

345 ( )ruralAK IV ×+−=+ 8907.01676.3 (347) ( )ruralB IV ×+−= 2207.0476.1 (348) The probability of each severity level is obtained by combining Equations 334 to 336 with Equations 347 and 348. Predicted Probabilities for Signalized Crossroad Ramp Terminals Access Point Frequency. The access point frequency at a crossroad ramp terminal represents the total number of driveways and unsignalized public street approaches on the crossroad leg that is outside of the interchange. Driveways and approaches on both sides of the leg should be counted when they are within 250 ft of the ramp terminal. The count of driveways should only include active driveways (i.e., those driveways with an average daily volume of 10 veh/day or more). The relationship between access point frequency and severity level is shown in Figure 144. The positive value of the associated coefficient (in Table 110) indicates that, as the number of access points increases, the likelihood of severity levels K, A, and B also increases. The trends in Figure 144 indicate that the K+A crash percentage changes from 6.7 percent with no access points, to 8.4 percent with four access points. A similar trend is shown for severity level B. It is rationalized that crashes associated with driveway traffic tend to be of the right-angle type, which tend to be more severe than other crashes that occur on intersection approaches. Kim et al. (2006) found that the number of driveways within 250 ft of intersection center have a positive association with angle, rear-end, and sideswipe crash types, with angle crashes being the most severe among the three crash types. Oh et al. (2004) stated that driveways at intersections provide additional conflict points that increase the chance of driveway-related crashes. A study of the safety impacts of access management techniques in Utah found that the driveway consolidation decreased crash severity (Schultz et al., 2007).

346 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 1 2 3 4 Access Point Frequency D is tri bu tio n of C ra sh es b y Se ve rit y, % C B K+A Figure 144. Crossroad ramp terminal severity distribution based on access point frequency. Left-Turn Operation. This variable reflects the presence of protected-only left-turn operation on either crossroad approach (if signalized). If a ramp terminal has permissive or protected-permissive operation then it does not have protected operation. This focus on protected operation is based partly on the guidance in Chapter 14 of the HSM that indicates a change from permissive to protected-permissive operation has a negligible effect on safety. The relationship between left-turn operation and severity level is shown in Table 111. The negative value of the associated coefficient (in Table 110) indicates that a crash at a terminal without protected-only left-turn operation is likely to be more severe than a crash at a terminal with protected-only operation, when all other variables are controlled. The percentages in Table 111 indicate that the K+A crash percentage at a terminal with protected-only operation is 7.0 percent, and it is 8.7 percent at a terminal without protected-only operation. TABLE 111. Crossroad ramp terminal severity distribution–signalized Variable Type Severity Level Distribution, percent Fatal (K) or Incapacitating Injury (A) Non-Incapacitating Injury (B) Possible Injury (C) Left-turn operation Protected-only 7.0 21.8 71.2 Other 8.7 24.8 66.5 Non-ramp public st. leg Present 16.0 32.7 51.4 Not present 6.9 21.6 71.5 Area type Rural 7.0 21.8 71.2 Urban 4.2 16.1 79.7

347 It is rationalized that intersections without protected left-turn operation are more likely to have crashes between left-turn vehicles turning permissively through gaps in oncoming traffic. The collisions that result from permissive operation tend to involve oncoming traffic that is moving with high speed, relative to the vehicles involved in collisions associated with protected- only operation. Research by Wang and Abdel-Aty (2008) indicates that a protected left-turn phase is associated with less severe crashes. Non-Ramp Public Street Leg. This variable is applicable to any ramp terminal that has a fourth leg that: (1) is a public street serving two-way traffic and (2) intersects with the crossroad at the terminal. Public street legs are fairly rare (i.e., they were found at about 2 percent of the terminals in the database). At most ramp terminals, the public street leg will be on the opposite side of the crossroad from the exit ramp. The relationship between public street leg presence and severity level is shown in Table 111. The positive value of the associated coefficient (in Table 110) indicates that a crash at a terminal with a public street leg is likely to be more severe than a crash at a terminal without a public street leg, when all other variables are controlled. The percentages in Table 111 indicate that the K+A crash percentage at a terminal with a public street leg is 16.0 percent, and it is 6.9 percent at a terminal without a public street leg. It is rationalized that when a public street leg is present, there is an increased opportunity of head-on, angle and side-swipe-opposite-direction crashes, which are typically severe. The presence of a public street leg effectively converts a three-leg terminal into a four-leg terminal. Thus, the effect of public street leg presence on crash severity should be similar to that found when comparing three-leg and four-leg intersections. Jonsson et al. (2007) showed that three-leg intersections typically experience a higher percentage of less severe same direction crashes. Similarly, Vogt and Bared (1998) noted that the percentage of K, A, and B crashes at four-leg intersection is much larger than at three-leg intersections. Area Type. The relationship between area type and crash severity level was also considered during model calibration. It is generally recognized that probabilistic models should be developed separately for urban and rural crashes. However, separate models were not developed in this project due to the limited sample size. The relationship between area type and severity level is shown in Table 111. The positive value of the associated coefficient (in Table 110) indicates that a crash in a rural area is likely to be more severe than a crash in an urban area, when all other variables are controlled. This trend can be attributed to higher operating speeds on rural crossroads. A crash that occurs at higher speed typically has higher severity than a crash at lower speed. The percentages in Table 111 indicate that the K+A crash percentage at a rural ramp terminal is 7.0 percent, and it is 4.2 percent at an urban ramp terminal.

348 Predicted Probabilities for Unsignalized Crossroad Ramp Terminals Unsignalized ramp terminals are fairly common in rural areas. Of 301 ramp terminals in the database, about 65 percent are located in a rural area. However, only about 50 percent of the crashes in the database occurred at rural ramp terminals. The relationship between area type and severity level for unsignalized terminals is shown in Table 112. The positive value of the associated coefficient (in Table 110) indicates that a crash in a rural area is likely to be more severe than a crash in an urban area, when all other variables are controlled. This trend is similar to that found for signalized ramp terminals and can be attributed to higher operating speeds on rural crossroads. A comparison of the percentages in Tables 111 and 112 indicates that a crash is more likely to have severity level K or A if it occurs at an unsignalized ramp terminal, than if it occurs at a signalized terminal. TABLE 112. Crossroad ramp terminal severity distribution–unsignalized Variable Type Severity Level Distribution, percent Fatal (K) or Incapacitating Injury (A) Non-Incapacitating Injury (B) Possible Injury (C) Area type Rural 14.2 19.0 66.7 Urban 6.7 17.4 76.0