Abstract
The crash prediction models (CPMs) in Part C of the Highway Safety Manual (HSM) are often used to infer the safety effect of a change in facility type and control mode. However, several researchers have observed that the HSM CPM for signal-controlled intersections predicts a larger average crash frequency than the HSM CPM for stop-controlled intersections (for the same volume level). Most recently, some of the CPMs for roundabouts developed in National Cooperative Highway Research Program (NCHRP) Project 17-70 for the second edition of HSM were observed to predict a larger average crash frequency than the HSM CPMs for stop- and signal-controlled intersections. This paper discusses why comparing two HSM CPMs to infer that the safety effect is problematic when the associated characteristic is endogenous to the comparison. The characteristics “convert to signal” and “convert to roundabout” are shown to be endogenous to the HSM CPMs being compared. The correct interpretation of the results from this comparison are described and possible reasons are offered to explain why these results should not be expected to agree with a CMF (for the same change in character). It is recommended that the HSM should offer guidance on the correct interpretation of the results obtained when comparing two HSM CPMs to infer safety effect of a change in character. The roundabout SPFs that were changed for inclusion in HSM2 no longer appear to give consistent or convincing results when comparing roundabouts with three- versus four-legs or with one versus two circulating lanes.
Introduction
National Cooperative Highway Research Program (NCHRP) Project 17-70 ( 1 ) developed safety performance functions (SPFs) for evaluating roundabout safety. The SPFs were recommended for inclusion in a future edition of the Highway Safety Manual (HSM1) ( 2 ). The SPFs were changed before their inclusion in the second edition of Highway Safety Manual (HSM2). The rationale for these changes is described in the following quote from NCHRP Report 1140 ( 3 ).
“An issue identified in the review of the NCHRP Project 17-70 research results is that the crash prediction models for roundabouts predict many more crashes than the comparable HSM1 and HSM2 models for conventional intersections. Available research results suggest that the opposite should be the case. For example, HSM1 Part D shows that typical crash modification factors (CMFs) for total crashes for converting conventional intersections to roundabouts for all settings and crash severity levels are 0.52 for signalized intersection to roundabout conversions in HSM1 Table 14-3 and 0.56 for stop-controlled intersection to roundabout conversions in HSM1 Table 14-4. The base condition for these CMFs was the absence of a roundabout. Such CMFs were used in adjusting the roundabout SPFs from NCHRP Project 17-70 to reflect the known effectiveness of roundabouts to be more appropriate relative to other intersection types.” (
3
; p. 35).
A recent, empirical-Bayes-based before–after study of the safety effect of roundabout conversion produced total-crash CMF values based on the conversion of 43 signalized intersections and 46 stop-controlled intersections in Michigan ( 4 ). The reported total-crash CMF for converting a signalized intersection to a roundabout with one or two lanes is 1.92 and that for converting a stop-controlled intersection is 1.29. A similar trend was reported by Leuer for two-lane roundabouts ( 5 ). These CMF values differ significantly from the HSM1 values in the above citation. This difference suggests that there is still some uncertainty about the safety effect of roundabout conversion; they cast some doubt about the suitability of using the HSM1 CMF values as a basis for changing the roundabout SPF coefficients.
This paper examines the changes made to the roundabout SPFs by Torbic et al. ( 3 ), the use of CMFs as a basis for these changes, and the possible implications of these changes on the reliability of the roundabout SPFs prepared for HSM2.
Background
Each crash prediction model (CPM) in Part C of HSM1 describes the relationship between average crash frequency and a specified site type. The “site type” is generally described by its facility type (e.g., rural multilane highway intersection), control mode (e.g., minor stop), and possibly other site characteristics that have a significant influence on its relative safety (e.g., number of lanes, number of legs). Each CPM includes a “base-condition SPF,” one or more SPF adjustment factors (AFs) (previously referred to as crash modification factors), and a local calibration factor.
The “base-condition SPF” (hereafter referred to simply as “SPF”) includes variables that describe the exposure elements at a site (e.g., volume, length). AFs are used with the SPF to obtain an estimate of the predicted crash frequency for a site with one or more characteristics that are not consistent with the base conditions.
The SPF provides an estimate of the predicted crash frequency for a site with specified set of base conditions. Each base condition corresponds to a site characteristic with a demonstrated association with crash frequency. The base conditions for each HSM SPF have been defined by the researcher that developed the SPF. A review of these base conditions for the HSM SPFs indicates that they tend to describe commonly found values for selected site characteristics. These characteristics may include (a) the presence (or absence) of specified a site characteristic (e.g., left-turn bay not present) or (b) the width of a cross-section element (e.g., a lane width of 12 ft).
The HSM SPFs were estimated using regression analysis of cross-sectional data. The sites included in the data were selected from the study area to be representative of the specified site type. There was no focus during site selection to include only sites that could be candidates for conversion to another site type. For example, the sites used to estimate the SPF for minor-stop-controlled intersections were not screened to include only those sites that would likely justify conversion to signal control. Rather, because the sites were selected to be regionally representative, some of the sites used to estimate the SPF for minor-stop-controlled intersections would likely justify conversion to signal control but most of the sites would not likely justify this conversion.
Given the site selection process for the HSM SPFs, they are referred to here as “typical-site” SPFs and the CPMs that include them are referred to as HSM CPMs or “typical-site” CPMs.
In a change from HSM1, HSM2 reserves the term “crash modification factor” (CMF) to describe a value developed from a before–after study. High-quality CMFs are produced by studies that account for regression-to-the-mean, traffic volume changes over time, and non-treatment-related time trends. CMFs are based on observational studies because the decision to implement the change is based on the operating agency’s policies and project programming objectives. As a result, CMFs describe the safety effect of a change at only those sites where the agency has determined that the change is justified.
CPM Application 1—Comparison of Site Design Alternatives
The primary purpose of the HSM CPMs is to facilitate the evaluation of alternative design and operational strategies for a given site having a specified facility type and control mode. Through repeated application of the CPM, the analyst compares design alternatives using the available AFs and makes inferences about the relative safety of different design variations (e.g., increase lane width, increase inscribed circle diameter, provide turn bay).
CPM Application 2—Comparison of Alternative Site Types
During development of the HSM it was realized that there would be interest in comparing the CPMs for alternative site types (e.g., alternative facility type, alternative control mode). In this regard, it became apparent to the HSM developers that the CPMs would be used by analysts to compare alternative facility types (e.g., four-lane undivided arterial street versus four-lane divided arterial street), alternative control modes (e.g., minor-stop-controlled intersection versus signal-controlled intersection), or both (e.g., roundabout versus minor-stop-controlled intersection).
Challenges when Using CPMs to Compare Alternatives
Presence of Endogenous Site Characteristics
In general, some design and traffic control characteristics of a site are added (or changed) by the operating agency based partly on safety considerations. This trait can make the characteristic endogenous when it is (a) represented as a variable in a CPM for the associated site type and (b) not accounted for in study design or by statistical method during CPM development ( 6 ). In general, endogeneity is more likely found in site characteristics for which there are agency guidelines that describe when the characteristic’s addition (or change) is justified, and this justification is based partly on safety considerations (e.g., it satisfies warranting criteria; its safety and other road-user benefits exceed its implementation cost).
In general, if endogeneity is present in a site characteristic but this endogeneity is not accounted for when inferring the characteristic’s safety effect, then the magnitude of the inferred effect may not agree with the CMF value produced by a before–after study of this characteristic ( 6 – 8 ).
The presence of endogeneity has been reported in regression models (developed with cross-sectional data) that were used to quantify the effect of the following countermeasures: “add warning sign,”“add turn bay,” and “decrease speed limit” ( 6 , 7 ). In each case, an initial regression analysis of the data (that included sites with and without the countermeasure) indicated that the countermeasure was associated with an increase in crash frequency. However, when statistical methods were used to estimate each site’s likelihood of justifying the countermeasure, the resulting regression analysis indicated that the countermeasure was associated with a decrease in crash frequency at sites that justified its implementation.
In summary, endogeneity in a regression model variable can result in an inferred safety effect that is different from that produced by a before–after study. This difference is referred to as “selectivity-bias” by Mannering and Bhat ( 6 ) and as “endogeneity bias” by Elvik ( 9 ). However, it is asserted here that this potential for disagreement does not mean that one result is wrong and the other is right. Rather, both an inferred safety effect and a before–after-based CMF can be correct when interpreted in the context of the sites that are being evaluated. This assertion will be explained further in a subsequent section.
CPMs Estimated using Data from Different States
The CPMs developed for the HSM are a product of several research projects. Some projects focused on the development of a set of CPMs to address the more common types of sites found on a specified roadway class (e.g., four-leg stop-controlled intersection on rural two-lane two-way road). Other projects focused on the development of a set of CPMs to address the less common types of sites (e.g., roundabout) across all roadway classes. For each project, the researchers used crash data for a set of states that were suitable for developing the subject CPMs. The states were selected for use based on consideration of the number of existing sites in the state, availability of crash data from local agencies, and the researcher’s ability to leverage project resources by using data collected for previous projects.
Early efforts by the HSM1 developers revealed that state-to-state differences in safety-related elements (e.g., crash data element definitions, crash location assignment rules, crash reporting thresholds, weather, design policy, and driver behavior) were correlated with the CPM predictions. To mitigate these state-to-state differences in the HSM1 CPM predictions, the HSM developers had all the intersection and segment CPMs re-calibrated using data for California and Washington, respectively.
For HSM2, the HSM developers undertook a second “common-state calibration” activity through NCHRP Project 17-72 ( 12 ). The Project 17-72 researchers recalibrated the CPM for many (but not all) of the site types in HSM2. They did not recalibrate the CPMs associated with some less common site types because of difficulties encountered in identifying a statistically valid site sample size.
This issue has limited effect on the reliability of results from CPM Application 1. However, the results of CPM Application 2 are likely to be unreliable when the two HSM CPMs being compared are not calibrated for the same state or region ( 13 ). In contrast, the results are likely more reliable when the two HSM CPMs are calibrated for the same state or region in which the subject site is located ( 2 , p. C-18).
Using CPMs to Compare Alternatives
Illustration of the Endogeneity Issue in “Convert to Signal”
As noted previously, one application of the HSM CPMs is to use them to infer the safety effect of a proposed change in facility type or control mode (i.e., CPM Application 2). This type of comparison has been documented in the literature to address the question of “what is the effect of signal installation on intersection safety?” ( 8 , 14 – 16 ). A review of the results of these studies indicates a wide range of results—from “signalization decreases crash risk” to “signalization increases crash risk” ( 17 ). Persaud ( 14 ) cites several studies of the effect of “convert to signal.” He found that (a) studies comparing crash rates (or typical-site SPF predicted values) tend to indicate that signalization increases crash risk and (b) before–after studies tend to indicate that signalization decreases crash risk. A recently funded project by NCHRP (i.e., Project 17-142) is evidence that the question is still unresolved.
In general, the contradictory nature of the results related to the question of signalization’s safety effect is consistent with a site characteristic (e.g., “signal presence”) that is endogenous when inferred from CPMs. The review also revealed that this trait is typically not considered when interpreting study results.
Trend 1
Trends in crash rate reported for typical rural multilane highway intersections are listed in the first five rows of Table 1. The crash rates in these rows suggest that “convert to signal” increases crash risk at the typical intersection (many of which are unlikely to be eligible for signalization). This increase is indicated by a crash rate ratio greater than 1.0 in the last column. These results are consistent with the findings of Persaud et al. ( 18 ) who found that crash frequency was reduced by removing the signal at intersections at which the signal was not justified.
Crash Rates for Four-leg Intersections on Rural Multilane Highways
Note: cr/mev = crashes per million entering vehicles; na = not applicable.
Olge and Rajabi ( 19 );
Storm and Richfield ( 20 );
Based on comparison site data reported by Harwood et al. ( 21 , Table 20);
Based on crash data reported by Harwood et al. ( 21 , Table 20) for minor-stop-controlled intersections in the years just before the implementation of signal control.
“Total” crashes include fatal-and-injury (FI) and property-damage-only (PDO) crashes of all crash types.
The crash rate trend in the first five rows of Table 1 is consistent with the trend obtained when comparing the corresponding HSM1 CPMs for four-leg intersections on rural multilane highways, as shown in Figure 1 ( 17 ). The two thick lines in this figure correspond to the HSM1 CPM for signalized intersections. The upper line of the pair is obtained when the combined AFs are greater than 1.0 (i.e., the site has few safety features) and the lower line of the pair is obtained when the combined AFs are less than 1.0. The relative position of the lines in this figure indicates that “convert to signal”increases crash risk at the typical intersection. This trend was also observed by Hauer ( 8 ) when comparing the HSM2 SPFs for four-leg intersections on rural multilane highways and when comparing the HSM2 SPFs for intersections on urban and suburban streets.
Predicted crash frequency for four-leg intersections on rural multilane highways.
Trend 2
The last row of Table 1 identifies the crash rate for minor-stop-controlled intersections that were subsequently signalized. Based on their eminent signalization, it is reasonable to conclude that these intersections were eligible for conversion to signalization based on an engineering study that included consideration of the Manual on Uniform Traffic Control Devices’ (MUTCD) traffic signal warrants ( 22 ). The crash rate of 1.12 cr/mev (crashes/million entering vehicles) for these intersections is larger than the 0.35 cr/mev in row 5, which describes typical intersections in the same states (many of which are not eligible for signalization). This trend suggests that intersections that justify signalization tend to have a higher crash risk than the typical intersection.
Trend 3
The crash rate of 1.12 cr/mev for the “eligible” minor-road stop-controlled intersections is more than twice that found for signalized intersections (i.e., 0.51 cr/mev) in the same states. It can be inferred from these two rates that “convert to signal”decreases total crash risk at intersections for which a signal was justified. This inference is consistent with a “convert to signal” CMF developed by Srinivasan et al. ( 23 ). They evaluated 117 rural and suburban intersections that were identified for signalization as part of the state Department of Transportation’s (DOT’s) Spot Safety Evaluation reports. Given the nature of the DOT’s selection of sites for signalization, it is reasonable to conclude that these sites were eligible for conversion to signalization based on an engineering study that included consideration of the MUTCD’s traffic signal warrants ( 22 ). Their study produced a CMF for “add signal to rural four-leg stop-controlled intersection” equal to 0.61, indicating that “convert to signal”decreases crash risk at intersections for which a signal was justified.
Summary
The tendency for eligible minor-stop intersections to have a higher crash rate than the typical minor-stop intersection (i.e., trend 2) and the tendency for the two minor-stop intersection groups to have a different response to the conversion (i.e., trends 1 and 3) is evidence of endogeneity in the “convert to signal” site characteristic.
One of three outcomes can occur when considering the typical signalized intersection crash rate in the last two rows of Table 1. First, if the typical signalized intersection crash rate was less than that of the typical minor-stop intersection (say, 0.30 cr/mev instead of 0.51 cr/mev), then the inferred safety effect of the change would likely be smaller than a before–after-based CMF but both would agree that “convert to signal” decreases crashes. Second, if the typical signalized intersection crash rate was greater than that of the eligible minor-stop intersection (say, 1.2 cr/mev), then the inferred safety effect of the change would likely be larger than a before–after-based CMF but both would agree that “convert to signal” increases crashes. Third, if the typical signalized intersection crash rate is between that of the eligible and typical minor-stop intersection (as shown in the table), then the inferred safety effect would be contrary to a before–after-based CMF. This third outcome has proven to be most problematic because it produces results that are contrary to expectation. It has resulted in considerable discussion in the research literature about the reliability of typical-site CPMs when used to infer the safety effect of “convert to signal” ( 8 , 15 , 16 ).
Illustration of the Endogeneity Issue in “Convert to Roundabout”
A report by Leuer ( 5 , p. 5) states that the Minnesota Department of Transportation’s (MnDOT) practice concerning roundabout justification is “In general terms, any intersection—whether in an urban or rural environment—that meets the criteria for additional traffic control beyond a thru stop condition, also qualifies for evaluation as a modern roundabout.” This practice is likely to result in the “convert to roundabout” characteristic being endogenous when comparing typical roundabouts to typical minor-stop-controlled intersections.
The potential for endogeneity in “convert to roundabout” can be examined using crash rates reported by Leuer ( 5 ) for intersections and roundabouts. These crash rates are listed in Table 2. The roundabout crash rates are based on data for 144 roundabouts in Minnesota. All of the roundabouts were converted from an existing stop-controlled or signalized intersection. The “eligible intersection” crash rates are computed using the data reported for the intersections in the years just before their conversion to roundabout. The “typical intersection” crash rates are based on data provided in MnDOT’s Intersection Toolkit spreadsheet and as such, are considered to be representative of typical Minnesota intersections.
Crash Rates for Roundabouts and Traditional Intersections in Minnesota
Note: cr/mev = crashes per million entering vehicles; FI = fatal and injury; PDO = property damage only; na = not applicable.
Eligible intersection crash rate based on the three- and four-leg signalized intersections and minor-stop-controlled intersections in the years just before conversion to roundabout.
Typical intersection crash rates based on the three- and four-leg intersections listed in MnDOT’s Intersection Toolkit spreadsheet (https://www.dot.state.mn.us/stateaid/trafficsafety.html) and as such, are considered to be representative of typical Minnesota intersections. Rates for FI crashes are based on the Toolkit for 2019–2023. Rates for “All levels” crashes are based on the Toolkit for 2011–2015 (as reported by Leuer [5]).
Roundabout crash rate includes both three- and four-leg roundabouts.
Source: Leuer ( 5 ).
Trend 1
The crash rates in Table 2 for typical minor-stop intersections and for typical signalized intersections with four major-road lanes are smaller than those for roundabouts. This trend suggests that “convert to roundabout” increases crash risk for the typical minor-stop controlled intersection and for the typical signalized intersection on multilane roads. This observation is contrary to the CMF values for roundabout conversion in Part D of HSM1 ( 2 , Chapter 14). This contradiction is similar to that reported by Persaud ( 14 ) when examining studies of the effect of “convert to signal.”
The trends noted in the previous paragraph are consistent with those found by comparing the SPFs developed for NCHRP Project 17-70 with the HSM1 SPFs for minor-stop intersections and signalized intersections. These SPFs are compared in Figure 2 for urban, four-leg intersections. The length of the trend lines for the minor-stop intersection and the signalized intersection roughly corresponds to the range of volumes wherein signal control does/does not satisfy the MUTCD traffic signal warrants ( 22 ).
Predicted crash frequency for four-leg intersections and roundabouts on urban streets. (a) roundabout with one circulating lane; (b) roundabout with two circulating lanes.
Figure 2a compares the SPFs from HSM1 ( 2 , Chapter 12) with the 17-70 SPF for roundabouts with one circulating lane. The trend lines indicate that the roundabout has a slightly larger crash frequency than the minor-stop intersection for entering volumes of less than 7,500 vehicles per day (veh/d). In contrast, the roundabout has a smaller crash frequency than the signalized intersection. This trend is consistent with Table 2.
Figure 2b compares the SPFs from HSM1 ( 2 , Chapter 12) with the 17-70 SPF for roundabouts with two circulating lanes. The trend lines in this figure indicate that the 17-70 SPF predicts a larger crash frequency than the minor-stop intersection and the signalized intersection. This trend is consistent with Table 2.
Trend 2
The “eligible intersection” column of Table 2 identifies the crash rate for intersections that were subsequently converted to roundabout. Based on their eminent conversion to roundabout and the aforementioned MnDOT practice, it is reasonable to conclude that these intersections were eligible for conversion to roundabout based on an engineering study that included consideration of the MUTCD’s traffic signal warrants ( 22 ). With one exception, the crash rate for the eligible intersections is larger than that of the typical intersections (as shown in the last column). This trend suggests that intersections that justify conversion to roundabout tend to have a higher crash risk than the typical intersection.
Trend 3
The second-to-last column of the table compares the crash rate of the eligible intersections with that of the typical roundabout. It can be inferred from this comparison that “convert to roundabout” decreases total crash risk at intersections for which a roundabout with one circulating lane was justified; a finding that is consistent with the aforementioned CMFs reported in Part D of HSM1 ( 2 ). In contrast, the crash rate ratio in the second-to-last column for roundabouts with two-circulating lanes indicates a tendency to significantly increase total crashes. This finding is consistent with the findings from a before–after study conducted by Savolainen et al. ( 4 ), but it is in contrast to the CMFs reported in Part D of HSM1 ( 2 ).
Summary
The tendency for eligible intersections to have a higher crash rate than the typical intersection (i.e., trend 2) and the tendency for the two intersection groups to have a different response to the conversion (i.e., trends 1 and 3) is evidence of endogeneity in the “convert to roundabout” site characteristic. The last column of Table 2 illustrates the tendency associated with trend 2 to exist in seven of the eight combinations of crash severity, major road lanes, and control mode before conversion.
Of the three outcomes that can occur when considering the typical roundabout crash rate, the most problematic outcome is observed for conversions from minor-stop intersection to one-circulating lane roundabout. The typical roundabout crash rate is between that of the eligible and typical minor-stop intersection. The inferred safety effect is likely to be contrary to a before–after-based CMF.
A second outcome is observed for the conversion to a two-circulating-lane roundabout. The typical roundabout crash rate is larger than that for both the eligible intersection and the typical intersection. With this outcome, the inferred safety effect is likely to be larger than a before–after-based CMF but both agree that “convert to roundabout” increases crashes. Both of these outcomes were noted by Torbic et al. ( 3 ) to be contrary to expectation and served as justification for their changes to the Project 17-70 SPFs.
Eligibility for a Change in Character
A site’s eligibility for a proposed condition should reflect consideration of formal or informal agency practice to consistently implement the proposed condition when specific criteria are satisfied (and this implementation has an influence on safety). In general, eligibility criteria would identify a threshold observed crash frequency or a threshold benefit–cost ratio that justifies the implementation of the proposed condition. The benefit–cost ratio would be obtained from an economic analysis that considers safety and other road-user benefits.
A site’s eligibility can be readily determined when the operating agency has a safety-based guideline specifying criteria that justify implementation of the proposed condition. An example of this type of guideline is the MUTCD and, notably, its traffic signal warrants that describe site characteristics that indicate when signalization may be justified.
Methods for Mitigating Endogeneity
When estimates from two CPMs are being compared to infer the safety effect of a proposed change, it is important to determine if the change corresponds to a potentially endogenous characteristic. For CPM Application 2 (i.e., comparison of site types), the characteristic being changed (i.e., facility type or control mode) is often endogenous to some degree. If endogeneity is likely present in the characteristic being changed and it is important to quantify the safety effect of this change when made only to sites eligible for that change, then endogeneity should be mitigated to ensure the quantified safety effect is unbiased.
If the conditions outlined in the previous paragraph are met (i.e., comparing two CPMs to infer the safety effect of an endogenous characteristic that is changed only at sites eligible for change), then endogeneity can be mitigated by two methods. These methods are described in the following paragraphs. For both methods, the “proposed condition” CPM is used to compute the predicted average crash frequency for typical sites with the proposed condition. Additionally, both CPMs being compared are calibrated to the state or region in which the existing site is located.
Method 1—Mitigate During CPM Development
This method requires the “existing condition” CPM to be developed to account for the endogenous site-type characteristic. This CPM would be used to compute the predicted average crash frequency of a site eligible for the proposed condition. Endogeneity can be accounted for through (a) site selection (i.e., the CPM development database includes only eligible sites), or (b) use of statistical methods to account for site eligibility in the data ( 7 , 24 , 25 ).
Method 2—Mitigate During CPM Application
This method is based on a procedure developed by Persaud et al. ( 11 , 26 ). It does not require the “existing condition” CPM to be developed to account for the endogenous site-type characteristic. Rather, the “existing condition” CPM is developed to compute the predicted average crash frequency for typical sites with the existing condition. This “existing condition” CPM is then applied only to sites that satisfy the eligibility criteria established by the operating agency. The CPM predicted value is used with the empirical Bayes method to compute the expected average crash frequency of each eligible site. When this method is used for Application 2, it has been shown to provide reliable CMF estimates ( 26 ). Further research may be needed to determine if the method’s results are less reliable when applied to sites whose eligibility is based on non-crash-based criteria.
Interpretation of CPM Comparison Results
Assessing the CPMs Being Compared
In general, there are two potential interpretations that can be made of the results obtained when comparing the predicted value from a CPM representing the existing facility type and control mode condition to that from a second CPM describing the proposed facility type and control mode condition. The correct interpretation is based on the answer to the following question:
Can the “existing condition” CPM be used to obtain an unbiased prediction of the average crash frequency of only those sites known to be “eligible” for the proposed condition?
A “Yes” answer to this question can be obtained if the CPM was developed to account for endogeneity in the site-type characteristic being changed (e.g., facility type, control mode). This accommodation is achieved through the development of a CPM that could be used with Method 1 (i.e., an eligible-site-only CPM) or Method 2 (i.e., a typical-site CPM applied to a set of eligible sites).
A review of the reports describing the development of the HSM CPMs indicates that none of the CPMs were explicitly developed to support Method 1. Further examination of these reports and the sites studied will be needed to confirm this finding for all possible facility type and control mode changes. However, this examination will be challenging because some existing condition facility types and control modes have many possible conversion options (e.g., minor-road stop can be converted to roundabout, all-way stop, signal, etc.). Regardless, without this determination, a conservative position for the interpretations described here is to assume that none of the HSM1 and HSM2 CPMs support Method 1.
Interpretation Options
This section describes two different interpretations of the results obtained when comparing two CPMs for the purpose of inferring the change in safety associated with a change in facility type or control mode. For both interpretations, the “proposed condition” CPM is used to compute the predicted average crash frequency for typical sites with the proposed condition.
Interpretation A—Endogeneity Mitigated
Two methods were previously described for mitigating the endogeneity associated with the comparison of two CPMs in this manner. If either method is used, then any difference in the average crash frequency between the existing condition and the proposed condition should be a reliable indication of the change in safety associated with implementation of the proposed condition
Interpretation B—Endogeneity Not Mitigated
For this interpretation, the “existing condition” CPM is used to compute the predicted average crash frequency of typical sites with the existing condition (as opposed to just those that are eligible for the proposed condition). Any difference in the predicted average crash frequency between the existing condition and the proposed condition should be a reliable indication of the change in safety associated with implementation of the proposed condition
Example 1—Interpretation A
Consider the case where two traffic control modes (i.e., signal, minor-stop) are being considered for a proposed new intersection. Two CPMs are being used to quantify the effect of converting from stop control to signal control. The “existing condition” CPM was developed using only minor-stop-controlled sites for which an engineering study (using MUTCD traffic signal warrants) indicated a signal was justified. In this case, Interpretation A applies (as supported by Method 1). The results of the CPM comparison should provide a reliable indication of the safety effect of adding a signal to the minor-stop-controlled intersection provided that an engineering study confirms a signal is justified.
Example 2—Interpretation B
Continuing Example 1, consider the case where the “existing condition” CPM was developed using a regionally-representative (i.e., typical) set of minor-stop-controlled sites. Crash history data for the existing site is not available. In this case, Interpretation B applies. The results of the CPM comparison should provide a reliable indication of the safety effect of adding a signal to a typical minor-stop-controlled intersection (many of which are unlikely to be eligible for signalization).
Summary of Section
• HSM CPMs are used for two applications. CPM Application 1 refers to the use of a CPM to evaluate site design alternatives. CPM Application 2 refers to the use of two CPMs to compare alternative facility types or control modes.
• When using HSM CPMs for Application 2, reliable results can only be obtained when the two CPMs are calibrated to a common state or region.
• The use of HSM CPMs for Application 2 can produce an inferred safety effect (associated with a change in facility type or control mode) that is different from that described by a CMF for the same type of change. This potential for disagreement does not mean that one result is wrong and the other is right. Rather, both an inferred safety effect and a CMF can be correct when interpreted in the context of the sites that are being evaluated.
Recent studies attempting to quantify the safety effect of adding signal control to a stop-controlled intersection have produced a wide range of results—ranging from “signalization decreases crash risk” to “signalization increases crash risk.” One explanation for this range of results is that the studies are focused on different populations of stop-controlled intersections. The studies that found signalization decreased crash risk are based on the before–after study design that examined only stop-controlled intersections that the operating agency determined were eligible for signalization. The correct interpretation of the result from these before–after studies is “given a stop-controlled intersection that is eligible for signalization, signalizing this intersection will likely decrease its average crash frequency.”
The studies that found signalization increased crash risk were based on the comparison of two CPMs that were developed from data for typical stop-controlled intersections and signalized intersections. The correct interpretation of the result from these CPM-based studies is “given that most stop-controlled intersections are unlikely to be eligible for signalization, signalizing a typical stop-controlled intersection will likely increase its average crash frequency.”
• When comparing two CPMs to infer the safety effect of an endogenous site characteristic, the endogeneity can be mitigated by two methods. Method 1 mitigates endogeneity during CPM development. Method 2 mitigates endogeneity during the application of typical-site (e.g., HSM) CPMs.
• The HSM CPMs are developed using data representing typical sites with the associated facility type and control mode. As a result, Method 1 is not available when using HSM CPMs.
• When using HSM CPMs for Application 2 and Method 2 is used, the results can be explained as follows:
Interpretation A: “Any difference in the average crash frequency between the existing condition and the proposed condition should be a reliable indication of the change in safety associated with implementation of the proposed condition
• When using HSM CPMs for Application 2 but Method 2 cannot be used, the results can be explained as follows:
Interpretation B. “Any difference in the predicted average crash frequency between the existing condition and the proposed condition should be a reliable indication of the change in safety associated with implementation of the proposed condition
Interpretation A is not available in this case because (a) endogeneity is induced in engineering practice by requiring justification for the conversion based partly on safety considerations (e.g., it satisfies warranting criteria; its safety and other road-user benefits exceed its implementation cost) and (b) this endogeneity is not accounted for in HSM CPM development.
Changes to the Roundabout SPFs
Overview
During the development of HSM2 Torbic et al. ( 3 ) compared the SPFs for alternative facility types and control modes. Their objective was to ensure that selected SPF pairs provided results that were consistent with the results of previously conducted before–after studies. This objective is understandable given that CPM Application 2 (i.e., comparison of site types) is popular among transportation agencies wanting to fund safety projects and meet safety goals.
Torbic et al. (
3
) noted discrepancies between the predicted crash frequency for the roundabout SPFs and several traditional intersection SPFs planned for inclusion in HSM2. They characterized their concerns in the following statement: “…the roundabout models developed in NCHRP Project 17-70 generally predicted higher crash frequencies than the models for comparable signalized and unsignalized intersections. CMFs for conversion of conventional intersections to roundabouts show that just the opposite would be expected” (
3
, p. 70).
The roundabout CPMs developed for NCHRP Project 17-70 were not estimated using data from the same states as the other HSM CPMs ( 1 ). However, they were calibrated to a common state (as were other HSM SPFs) in NCHRP Project 17-72 for inclusion in HSM2 ( 12 ). It is assumed here that the Project 17-72 calibration factors were incorporated in the HSM SPFs before Torbic et al.’s examination of SPF discrepancies. In other words, it is assumed that the aforementioned discrepancies noted by Torbic et al. ( 3 ) reflect their examination of the Project 17-70 SPFs after being adjusted using the calibration factors prepared by Srinivasan et al. ( 12 ).
Torbic et al. rationalized that they should make adjustments to the SPF coefficients in the roundabout CPMs to ensure that, when compared to other CPMs, the difference in predicted crash frequency is consistent with the CMFs in HSM1 Part D for the corresponding change in facility type or control mode.
Source of Discrepancy
The discrepancies noted by Torbic et al. ( 3 ) with regard to the roundabout SPFs are likely owing to endogeneity in the facility type and control mode variables being compared. As noted previously, endogeneity is inherent to HSM CPM (and SPF) comparisons. It is likely to exist in roundabout SPF comparisons given that the conversion to a roundabout is typically based on consideration of safety and other road-user benefits ( 5 , 27 ). This endogeneity tends to result in an inferred safety effect from CPM comparisons that is different from that obtained from a before–after study.
Torbic et al. ( 3 ) compared HSM SPF pairs for the purpose of inferring the safety effect associated with a change in facility type or control mode (e.g., stop-control versus signal-control, roundabout versus stop-control, TWLTL versus divided). Their comparisons were not specific to an existing site, so crash history was not available (and Method 2 could not be used to mitigate the endogeneity). As a result, Interpretation B is appropriate for their comparisons. There should be no expectation that the inferred safety effect from these SPF comparisons would agree with a CMF value for the same change in facility type or control mode.
Potential Consequences of CPM Changes
Project 17-70 produced 16 roundabout CPMs (and associated SPFs). These CPMs correspond to different combinations of area type, number-of-legs, number-of-circulating-lanes, and severity level ( 1 ). The original CPM coefficients produced by Project 17-70 were confirmed by the researchers to provide reliable comparisons of alternative number-of-legs and number-of-circulating-lanes for roundabouts in urban and rural areas, as intended to support CPM Application 1 (i.e., comparison of site design alternatives).
Torbic et al. ( 3 ) do not state why they decided to make changes to the roundabout SPFs, as opposed to making changes to the SPFs for the other intersection-type-and-control-mode combinations to which they were compared. In general, if two SPFs are being fairly compared and the results appear illogical, then it would seem appropriate to first determine which SPF is the source of the discrepancy (or if both SPFs are contributing to the discrepancy). However, Torbic et al. ( 3 ) appear to have decided in advance that only the common-state-adjusted roundabout SPFs were producing unreliable results.
Regardless of the reason why the roundabout SPFs were changed, the changed SPFs should be checked to ensure that they (with their associated CPMs) provide reliable predicted values for CPM Application 1. Notably, if the original coefficients are changed to improve their use for CPM Application 2, the ability of the changed CPMs to reliably support CPM Application 1 should also be checked and confirmed. Torbic et al. ( 3 ) do not discuss having completed this check for the roundabout CPMs they adjusted for HSM2. The implications of omitting this check are examined in a subsequent section.
Examination of the Coefficient Changes
The roundabout SPF coefficients prepared for NCHRP Project 17-70 and those prepared for HSM2 are listed in Table 3 for 16 roundabout configurations. Each configuration reflects a different combination of area type, number-of-legs, number-of-circulating lanes, and crash severity category. The coefficients that have been changed for HSM2 are identified using a gray background. For all but one SPF, the “a” (a.k.a. “intercept” or “scale”) coefficient was changed. For six SPFs, a change was also made to the “b” (a.k.a. “volume” or “shape”) coefficient.
Comparison of Roundabout Safety Performance Functions (SPF) Coefficients from Project 17-70 with Those in Highway Safety Manual, Second Edition (HSM2)
Note: FI = fatal-and-injury crashes; PDO = property-damage-only crashes; na = not applicable. a = SPF equations: N = exp[a + b x ln(TEV)] or N = exp[a + d x ln(ADTmaj)+e x ln(ADTmin)]; with TEV = (ADTmaj+ ADTmin)/1000. Gray areas denote coefficients that have been changed for HSM2.
Torbic et al. ( 3 , p. 70) state that “…the a coefficients in the roundabout SPFs used in HSM2…were adjusted based on known CMFs for roundabout conversion projects…”. In fact, Torbic et al. ( 3 ) changed all of the coefficients in six of the sixteen roundabout SPFs prepared by Project 17-70. Effectively, they “replaced” the six Project 17-70 SPFs (as opposed to simply “adjusting” them). It is unclear from the report by Torbic et al. ( 3 ) whether (a) the replacement SPFs have the same base conditions as the Project 17-70 SPFs (in which case they can be used with the Project 17-70 AFs) or (b) other AFs have been provided that can be used with the replacement SPFs. Compatibility between an SPF and its associated AFs is important because research by Srinivasan et al. ( 28 , Chapter 3) indicates that the use of AFs that do not match the SPF’s base conditions will bias the predicted crash frequency from the SPF.
The overdispersion parameter (k) for six SPFs is changed for HSM2. Five of the six values are larger than those of the SPFs prepared for Project 17-70. In general, the overdispersion parameter is larger when the set of sites used to estimate the SPF are less similar. As the overdispersion parameter increases, the predicted crash frequency is more uncertain, and as a result, less weight is given to the predicted crash frequency when computing the expected crash frequency. In general, larger overdispersion parameters lead to (a) a wider confidence interval for the predicted crash frequency and (b) a larger potential for bias in the expected crash frequency (obtained when using the empirical Bayes method) owing to regression-to-the-mean remnants ( 25 ). Thus, the increase in overdispersion parameter for the five SPFs represents an undesirable outcome of the SPF replacement.
Comparison With Other SPFs
This section compares the predicted crash frequency obtained from the HSM2 CPMs with those from Project 17-70 as well as other CPMs reported in the literature. All of the CPMs are considered to be “typical-site” CPMs suitable for Interpretation B. The AFs developed for Project 17-70 are used with both CPMs.
Fatal-and-Injury Crashes, One Circulating Lane
The relationship between fatal-and-injury (FI) crash frequency and traffic demand, as obtained from various CPMs, is shown in Figure 3 for roundabouts with one circulating lane. The inscribed circle diameter, outbound-leg presence, and right-turn bypass lane presence conditions are such that the associated AFs have a value of 1.0 in the HSM2 and 17-70 CPMs. It was assumed that there was one access point on each leg and that the leg annual average daily traffic (AADT) volume was the same on each leg (for the purpose of computing the access point frequency AF).
Highway Safety Manual, second edition (HSM2) predictive models, fatal-and-injury (FI) crashes, one circulating lane. (a) HSM models for urban roundabouts. (b) HSM models for rural roundabouts. (c) Comparison with other roundabout models. (d) Comparison with rural intersection models; Source: Torbic et al. (3). Color online only.
The trend lines in Figure 3a compare the urban roundabout CPMs prepared by Project 17-70 (labeled “17-70”) with those prepared by Torbic et al. ( 3 ) (labeled “HSM2”). These trends indicate that the predicted FI crash frequency from the HSM2 CPM for four-leg roundabouts has increased by about 80%, relative to the 17-70 four-leg CPM. In contrast, there was no change in the CPM prediction for three-leg roundabouts.
The trend lines in Figure 3b compare the rural roundabout CPMs prepared by Project 17-70 with those prepared by Torbic et al. ( 3 ). These trends indicate that the predicted FI crash frequency from the three- and four-leg HSM2 CPMs have increased by about 20%, relative to the 17-70 CPMs.
The trend lines in Figure 3c compare the HSM2 models for urban one-circulating-lane roundabouts with those identified by a review of the literature. The HSM2 models for urban roundabouts are shown using the solid red trend line. (Color online only.) Trend lines for the other models are shown using black lines. Notable in this figure is the wide range of predicted values from the collective set of CPMs for a given total entering AADT volume.
Differences between the HSM2 CPMs and the reported models in Figure 3c may be explained by geometric differences (e.g., inscribed circle diameter, outbound-only lane presence, right-turn bypass lane presence, and number of access points on each leg) that exist among the sites used to calibrate the models.
Figure 3d is obtained from Appendix B of the report by Torbic et al. ( 3 , Figure B-2). This figure compares the HSM2 SPFs with the HSM SPFs for other intersection configurations. The figure is based on the use of SPFs (as opposed to CPMs) so the corresponding predicted FI crash frequency corresponds to the SPF’s specified base conditions. The label for each trend line has the form of “first number, text, last number”. The first number indicates the number of intersection legs (3 or 4), the text indicates the type of control (i.e., ST: minor-road stop control; SG: signal control; R: roundabout; STT: minor-road stop-control with through movement turning through intersection; AST: all-way stop control), the last number is used to indicate the number of circulating lanes at the roundabout (1 or 2).
The trend lines in Figure 3d indicate that, with one exception, the two rural roundabout SPFs predict a smaller FI crash frequency than all other configurations for the same volume level. A similar trend is found for HSM2’s urban roundabout SPFs. This trend is consistent with Torbic et al.’s objective to adjust the roundabout SPFs such that they predict fewer crashes than the signal and stop-control SPFs (as stated in the quote in the Introduction section of this paper). The exception is the four-leg all-way-stop control SPF which predicts about the same crash frequency as the three-leg roundabout.
Fatal-and-Injury Crashes, Two Circulating Lanes
The relationship between FI crash frequency and traffic demand, as obtained from various CPMs, is shown in Figure 4 for roundabouts with two circulating lanes. The outbound-leg presence, right-turn bypass lane presence, and entry width conditions are such that the associated AFs have a value of 1.0 in the HSM2 and 17-70 CPMs. Other relevant assumptions for the HSM2 and 17-70 CPMs are described in the next paragraph.
Highway Safety Manual, second edition (HSM2) predictive models, FI crashes, two circulating lanes. (a) HSM models for urban roundabouts. (b) HSM models for rural roundabouts. (c) Comparison with other roundabout models. (d) Comparison with rural intersection models; Source: Torbic et al. (3). Color online only.
For the three-leg trend lines, it was assumed that there were (1) two legs with one entry lane per leg, each leg having one conflicting circulating lane; and (2) one leg with two entry lanes and two conflicting circulating lanes. For the four-leg trend lines, it was assumed that there were (1) two legs with one entry lane per leg, each leg having one conflicting circulating lane; and (2) two legs with two entry lanes per leg, each leg having two conflicting circulating lanes.
The trend lines in Figure 4a compare the urban roundabout CPMs prepared by Project 17-70 (labeled “17-70”) and by Torbic et al. (labeled “HSM2”). In contrast to the changes made to the urban, one circulating lane CPMs, the trend lines in this figure indicate that the predicted FI crash frequency from the HSM2 CPM for three- and four-leg roundabouts with two circulating lanes has decreased by about 45%.
The trend lines in Figure 4b compare the rural roundabout CPMs prepared by Project 17-70 and by Torbic et al. ( 3 ). In contrast to the changes made to the rural, one circulating lane CPMs, the trend lines in this figure indicate that the predicted FI crash frequency from the HSM2 CPM for three- and four-leg roundabouts with two circulating lanes has decreased by 65 to 85%.
The trend lines in Figure 4c compare the HSM2 models for urban two-circulating-lane roundabouts with those identified by a review of the literature. The HSM2 models for urban roundabouts are shown using the solid red trend lines. (Color online only.) Trend lines for the other models are shown using black lines. In general, the trends for the HSM2 models are similar to those developed by Bagdade et al. ( 29 ). Those for the 17-70 models are similar to those described by Rodegerdts et al. ( 30 ). It is notable that the volume coefficient in the SPFs for both 17-70 and HSM2 has a value greater than 1.0 which causes the concave shape in the trend lines in Figure 4c. In contrast, the SPF reported by Bagdade et al. ( 29 ) and Rodegerdts et al. ( 30 ) have a volume coefficient less than 1.0 which causes the convex shape in the trend lines.
Figure 4d is obtained from Appendix B of the report by Torbic et al. ( 3 , Figure B-5). This figure compares the HSM2 SPFs with the HSM SPFs for other intersection configurations. The figure is based on the use of SPFs (as opposed to CPMs) so the corresponding predicted FI crash frequency corresponds to the SPF’s specified base conditions. An explanation of the labels used for each trend line in the figure is provided previously in the discussion associated with Figure 3d.
The trend lines in Figure 4d indicate that the two rural roundabout SPFs predict a smaller FI crash frequency than all other configurations for the same volume level. A similar trend is found for HSM2’s urban roundabout SPFs. This trend is consistent with Torbic et al.’s objective to adjust the roundabout SPFs such that they predict fewer crashes than the signal and stop-control SPFs.
Total and PDO Crashes, One Circulating Lane
The relationship between crash frequency and traffic demand, as obtained from various CPMs, is shown in Figure 5 for roundabouts with one circulating lane. It was assumed that there was one access point on each leg and that the leg AADT volume was the same for each leg (for the purpose of computing the access point frequency AF).
Highway Safety Manual, second edition (HSM2) predictive models, total and property-damage-only (PDO) crashes, one circulating lane. (a) HSM models for urban roundabouts. (b) HSM models for rural roundabouts. (c) Comparison with other roundabout models. (d) Comparison with rural intersection models; Source: Torbic et al. (3). Color online only.
The trends in Figure 5a compare the urban roundabout CPMs prepared by Project 17-70 (labeled “17-70”) with those prepared by Torbic et al. ( 3 ) (labeled “HSM2”). These trends indicate that the predicted PDO crash frequency from the HSM2 CPM for four-leg roundabouts has decreased by about 70%, relative to the 17-70 four-leg CPM. That for three-leg roundabouts has decreased by about 10%.
The trends in Figure 5b compare the rural roundabout CPMs prepared by Project 17-70 with those prepared by Torbic et al. ( 3 ). These trends indicate that the predicted PDO crash frequency from the three- and four-leg HSM2 CPMs have decreased by 50 to 70%, relative to the 17-70 CPMs.
The trends in Figure 5c compare the HSM2 models for urban one-circulating-lane roundabouts with those identified by a review of the literature. The HSM2 models for urban roundabouts are shown using the solid red trend line. (Color online only.) Trend lines for the other models are shown using black lines. Notable in this figure is that the HSM2 trend line for four-leg roundabouts predicts a smaller total crash frequency than all but one of the roundabout CPMs reported in the literature.
Figure 5d is obtained from Appendix B of the report by Torbic et al. ( 3 , Figure B-1). This figure compares the HSM2 SPFs with the HSM SPFs for other intersection configurations. The figure is based on the use of SPFs (as opposed to CPMs) so the corresponding predicted total crash frequency corresponds to the SPF’s specified base conditions. An explanation of the labels used for each trend line in the figure is provided previously in the discussion associated with Figure 3d.
The trend lines in Figure 5d indicate that the two rural roundabout SPFs predict a smaller total crash frequency than all other configurations for the same volume level. A similar trend is found for HSM2’s urban roundabout SPFs. This trend is consistent with Torbic et al.’s objective to adjust the roundabout SPFs such that they predict fewer crashes than the signal and stop-control SPFs.
Total and PDO Crashes, Two Circulating Lanes
The relationship between crash frequency and traffic demand, as obtained from various CPMs, is shown in Figure 6 for roundabouts with two circulating lanes. The entry width conditions are such that the associated AF has a value of 1.0 in the HSM2 and 17-70 CPMs. For the three-leg trend lines, it was assumed that there were (1) two legs with one entry lane per leg, each leg having one conflicting circulating lane; and (2) one leg with two entry lanes and two conflicting circulating lanes. For the four-leg trend lines, it was assumed that there were (1) two legs with one entry lane per leg, each leg having one conflicting circulating lane; and (2) two legs with two entry lanes per leg, each leg having two conflicting circulating lanes.
Highway Safety Manual, second edition (HSM2) predictive models, total and property-damage-only (PDO) crashes, two circulating lanes. (a) HSM models for urban roundabouts. (b) HSM models for rural roundabouts. (c) Comparison with other roundabout models. (d) Comparison with rural intersection models; Source: Torbic et al. (3). Color online only.
The trends in Figure 6a compare the urban roundabout CPMs prepared by Project 17-70 (labeled “17-70”) with those prepared by Torbic et al. ( 3 ) (labeled “HSM2”). These trends indicate that the predicted PDO crash frequency from the HSM2 CPM for four-leg roundabouts has decreased by about 90%, relative to the 17-70 four-leg CPM. That for three-leg roundabouts has decreased by about 80%.
The trends in Figure 6b compare the rural roundabout CPMs prepared by Project 17-70 with those prepared by Torbic et al. ( 3 ). These trends indicate that the predicted PDO crash frequency from the three- and four-leg HSM2 CPMs have decreased by about 95%, relative to the 17-70 CPMs.
The trends in Figure 6c compare the HSM2 models for urban two-circulating-lane roundabouts with those identified by a review of the literature. The HSM2 models for urban roundabouts are shown using the solid red trend line. (Color online only.) Trend lines for the other models are shown using black lines. Notable in this figure is that the HSM2 trend lines for three- and four-leg roundabouts predict a smaller total crash frequency than all of the roundabout CPMs reported in the literature.
Figure 6d is obtained from Appendix B of the report by Torbic et al. ( 3 , Figure B-4). This figure compares the HSM2 SPFs with the HSM SPFs for other intersection configurations. The figure is based on the use of SPFs (as opposed to CPMs) so the corresponding predicted total crash frequency corresponds to the SPF’s specified base conditions. An explanation of the labels used for each trend line in the figure is provided previously in the discussion associated with Figure 3d.
The trend lines in Figure 6d indicate that the two roundabout SPFs predict a smaller total crash frequency than all other configurations for the same volume level. This trend is consistent with Torbic et al.’s objective to adjust the roundabout SPFs such that they predict fewer crashes than the signal and stop-control SPFs.
Comparison With Alternative Roundabout Configurations
The focus of the changes to the roundabout SPFs by Torbic et al. ( 3 ) was their desire to support CPM Application 2 (i.e., comparison of alternative site types). They made changes to the roundabout SPFs to ensure that a comparison of SPF predictions for the roundabout with those of other control modes provided results that were consistent with reported CMFs. This section examines the effect of these changes on the roundabout SPF predictions when used for CPM Application 1 (i.e., comparison of site design alternatives).
Table 4 lists the results from a comparison of the HSM2 and NCHRP Project 17-70 roundabout SPFs. To develop the values shown in this table, the roundabout SPFs were used to compute the predicted crash frequency for a 10,000 vpd total entering volume. These values are shown in columns 5 and 6. The crash frequency from the two SPF sources were then compared by ratio in columns 7 to 15. The computed crash frequency ratios shown vary only slightly for total entering volumes in the range of 5,000 to 15,000 vpd.
Comparison of Highway Safety Manual, Second Edition (HSM2) and Project 17-70 Safety Performance Functions (SPFs)
Note: cr/year = crashes per year; FI = fatal-and-injury crashes; PDO = property-damage-only crashes; vpd = vehicles per day; freq. = frequency; na = not applicable.
The crash frequency ratios in column 7 of Table 4 represent the ratio of the HSM2 SPF prediction divided by the 17-70 SPF prediction. In general, 12 of the 16 ratios listed are less than 1.0, indicating that the predicted crash frequency from the HSM2 SPF is smaller than that from the 17-70 SPFs. The exception to this trend is the FI crash frequency predicted by the four one-circulating-lane SPFs. For these SPFs, the predicted crash frequency from the HSM2 SPFs equals or exceeds than that from the 17-70 SPFs.
The crash frequency ratios in columns 8 and 9 of Table 4 represent the ratio of the two-circulating-lane SPF prediction divided by the one-circulating-lane SPF prediction. Columns 8 and 9 list the ratios for the 17-70 SPFs and HSM2 SPFs, respectively. The values in column 8 indicate that the 17-70 SPFs are consistent in indicating that typical two-circulating-lane roundabouts are predicted to have more crashes than one-circulating-lane roundabouts. This outcome is consistent with the findings for Leuer ( 5 ) and Savolainen et al. ( 4 ). In contrast, the values in column 9 indicate that the HSM2 SPFs are fairly consistent in indicating that the typical two-circulating-lane roundabouts are predicted to have fewer crashes than one-circulating-lane roundabouts. One “outlier” HSM2 SPF does indicate that the typical urban two-circulating-lane roundabout is predicted to have 5 to 10% more FI crashes than the typical urban one-circulating-lane roundabout. The question of whether a typical two-circulating-lane roundabout has more (or less) crashes than a typical one-circulating-lane roundabout is important for CPM Application 1. A consistent (and convincing) answer to this question does not seem to be available from the HSM2 SPFs.
The crash frequency ratios in columns 10 and 11 of Table 4 represent the ratio of the four-leg SPF prediction divided by the three-leg SPF prediction. Columns 10 and 11 list the ratios for the 17-70 SPFs and HSM2 SPFs, respectively. The values in column 10 indicate that the 17-70 SPFs are consistent in indicating that typical four-leg roundabouts have more crashes than three-leg roundabouts. This trend is logical given that a four-leg roundabout has more conflict points than a three-leg roundabout. In contrast, there is no clear trend in the values in column 11 for the HSM2 SPFs. Notably, the HSM2 SPF predict PDO crash frequency at typical urban four-leg roundabouts to be smaller than the PDO crash frequency for typical urban three-leg roundabouts. The question of whether a typical four-leg roundabout has more (or less) crashes than a typical three-leg roundabout is important for CPM Application 1. A consistent (and convincing) answer to this question does not seem to be available from the HSM2 SPFs.
The crash frequency ratios in columns 12 and 13 of Table 4 represent the ratio of the rural SPF prediction divided by the urban SPF prediction. Columns 12 and 13 list the ratios for the 17-70 SPFs and HSM2 SPFs, respectively. The values in column 12 indicate that the 17-70 SPFs are consistent in indicating that typical rural roundabouts have more crashes than urban roundabouts. This trend is consistent when comparing the rural HSM1 SPFs in Chapters 10 and 11 for minor-stop intersections and signalized intersections with those for urban intersections in HSM1 Chapter 12. In contrast, there is no clear trend in the values in column 13 for the HSM2 SPFs. Several of the HSM2 SPFs predict crash frequency at typical rural roundabouts to be smaller than the crash frequency for typical urban roundabouts. The question of whether a typical rural roundabout has more (or less) crashes than a typical urban roundabout is important for CPM Application 1. A consistent (and convincing) answer to this question does not seem to be available from the HSM2 SPFs.
The crash frequency ratios in columns 14 and 15 of Table 4 represent the ratio of the PDO SPF prediction divided by the FI SPF prediction. Columns 14 and 15 list the ratios for the 17-70 SPFs and HSM2 SPFs, respectively. The values in column 14 indicate that the 17-70 SPFs are consistent in indicating that typical roundabouts have more PDO crashes than FI crashes, which is consistent with the intersection SPFs in HSM1. These ratios indicate that PDO crashes represent 80 to 90% of all roundabout crashes, which is consistent with research by Savolainen et al. ( 4 ). In contrast, there is no clear trend in the values in column 15 for the HSM2 SPFs. Several of the HSM2 SPFs predict PDO crash frequency as being smaller than the FI crash frequency. The question of whether a typical roundabout has more (or less) PDO crashes than FI crashes is important for CPM Application 1. A consistent (and convincing) answer to this question does not seem to be available from the HSM2 SPFs.
Summary of Section
During development of HSM2, Torbic et al. ( 3 ) rationalized that the roundabout SPFs developed for Project 17-70 were producing inconsistent results when compared with other intersection SPFs. The basis for this claim was that the inferred safety effect from the SPF comparisons were not in agreement with the CMF values for “convert to roundabout” that are reported in Part D of HSM1.
A comparison of the HSM2 roundabout SPFs with those for other intersection control modes has endogeneity present in the “convert to roundabout” characteristic. As a result, there should be no expectation that the inferred safety effect from these SPF comparisons would agree with the CMF values for “convert to roundabout” (at least not to the extent that the CMF value is an appropriate basis for changing SPF coefficient values).
Based on their SPF comparisons, Torbic et al. ( 3 ) decided that changes were needed to the roundabout SPFs (and that the other SPFs were correct). The intent of the changes was to provide better agreement with reported “convert to roundabout” CMF values. However, these changes appear to have resulted in the HSM2 roundabout SPFs providing less reliable results for CPM Application 1 (i.e., comparison of site design alternatives).
Torbic et al. ( 3 ) reported that their adjustments to the roundabout SPFs were limited to one coefficient. However, six of the sixteen roundabout SPFs had all of their coefficients changed, which effectively represents a replacement of the Project 17-70 SPFs. It is unclear from the report by Torbic et al. ( 3 ) whether the replacement SPFs were confirmed to be compatible with the AFs developed for Project 17-70, or whether new AFs are being provided in HSM2 specifically for use with the replacement SPFs. A mismatch between an SPF’s base conditions and its associated AFs will bias the predicted crash frequency.
A comparison of the HSM2 roundabout SPFs with those developed by Project 17-70 and other researchers led to the following observations.
The HSM2 SPF for four-leg urban roundabouts with one circulating lane predicts an 80% larger average FI crash frequency than that from Project 17-70.
The HSM2 SPFs for roundabouts with two circulating lanes predict a 45 to 80% smaller average FI crash frequency than those from Project 17-70.
The HSM2 SPFs for three- and four-leg roundabouts predict an average PDO crash frequency that is less than one-half that of the SPFs from Project 17-70.
Most of the HSM2 SPFs tend to underpredict the average crash frequency obtained from the collective set of roundabout SPFs reported in the literature.
The HSM2 roundabout SPFs were compared with Project 17-70 SPFs for the purpose of assessing the suitability of the HSM2 SPFs for CPM Application 1. This comparison led to the following observations.
The 17-70 SPFs are consistent in indicating that typical two-circulating-lane roundabouts are predicted to have more crashes than one-circulating-lane roundabouts. This outcome is consistent with the findings for Leuer ( 5 ) and Savolainen et al. ( 4 ). In contrast, the HSM2 SPFs are fairly consistent in indicating that the typical two-circulating-lane roundabouts are predicted to have fewer crashes than one-circulating-lane roundabouts.
The 17-70 SPFs are consistent in indicating that typical four-leg roundabouts have more crashes than three-leg roundabouts. This trend is logical given that a four-leg roundabout has more conflict points than a three-leg roundabout. In contrast, the HSM2 SPFs predict PDO crash frequency at typical urban four-leg roundabouts to be smaller than the PDO crash frequency for typical urban three-leg roundabouts.
The 17-70 SPFs are consistent in indicating that typical rural roundabouts have more crashes than urban roundabouts. This trend is consistent when comparing the rural HSM1 SPFs in Chapters 10 and 11 for minor-stop intersections and signalized intersections with those for urban intersections in HSM1 Chapter 12. In contrast, several of the HSM2 SPFs predict crash frequency at typical rural roundabouts to be smaller than the crash frequency for typical urban roundabouts.
The 17-70 SPFs are consistent in indicating that typical roundabouts have more PDO crashes than FI crashes, which is consistent with the intersection SPFs in HSM1. These ratios correspond to PDO crashes as representing 80%–90% of all roundabout crashes, which is consistent with research by Savolainen et al. ( 4 ). In contrast, several of the HSM2 SPFs predict PDO crash frequency as being smaller than the FI crash frequency.
Closure
Torbic et al. ( 3 ) were challenged by several issues during their production of HSM2. One of these issues was the apparent discrepancy between published CMFs and the associated CPMs prepared for HSM2 by various researchers working under independent contacts. None of these researchers were charged with developing CPMs that were suitable for comparing alternative site types. As a result, the burden was placed on Torbic et al. ( 3 ) to resolve the discrepancies in the associated SPFs in a relatively short time.
The changes by Torbic et al. ( 3 ) appear to be made without the benefit of insight from (a) a re-examination of the data used to develop the subject CPMs or (b) an analysis of newly collected data to inform the changes. Rather, they used CMF values as the basis for changing the SPF coefficients. Given that HSM CPMs describe typical sites, this use of CMF values is problematic owing to the inherent endogeneity in site type comparisons and will likely lead to unreliable CPM predictions. The scientific principles by which the HSM was founded suggest that data should always be the basis for changes to the HSM’s CPMs.
The HSM2 roundabout SPF’s prediction of average crash frequency is notably different from that obtained from the Project 17-70 SPFs. The magnitude of the differences is far larger than can be explained by state-to-state differences and inconsistent with other roundabout safety research. Hauer ( 8 ) also compared the predictions from several proposed HSM2 SPFs with values obtained from their HSM1 counterparts. He noted large differences in the predicted values—larger than could be explained by changes in driver behavior, agency policy, design practice, or statistical method over time. His concern is that if large changes like these cannot be confidently explained to practitioners, then their confidence in the HSM could be diminished or lost. The issues identified in this paper may add to this concern.
The HSM CPMs are often used to infer the safety effect of a change in site type (i.e., facility type and control mode). This use is problematic when the associated characteristic is endogenous to the comparison and, to date, has often mislead analysts whose expectation is that the result should agree with a reported CMF. This issue should be addressed in the HSM. The discussion should describe how to interpret the results from this type of comparison. The discussion should explain why the results may not agree with expectations or with a CMF value for the same change. Ideally, it would describe how to use the HSM2 CPMs to reliably inform site type comparisons.
Research should be undertaken to develop a procedure for using CPMs and CMFs to evaluate the safety of alternative site types based on unbiased estimates of their average crash frequency (and severity). The procedure should address the following two cases: (1) an existing site is being considered for conversion to an alternative site type and (2) site type selection for new alignment (no existing site).
Research should also be undertaken to reexamine the HSM2 roundabout CPMs (and any other CPMs that were adjusted to be consistent with CMFs). The examination should confirm that each CPM is providing an estimate of average crash frequency that is consistent with that of representative sites in a common state. The research should recommend corrections to the HSM2 CPMs that are not consistent in this manner.
Footnotes
Author Contributions
The author confirms sole responsibility for the following: study conception and design, data collection, analysis and interpretation of results, and manuscript preparation.
Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author received no financial support for the research, authorship, and/or publication of this article.