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Publication Number: FHWARD03037
Date: May 2005 

Validation of Accident Models for IntersectionsFHWA Contact: John Doremi, PDF Version (1.61 MB)
PDF files can be viewed with the Acrobat® Reader® 3. RECALIBRATION (Continuation)Type III INJURY AccidentsThe AMFs derived for INJURY accidents for Type III intersections are intersection SKEW angle, commercial driveways on major road, hazard rating on major road, peak truck percentage on major road, and peak turning percentage. The sensitivity test results for these AMFs are presented below. Table 211. Sensitivity of Safety to Skew Angles for Type III INJURY Accidents Per Year
Note: Group B AADT base model was used A: AMF derived from full models. B: AMF derived from regression models. Table 212. Sensitivity of Safety to Commercial Driveways on Major Road for Type III INJURYAccidents Per Year
Note: Group B AADT base model was used The AMF for Commercial driveways on major road was derived from full models. Table 213. Sensitivity of Safety to Hazard Rating on Major Road (HAZRAT1) for Type III INJURY Accidents Per Year
Note: Group B AADT base model was used The AMF for HAZRAT1 was derived from full models. Table 214. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKTRUCK was derived from full models.. Table 215. Sensitivity of Safety to Peak Turning Percentage (PKTURN) for Type III TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKTURN was derived from full models. 3.6.4 Type IV IntersectionsThe predicted TOTAL and INJURY accident frequencies per year for each AMF derived from the full models and regression base models are presented in tables 216 through 224. Type IV TOTAL Accidents The AMFs derived for TOTAL accidents for Type IV intersections are intersection SKEW angle, right sight distance from minor road, peak truck percentage, peak through percentage on minor road, and peak leftturn percentage. The sensitivity test results for these AMFs are presented in tables 216 through 220. Table 216. Sensitivity of Safety to Skew Angles for Type IV TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for Intersection SKEW angle was derived from regression base models. Table 217. Sensitivity of Safety to Right Sight Distance from Minor Road (SDR2) for Type IV TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for SDR2 was derived from full models. Table 218. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type III TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKTRUCK was derived from full models. Table 219. Sensitivity of Safety to Peak Through Percentage on Minor Road (PKTHRU2) for Type IV TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKTHRU2 was derived from full models. Table 220. Sensitivity of Safety to Peak LeftTurn Percentage (PKLEFT) for Type IV TOTAL Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKLEFT was derived from full models. Type IV INJURY AccidentsThe AMFs derived for INJURY accidents for Type IV intersections are intersection SKEW angle, major rightturn lane, peak truck percentage, and peak leftturn percentage. The sensitivity test results for these AMFs are presented in tables 221 through 224. Table 221. Sensitivity of Safety to Skew Angles for Type IV INJURY Accidents Per Year
Note: Group B AADT base model was used. The AMF for Intersection SKEW angle was derived from regression base models. Table 222. Sensitivity of Safety to Major RightTurn Lane for Type IV INJURYAccidents Per Year
Note: Group B AADT base model was used. The AMF for Major RightTurn Lane was derived from full models. Table 223. Sensitivity of Safety to Peak Truck Percentage (PKTRUCK) for Type IV INJURY Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKTRUCK was derived from full models. Table 224. Sensitivity of Safety to Peak LeftTurn Percentage (PKLEFT) for Type IV INJURY Accidents Per Year
Note: Group B AADT base model was used. The AMF for PKLEFT was derived from full model 3.6.5 Type V IntersectionsThe predicted TOTAL and INJURY accident frequencies per year for each AMF derived from the full models and regression base models are presented in tables 225 through 229. Type V TOTAL AccidentsThe AMFs derived for TOTAL accidents for Type IV intersections are commercial driveways on major road, horizontal curve combinations on major and minor roads, and light. The sensitivity test results for these AMFs are presented in tables 225 through 227. Table 225. Sensitivity of Safety to Commercial Driveways on Major Road for Type V TOTAL Accidents Per Year
Note: Group A AADT base model was used. The AMF for Commercial driveways on major road was derived from full models. Table 226. Sensitivity of Safety to Horizontal Curve Combinations on Major and Minor Roads (HEICOM) for Type III TOTAL Accidents Per Year
Note: Group A AADT base model was used. The AMF for HEICOM was derived from full models. Table 227. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year
Note: Group A AADT base model was used. The AMF for LIGHT was derived from full models. Type V INJURY AccidentsThe AMFs derived for INJURY accidents for Type V intersections are horizontal curves on minor roads and light on intersections. The sensitivity test results for these AMFs are presented in tables 228 to 229. Table 228. Sensitivity of Safety to Horizontal Curves on Minor Road (HEI2) for Type IV TOTAL Accidents Per Year
Note: Group A AADT base model was used. The AMF for HEI2 was derived from full models. Table 229. Sensitivity of Safety to Light for Type IV TOTAL Accidents Per Year
Note: Group A AADT base model was used. The AMF for LIGHT was derived from full models. 3.7 SUMMARY, DISCUSSION, AND CONCLUSIONSIn summarizing and discussing the model recalibration exercise, it is important not to lose sight of the fundamental purpose of the statistical models that are the focus of this research. Because the models are required for use in the IHSDM accident prediction algorithm, the recalibration efforts were focused on this application. In this sense, the research reflected here represents a different perspective from the original calibration by Vogt since, at that time, the algorithm was not developed and the calibration philosophy was somewhat different. Models with a comprehensive set of regression parameters were to be used directly for predicting the expected number of accidents at intersections and for deriving AMFs for the five types of intersection crash models examined in this research. To remind the reader, the five intersection types examined are:
The accident prediction algorithm enables the number of total intersectionrelated accidents per year to be estimated by multiplying the predicted number of such accidents for base conditions by AMFs for various features specific to an intersection. The Harwood et al. "Red Book" presented base models and AMFs for three and fourlegged intersections of twolane rural roads with STOP control, and fourlegged signalized intersections of twolane roads. These base models were the best of available accident prediction models developed in the earlier Vogt FHWA projects and included only variables that were statistically significant at the 15 percent level. Those projects also developed full models with additional variables with the intention of using the variable coefficients to estimate AMFs for use in IHSDM. The full models, along with several variants, are presented in two FHWA reports. Vogt and Bared present models for three and fourlegged intersections of twolane roads, while Vogt documents models for three other types of rural intersections: three and fourlegged stop controlled with four lanes on the major and two on the minor, and signalized intersections of twolane roads.^{(1,2)} Understanding what was required for the recalibration effort is an improvement of the base models and AMFs to be used in the IHSDM accident prediction algorithmincluding possible enhancements to model functional forms, addition or exclusion of variables, and updated parameter estimates. This requirement guided the approach. At the same time, full models were developed in keeping with the original intent of the project and with the expectation that it may be possible to derive AMFs similar to what were accomplished in the earlier FHWA work. The discussion provided here focuses primarily on summarizing and briefly discussing the results of the recalibration detailed in the body of this report, and translating these results into meaningful observations and conclusions. The reader interested in additional details, such as sources of published results for the earlier models and comparison tables, should refer to the earlier sections of this report. Descriptions of all variable abbreviations and definitions used in this report can be found at the beginning of this document. 3.7.1 Model RecalibrationFor the five intersection types previously described, statistical models were developed for total accidents (TOTACC) and injury (fatal + nonfatal injury) accidents (INJACC) within 76.25 m (250 ft) of the intersection center. For each intersection type, two fundamental classes of statistical models were developedmodels using AADT as the sole predictor of crashes (referred as base or AADT models) and models containing a fairly comprehensive set of predictor variables (referred as full models). There are two levels for each class. Not all levels were calibrated for all model Types (I to V). These details of the models calibrated and data used are summarized in table 230. Table 230. Summary of Models Recalibrated and Data Used
^{*} The California project data for Types II, IV, and V were not used. AADT Models OverviewThe AADT statistical models include AADT as the sole predictor variable and are proposed for consideration as base models to be used in IHSDM. The reasoning behind this apparently simplistic approach is that models with AADT as the only predictor are more likely to be transferable across jurisdictions than models that include other variables. This is an appealing feature, considering that the models are calibrated on data from three States within the United States; however, the likely application is to apply them for forecasting crashes across the entire country. This research strongly supported their use. Two types of AADT models are presented for Type I and II sites, and three types for Type III, IV, and V sites. First, models were calibrated using all available data from the HSIS California database, original sites from Minnesota and Michigan, and Georgia validation data. Second, models were developed for a subset of these sites that met specified conditions for possible use as base models in the IHSDM accident prediction algorithm. For Types III, IV, and V sites, additional AADT models were calibrated from a dataset that met the base conditions of the significant variables in the full models. These AADTonly models were calibrated on data from the original sites (intersections) from California, Michigan, and the sites used for the Georgia validation data. Full Models OverviewStatistical models with relatively comprehensive sets of predictor variables were also developed. Unlike their AADT counterparts, these models include many variables, with the intent to explain as much of variation in crash occurrence as possible, given the available set of potential explanatory variables. For Types I and II, full models were developed using two groups of data. The first, Group A, was comprised of the sites from Minnesota and Georgia and consisted of many variables, including horizontal and vertical curvature. The California sites were not in this group because many of the variables were not available. Group B consisted of the Minnesota, Georgia, and California HSIS sites, but fewer variables were available for modeling. For Types III, IV, and V, the data used to calibrate full models consisted of the California and Michigan sites from the original study, including the additional years of accident data, and the Georgia sites. There was no equivalent to Group B of the Types I and II models because there were very few HSIS sites, and these had almost no variables of interest. Type I Model ResultsType I AADT Models (see table 134 and table 135) The recalibrated models for total accidents represent improvements to the one reported in Harwood et al. (such a model was not presented in the Vogt reports).^{(3)} The coefficient of the log of major road AADT is about two times that for minor road AADT, which seems to be a reasonable expectation on the basis of other models reported in the literature. The CURE plots confirmed the superiority of the chosen model form, which testifies to the reasonableness of the calibrated models. For the TOTACC model, the base condition model (calibrated from data that met specified base conditions) was estimated with a lower overall overdispersion parameter than the model using all sites. This was expected, because the base condition sites should be more homogeneous in their design characteristics. For the INJACC model the overdispersion was similar for the two AADT models. Type I Full Models (see table 160, table 161, and table 162) Full models were developed using two groups of data. The first, Group A, was comprised of the sites from Minnesota and Georgia and consisted of many variables, including horizontal and vertical curvature. The second, Group B, added California HSIS sites, which resulted in fewer variables being available for modeling. Two model variants are reported. One includes a State indicator term and the other does not. For the Group A models, when a State indicator variable was used in the models, the only geometric variable that proved to be significant was HI1. Without the State indicator, more geometric variables were statistically significant. This effect suggests that geometric variables are correlated with State of origin, with certain States possessing intersections that systematically share geometric traits. There were some similarities and differences between the recalibrated models and the Vogt and Bared models. For total accidents, posted speed limit on major roads and the angle variable HAU were not included in the recalibrated model, while rightturn lanes on minor roads and leftturn lanes on major roads were included. For injury accidents, rightturns on major roads, posted speed on major, number of driveways on major roads, and the angle variable HAU were not included while leftturn lanes on major roads was included. The GOF as measured by the overdispersion parameter was improved over the Vogt and Bared models, just one of numerous GOF measures. For both of the Group B models, with and without the State indicator variable, rightturn lanes on minor roads and leftturn lanes on major roads are significant in addition to rightturn lanes on major roads. Type II Model ResultsType II AADT Models (see table 135 and table 139) Unlike the case for Type I models, the recalibrated Type II models for total accidents have more overdispersion than models reported in Harwood et al. (such a model was not presented in the Vogt reports).^{(3)} In particular, the models do a poorer job for the Georgia and California sites. Nevertheless, the coefficient of the log of major road AADT is about 2030 percent higher than that for minor road AADT, which appears to be reasonable. For both the TOTACC and INJACC models, the base condition models were estimated with a lower overdispersion than the model using all sites, again not surprising, because the base condition sites should be more homogeneous in their design characteristics. Type II Full Models (see table 163, table 164, table 165, and table 166) As was the case for Type I, full models were developed using two groups of data. The first, Group A, was comprised of sites from Minnesota and Georgia and included variables such as horizontal and vertical curvature. The second, Group B, added California HSIS sites, which resulted in fewer variables being available for modeling. Two model variants were reported. As for Type I, one included a State indicator term and the other did not. For the Group A models, there were some similarities and differences between the recalibrated models and the Vogt and Bared models. For the recalibrated models, significant geometric variables at approximately the 10 percent level of significance or better for TOTACC included rightturn lane on major roads and the number of driveways for the model l variant, including a State indicator variable, and number of driveways and the vertical curvature variable VCI1 for the variant without the State indicator variable. The Vogt and Bared model also included the angle variable HAU, the major road posted speed, and the horizontal curvature variable HI1, although these last two were of low significance. For the INJACC models, number of driveways and horizontal curvature within 76.25 m (250 ft) of the intersection center were significant at the 10 percent level or better for both the State indicator and nonState indicator variants. The Vogt model included roadside hazard rating as a significant variable and others that were not significant. The GOF as measured by the overdispersion parameter was not as good as that for the Vogt and Bared model. In the case of the Group B models, for TOTACC, significant variables (in addition to major and minor road AADTs) include rightturn lanes on major roads for the variant with the State indicator variable, and right and leftturn lanes on major roads for the variant without the State indicator variable. For INJACC, medians and rightturn lanes on major roads were significant for both the State indicator and nonState indicator variants. Again, the GOF for all of the Group B models, as measured by the overdispersion parameter, was not as good as that for the Vogt and Bared model. Type III Model ResultsType III AADT Models (see table 142, table 143, and table 145) Unlike models for Type I and II intersections, a State indicator variable was insignificant for all models. The recalibrated models for TOTACC and INJACC generally have better GOF measures than comparable models from the earlier FHWA research. As expected, the GOF statistics were better for the models using base condition sites than for models using all sites. For the Group A models, for TOTACC, the coefficient of the log of major road AADT is about three to four times that for minor road AADT, which, once again, is reasonable. For INJACC, the AADT variable effect was captured as the product of the major and minor AADTs as opposed to the TOTACC model, which specified these variables as separate terms. In the case of the Group B models, for both TOTACC and INJACC, the coefficient of the log of major road AADT is significantly larger than that for minor road AADT, which is in accord with reasonable expectations. Type III Full Models (see table 167 and table 168) Two models each are reported for TOTACC and INJACC. The main model was selected based on the highest Pearson productmoment correlation coefficient, lowest overdispersion, MPB per year, and MAD per year. The other model was the one judged to be next best in terms of these measures. For TOTACC, major and minor AADTs, crest curve rates on major roads, intersection angle, commercial driveways on major roads, median width on major roads, and painted medians on major roads were found to be significant in the main model. Of these, only median widths on major roads and the AAADT variables were included in the Vogt model, but that model did have a driveway variable DRWY1 instead of COMDRWY1. State indicator variables were statistically insignificant in the recalibration. For INJACC, major and minor AADTs, roadside hazard ratings on major roads, intersection angles, commercial driveways on major roads, peak turning percentages, and peak truck percentages were found to be significant in the main model. None of these were included in the Vogt model, which had an angle variable HAU as the only geometric variable. Like TOTACC, State indicator variables were again statistically insignificant in the recalibration. The recalibrated models for both TOTACC and INJACC produce better GOF measures than the Vogt's models, except for the overdispersion parameter. Type IV Model ResultsType IV AADT Models (see table 148, table 149, and table 151) Unlike models for Type I and II intersections, a State indicator variable was not statistically significant for all models. The recalibrated models for TOTACC and INJACC resulted in generally improved GOF measures than comparable models from the previous FHWA research. For the Group A models, the small sample size was insufficient to provide good coefficients and pvalues for a model with specified base conditions. For the TOTACC model using all sites, the coefficient of the log of major road AADT is about one and one half times that for minor road AADT, conforming to expectations. The AADT variable effect for the INJACC model was captured as the product of the major and minor AADTs, as opposed to the TOTACC model, which specified these variables as separate terms. In the case of the Group B models, as seems reasonable, the coefficient of the log of major road AADT is significantly larger than that for minor road AADT for both TOTACC and INJACC. As expected, the GOF statistics were improved for the models using base condition sites compared to models using all sites. Type IV Full Models (see table 170) Two models were presented for both TOTACC and INJACC. Again, the main model was selected based on the highest Pearson productmoment correlation coefficient, lowest overdispersion, MPB per year, and MAD per year. For TOTACC, major and minor road AADTs, peak leftturn percentages, peak through percentages on minor roads, peak truck percentages, and rightside sight distances on minor roads were found to be significant in the main model. By contrast, the Vogt main model included only a peak leftturn percentage on major road variable PKLEFT1 and a leftturn lane on major road variable LTN1S in addition to the AADT variables. The main model showed the lowest overdispersion among candidate models and indicated the best GOF results. The State indicator variable was statistically insignificant in the main model, but for the variant model, a Michigan indicator variable was found to be significant, indicating more influence of the Michigan data on the model. For INJACC, major and minor road AADTs, peak leftturn percentages on major roads, peak truck percentages, and speed limits on minor roads were significant in the main model. The Vogt model contained a speed limit on minor road variable SPD2 and a peak leftturn percentage on major road variable PKLEFT1 in addition to the AADT variables. The variant model yields an improvement in overdispersion and Pearson productmoment correlation coefficient, but not in MPB per year and MAD per year. State indicator variables were statistically insignificant. The recalibrated models for TOTACC and INJACC generally provide better GOF measures than Vogt's models. The overdispersion values of the recalibrated models were lower than Vogt's for TOTACC but slightly higher for INJACC. Type V Model ResultsType V AADT Models (see table 154, table 155, and table 156) Statistical models could not be calibrated for specified base conditions due to lack of data. Unlike the case for the other model types, the Vogt report does not provide AADTonly models for Type V. Therefore, a comparison between the Vogt models and the newly calibrated AADT models for TOTACC and INJACC could not be done. For the Group A models, for TOTACC, the coefficient of the log of major road AADT is about two to three times greater than that for minor road AADT, which is reasonable. As was the case for the Type III and IV models, for the INJACC model, the AADT variable effect was captured as the product of the major and minor AADTs as opposed to the TOTACC model, which specified these variables as separate terms. In the case of the Group B models, the main Type V TOTACC and INJACC models calibrated using all sites have a coefficient of the log of major road AADT, in accord with expectations, about two to three times that for minor road AADT. Type V Full Models (see table 171 and table 172) Two models were developed for both TOTACC and INJACC. Again, the main model was selected based on the highest Pearson productmoment correlation coefficient, lowest overdispersion, MPB per year, and MAD per year. For TOTACC, major and minor AADTs, commercial driveways on major roads, speed limits on major roads, presence of lighting, and horizontal curvature variables were found to be significant in the main model. By contrast, the Vogt main model included a completely different set of nonAADT variables: peak truck percentage PKTRUCK, peak leftturn percentage on minor road PKLEFT2, protected left lane PROT_LT, and vertical curvature VEICOM. The variant model provides an improvement over the main model in overdispersion and Pearson productmoment correlation, but not in MPB per year and MAD per year. For INJACC, major and minor AADTs, peak leftturn percentages on minor roads, peak truck percentages, presence of lighting, and speed limits on major roads were significant variables in the main model. Again, the Vogt main model had a completely different set of nonAADT variables: peak leftturn percentage on minor road PKLEFT2, peak truck percentage PKTRUCK, protected left lane PROT_LT, and vertical curvature VEICOM. In addition, the AADT variable effect was captured as the product of the major minor AADTs, as opposed to specifying these variables as separate terms in the recalibrated model. Although the recalibrated model variant was superior to the main model in terms of lower overdispersion and better fit to the data, it does include a Michigan indicator variable, which means more influence of the Michigan data on the model. Because the IHSDM requires the main model to be recalibrated to work in any State, the model with the State indicator was selected as a variant and not as the main model, similar to what was done for Types I and II. The recalibrated models for both TOTACC and INJACC provide a better GOF measures than Vogt's models, except for the overdispersion parameter. 3.7.2 Summary of AMFsSeveral strategies for assessing and recalibrating the AMFs corresponding with the five intersection models were explored, including:
Tables 231, 232, 233, and 234 compare the AMFs from the "Red Book," those from Harwood et al.'s 2002 report, and those derived during the course of this research. None of the variables used showed any significant impacts on safety for Type V sites. In general, the AMF estimates developed were of the same direction of effect and reasonably close in magnitude to those provided by Harwood et al. in 2000 and 2002. Whereas the "Red Book" provides separate AMFs for major road rightand leftturn lanes at Type II intersections, sites in this dataset had turning lanes on both approaches, and separate effects could not be detected for one versus two approaches. It is believed that a SKEW AMF significantly different than 1 was not supported by the data. There were only few sites with deficient sight distance, so an AMF could not be estimated for the effect of this variable. For Type III and IV intersections, SKEW was estimated as statistically significant in the regression models. Rightturn lanes on major roads provided statistically significant AMFs for Type IV intersections. For Type V intersections, no variables showed any statistically significant impacts on safety in the regression model. Table 231. Comparison of Type IIIV AMFs for TOTACC
Table 232. Comparison of Type III AMFs for TOTACC
^{1} Group A = 1.19, Group B = 0.86 Table 233. Comparison of Type IIIV AMFs for TOTACC
Table 234. Comparison of AMFs for INJACC
3.7.3 Conclusions and RecommendationsExtensive work was conducted as part of this effort to examine the appropriateness and defensibility of various models in the IHSDM. Numerous GOF indices were used to assess the models, as described in previous sections. Based on these extensive analyses, and practical issues of concern, several conclusions and recommendations can be drawn with respect to full models, AADT models, and AMFs. These are made in the context of IHSDM and general applications. IHSDM ApplicationFor IHSDM model development, it is recommended that there be a continuation of the current approach whereby AMFs are applied to base model accident predictions to account for factors for intersections under consideration that are different from the base condition. For base models, those calibrated with AADT as the only explanatory variable are recommended. For these models, the main considerations for recommendation surround the issues of variable selection, GOF, and the most defensible and representative data set from which models were estimated. Because previous AADT models were not directly calibrated as AADTonly, and instead were created by substituting constants for the nonAADT variables in the calibrated models, models estimated in previous efforts should be replaced with improved versions described in this report. Two sets of AADT models are recommended for both total and injury accidents. The first were calibrated using all available data and the second for a subset of sites meeting base condition criteria. If these base condition criterion are not known, or the appropriate AMFs not available, the models calibrated using all sites should be used. Specifically, the models shown in table 235 are recommended for use in the IHSDM: Table 235. AADT Models Recommended for Use in IHSDM
For AMFs, the main consideration is logical appeal. It is important to recognize that AMFs derived from expert opinion lack the conventional statistical variability measures associated with statistically derived AMFs. Also important is that expert derived AMFs were borne out of a perceived need among respected safety professionals that statistical information on empirically derived AMFs is unreliable. Combined with the fact that the research team had difficulty producing sufficient sample sizes for testing and/or validating AMFs, the following recommendations regarding AMFs are made:
General Applications of Full ModelsAlthough this research was focused on IHSDM applications, useful byproducts are the full crash prediction models that have been calibrated. These models are appropriate for crash prediction applications such as network screening and safety treatment evaluation. In these applications, crash prediction models are most relevant to ongoing and planned Highway Safety Manual projects and to the FHWA initiative known as Safety Analyst that consists of software tools to help manage sitespecific safety improvements. The overriding concerns for full models surround the selection of variables in the models, the intuitive appeal and agreement with engineering expectations, and the GOF criterion. Some of the main considerations in this regard include whether or not to include indicator variables for individual State effects (as opposed to a single constant term) and the appeal of individual model variables. It is generally believed that individual State effect models should be used if the individual States (e.g., California) were the target of crash forecasts. If crashes in States other than those identified are to be forecast, then models without State effects should be applied. Considering these factors, the full models shown in table 236 are recommended as "best available" statistical models: Table 236. Full Models Recommended for Use in Crash Prediction
