Applying Categorical Data Analysis to Multi-way Contingency Table Location, Accident Type, and Related Factors With Severity Li wan Chen, LENDIS Corporation, McLean, VA David L. Harkey, Highway Safety Research Center, University of North Carolina Forrest M. Council, Highway Safety Research Center, University of North Carolina ABSTRACT This analysis was undertaken to explore the underlying factors and contributing causes associated with carsemitrailer collisions at specific types of locations (e.g., intersections). The data for this effort was acquired from the Federal Highway Administration s Highway Safety Information System (HSIS), which contains multi-year, multi-state data on accidents, roadways, and traffic volumes. The focus of this paper is on the statistical analysis strategy and procedures applied to determine the association of crash location, type, and driver variables and the severity of the resulting crash. A series of discrete categorical analyses were conducted using the procedures available within BASE SAS and SAS/STAT. Other software packages were utilized to assist with the presentation of the data. The distribution of the variables is presented along with a fitted model, which represents the explanation of observed association among variables. Results from the model are used to derive the strongest effects of the particular combination (or interaction) of the variables. Various issues such as low count and sampling zero are also discussed. INTRODUCTION This analysis was undertaken to explore the underlying factors associated with the severity of car-semitrailer crashes at specific locations. A series of discrete categorical analyses were conducted. The focus of the statistical analysis strategy was applied to determine the best explanation of observed association accident locations, collision types, vehicle maneuvers before the crash, contributing factors assigned to drivers, and severity 1. In the current study, severity had two definitions in two subsets of data crash severity and driver injury. The intent of this paper is not to provide the final findings form the car-truck crash research that is being conducted, but to present the results of the statistical procedures applied to this particular problem. The data files for the analysis were developed from a state of HSIS for the years 1994-1997. The threshold of the reporting accident for this state changed from $ 500 to $1000 in 1996. Only those crashes involving two vehicles were included: one of those vehicles had to be a semitrailer (i.e., truck) and the other a passenger car. Passenger cars included two or four door sedans, station wagons, pick-up trucks, and vans. To insure a vehicle-tovehicle collision, only the following collision types were 1 Throughout this paper, a special case of log-linear models was applied. The criterion analyzed in all models is the odds of the expected cell count for the crash severity or driver injury. More precisely, all the models we applied pertain to the log of the odds. included rear end, left turn, right turn, head on, sideswipe, angle, and backing 2. In this study, the number of observed car-semitrailer crashes was not fixed ahead of time. The data were cumulated during a fixed-time period. The 1994-1995 data were assigned as Cohort 1 (4,679 crashes in the first cohort) and 1996-1997 data Cohort 2 (4,675 crashes) based on the change in crash reporting threshold. The accident count was assumed to be a random variable per cohort period, which resulted in a Poisson distribution (Demaris, A., 1992). COLLAPSING THE CATEGORIES OF THE VARIABLES There are a relatively large number of possible collision types which could be explored in the data. In order to simplify interpretation, two methods of collapsing collision type categories were explored (see Table 1 and 2) -- Method A and Method B. Table 1 shows the crosstabulation of crash severity by collision type 3. The odds of a crash involving a fatal or A-injury versus a B-, C-, or no injury (the dependent variable) differ noticeably within some of the collision types. However, there is relatively little change occurring over the two cohorts. If the specific categories were collapsible in Method A (Knoke, D. and Burke, P.J., 1980), the categories after collapsing would have separate effects on the odds of crash severity in Method B. If the above two conditions are positive, the log-linear models fit. A few specific models were produced which gave a parsimonious accounting of the data (see Table 2). For example, Model A-I was the fitted model with original 10 collision types. Model A-III was developed to determine whether Left-Turn and Left-Turn Cross Trfc could be combined into Left-Turn collision type. Model B-III indicated whether Left-Turn and other types had separate effects on the odds of fatal or A- injury. The question of how to decide model fit is answered by using either the Pearson chi-square statistic (X 2 ) or the likelihood-ratio statistic (L 2 ). L 2 (see Equation 1 where i = a variable with i categories, k = a variable with k 2 There were 10 vehicle-to-vehicle collision types 14 = Rear-End Slow (rear end, slow or stop), 15 = Rear-End Turn, 16 = Left-Turn (left turn, same roadway), 17 = Left-Turn Cross Trfc (left turn, different roadways), 18 = Right-Turn (right turn, same roadway), 19 = Rgt-Turn Cross Trfc (right turn, different roadways), 20 = Head-on, 21 = Sideswipe, 22 = Angle, and 23 = Backing. 3 A-injury means incapacitating injury, B-injury is related to nonincapacitating injury, and C-injury means no visible-but complaint of pain.
categories, etc. ) follows the chi-square distribution with df. L 2 is preferable to X 2 because the expected frequency (F ijklm) 4 are estimated by maximum likelihood methods and L 2 can be partitioned uniquely for more powerful tests of conditional independence in multi-way tables (Knoke, D. and Burke, P.J., 1980). 2 L = 2 [ f log( f ijklm / F ijklm )] ijklm ijklm (1) The larger the L 2 relative to the available degree of freedom (df), the more F ijklm departure from the observed frequency (f ijklm). The large L 2 indicates the hypothesized model does not fit the data well and should be rejected as an inadequate representation of the observed count. In other words, in trying to find the best-fitting log-linear model to describe a cross-tabulation and hopefully accept the hypothesized model, the objective is to find a low L 2 value relative to df. The P-value is determined by using at least.10 probability level in the model fit. The results of Model A-III indicated that Left-Turn types were collapsible (L 2 = 15.898, df = 11, p = 0.145). Model B-III verified Left-Turn and other collision types had separate effects (L 2 = 14.314, df = 9, p = 0.112). The results for Rear-End types were mixed Model A-II fit (L 2 = 15.853, df = 11, p = 0.147); however, Model B-II did not fit (L 2 = 15.833, df = 9, p = 0.070). Furthermore, Model B- VI showed that the model with Rear-End and Left-Turn collision types together did not have separate effects (L 2 = 14.295, df = 8, p = 0.074). Thus, we decided to preserve the original 10 collision types in the next analyses. CONTINGENCY TABLE ANALYSES The data for this set of tabular analyses contained specific information from accident descriptors and vehicle/driver variables. The accident variables, which describe the overall crash, included accident location, collision type, and crash severity. The vehicle/driver variables, which are affiliated with each driver or vehicle, indicated vehicle maneuver before the crash, contributing factors assigned to the driver, and driver injury. Descriptions of each of these analyses are provided below. CRASH SEVERITY - ACCIDENT LOCATION VARIABLES - SEE TABLE 3-1 There were 10 different accident locations (L) - 5 defined for rural locations and 5 for urban locations 5. The types of locations included roadway sections (absent of any major crossing streets), intersections, driveways, ramps, and other. See Footnote 2 for collision types. The crash severity (S) contained 295 crashes involving a fatal or A- level injury and 4,384 crashes involving a B- or C-level or no injury. Approximately, 7 out of 100 car-semitrailer 4 Depending on the models, the subscripts may vary. 5 The 5 types of location 11 or 21 = Section (bridge, underpass, no special feature), 12 or 22 = inters (Intersections - alley intersection and intersection of roadways), 13 or 23 = Driveway (public and private driveway), 14 or 24 = Ramp (interchange ramp), and 15 or 25 = Other (non-intersection median crossing, end or beginning of divided highway, interchange service road, railroad crossing, tunnel, and other). crashes resulted in a fatal or A-injury, hereafter referred to as a severe injury. On average, when comparing the ratios of severe injury crashes versus minor/no injury crashes among the location variables, the highest ratios were for Rural- Driveways (about 2.266 times greater) and Rural- Intersections (about 1.891 times greater). With respect to collision type, the ratios for Head-on was 27.973 times greater, Angle was about 1.773 times greater, and Leftturn 1.498 times greater for severe vs. minor/no injury. DRIVER INJURY - VEHICLE/DRIVER VARIABLES - SEE TABLE 4-1 While the above analyses were related to the overall crash (e.g., the most serious injury in the crash), we also conducted analyses related to individual vehicles. Here, we were interested in two subsets -- the subset of cases in which the car driver was severely injured, and the subset in which the truck driver was severely injured. And one of the predictor variables of interest here was which vehicle was at fault. Vehicle maneuver (M) is an indication of the driver actions just prior to being involved in the collision and includes 16 different actions 6. The contributing factor(s) assigned to a driver involved in a crash is a surrogate indication of fault to a certain level and contains several factors 7. For this analysis, if a driver was assigned any contributing factors other than not stated or no violation, then the driver was considered to have contributed to the cause of the crash. Since either or neither driver may have been assigned a contributing factor for a given crash, there were four unique combinations of fault that could exist - Car Driver only, Truck Driver only, Both Drivers, and Neither Driver. Driver Injury (I) is similar to crash severity. The difference is that driver injury is associated specifically with the driver instead of the most severely injured occupant in the crash. CAR-DRIVER INJURY - ACCIDENT AND VEHICLE/DRIVER VARIABLES Overall, 257 out of 4422 crashes resulted in a severely injured car driver. The accident location categories with the highest ratios were Rural-Driveways and Rural- Intersections. The collision types with high ratios included Head-on, Rear-End Turn, and Angle. The Vehicle Maneuvers showing the highest ratios were Going Straight 6 Vehicle maneuver actions -- Stopping in Road (stopped in travel lane), Prkd out of Road (parked out of travel lanes), Prkd in Road (parked in travel lanes), Going Straight (going straight ahead), Changing Lanes (changing lanes or merging), Passing, Right Turn (making right turn), Left Turn (making left turn), U Turn (making U turn), Backing, Slowing,stopping (slowing or stopping), Starting in Road (starting in roadway), Parking, Leaving Prkd Pos (leaving parked position), Avoidg Obj in Rd (avoiding object in road), and Other Veh Manvr (other). 7 Contributing factors -- not stated, no violation indicated, DUI/alcohol, DUI/drugs, yield, stop sign, traffic signal, exceeding speed limit, exceeding safe speed, minimum speed law, pass stopped school bus, passing on hill, passing on curve, improper passing, improper lane change, use of improper lane, improper turn, improper or no signal, improper vehicle equipment, safe movement violation, following too closely, improper backing, improper parking, unable to determine, other, reckless driving, left of center, right turn on red, and failure to reduce speed.
and Passing. Finally, the highest ratio for severe vs. minor/no injury with respect to contributing factors assigned occurred when the car driver was the only driver assigned a factor. SEMITRAILER-DRIVER INJURY - ACCIDENT AND VEHICLE/DRIVER VARIABLES We attempted to conduct similar analyses to cases in which the truck driver was severely injured. However, overall, only 15 out of 4,664 car-semitrailer crashes resulted in a severely injured truck driver. This might result in over-fitting models given the sample zero, low count, and the amount of categories involved. Thus, we decided to pursue different injury categories for truck drivers. Here, we compared any injury to no injury. There were 250 truck drivers out of 4,664 who experienced an injury of some level (killed, A-, B-, C-injury -- see Table 4-1). Based on Table 4-1, 6 out of 100 car-semitrailer crashes resulted in truck drivers killed, A-, B-, or C-injury. The high ratios were -- accident locations - Rural-Driveway and Rural-inters, collision type - Head-on, Angle, and Rear- End Turn collision, vehicle maneuvers - Passing and Going Straight. Finally, when the car driver was assigned to contributing factors, the ratio was about 1.681 times greater on the odds of killed, A-injury truck driver. THE LOG-LINEAR MODEL In summary, based on the above results, the following categories had the high ratios on odds of more severe crashes: Crash Severity - Accident Location Variables Accident Location: Rural-Driveway and Rural-inters; Collision Type: Head-on, Angle, and Left-Turn. Car-Driver Injury - Accident And Vehicle/Driver Variables Accident Location: Rural-Driveway, Rural-Inters, and Rural-Other; Collision Type: Head-on and Angle; Vehicle Maneuvers: U Turn, Avoiding Object in Road, and Going Straight; Contributing Factors: car driver being the only driver assigned a factor. Semitrailer-Driver Injury - Accident And Vehicle/Driver Variables Accident Location: Rural-Driveway and Rural-inters; Collision Type: Head-on, Angle, and Rear-End Turn; Vehicle Maneuvers: Passing and Going Straight; Contributing Factors: car driver being the only driver assigned a factor. The next question to be answered which variable and what specific categories have stronger effects, considering the main and interaction effects among the above variables? A special case of log-linear models was used to address this question 8, with the log of the odds (severe 8 The log-linear model, which uses the expected cell frequencies as a function of the variables as criteria, encompasses both hierarchical and nonhierarchical approaches (Zelterman, D., 1999). In this paper, we applied hierarchical approach to estimate main effect and interaction parameters. injury/minor or no injury) used as the dependent variable in the accident level model (see Table 3-2). For the vehicle/driver level model, the log of the odds was the same for car drivers, but changed slightly for truck drivers to the odds of being injured versus no injury. TESTING FOR MODELS FIT In the absence of explicit a priori hypotheses about the association among variables, the analysis began we with a more parsimonious model as the starting point, with the addition of more complex associations in the multi-way tabulation. Crash severity of car-semitrailer collisions was designated as the dependent variable in the cross tabulation. A useful beginning model was one in which none of the independent variables was significantly associated with the dependent variable. (See Table 3-2 Model ACC-I.) See Collapsing The Categories Of The Variables to decide the model fit. The fitted log-linear models resulted in the smallest difference between f ijklm s and F ijklm s. Among the fitted models, the test of the difference between any two nested models subtracts L 2 values and compares it to the difference in df (alpha = 0.05). This difference in L 2 is distributed approximately as chi-square distribution with df equal to the difference in df s between two models. For example, the significant change in L 2 relative to the change in df between Model C-X and C-XIV in Table 4-2 indicated by adding accident location to Model C-XIV resulted in a significant improvement in fit (L 2 = 24.106, df = 8, p = 0.002) A good model should fit the data well and be as simple as possible. Thus, one would like to select a model that is less complex rather than a more complex model. This would imply selecting models from the upper part of Table 3-2, Table 4-2, and Table 4-3 if possible. In addition, if several models fit equally well, one would prefer the model that made the most sense substantively or theoretically. Models with the best-looking adjusted residual were selected 9. If the model fit the observed count well, these differences between the observed and expected counts, called residuals, should be small. It is useful to standardize the residuals by dividing them by their standard error, the square root of the expected counts. The absolute values of standardized residuals greater than two standard deviations suggest important discrepancies, since they are unlikely to occur if the model is adequate. And the residuals do not have any discernible pattern in the plot. To summarize, in trying to find the best-fitting log-linear model, a low L 2 value relative to df was desired. Among the fitted models, the test of the difference between any two nested models subtracts L 2 values and compares it to the difference in df. The best-fitting model was selected if the model was less complicated, had the best looking adjusted residuals, and made more sense. 9 The residuals are not shown in this paper, but it is available upon request.
THE FITTED MODEL PARAMETERS The natural logs of the cell frequencies in the cross tabulation is a function of the main and interaction effects in the log-linear model. The point estimate and confidence intervals were used to explain the effects (see Table 3-3 and Table 3-4). And of particular interest were the twoway interactions between the dependent variable and other related factors 10. For example, for the accident variables in Table 3-3, based on likelihood ratio for Type 3 analysis, collision types (X 2 = 168.24, df = 9, p<.0001) had a stronger effect on the odds ratio than accident location (X 2 = 70.2, df = 8, p<.0001). Each coefficient was a comparison between a particular category and the reference category (Backing collision). Within collision types, Head-on collisions were nearly about 32.917 times (exp(3.494)=32.917) as likely to have resulted in a severe injury crash. Sideswipe collisions had odds that were only about half of the odds for Backing collision (exp(-0.827)=43.7%). Urban- Sections had odds that were 6.73% of the odds for Urban- Other. An attempt was also made to estimate the parameters representing the significant increments or significant decrements from the natural logs of the total counts, the base value, given the same L 2 and df (see Table 3-4). The Head-on and Angle collisions had the increment effects from the base value (see Estimate and Odds in Table 3-4). And Rear-End Slow and Sideswipe collisions had the decrement effect. Rural-Driveway had the increment effect. For example, the odds of Fatal or A- injury vs. No or B-, C-injury for Head-on was 27.319, on average. CROSS-VALIDATION The observed car-semitrailer crashes were cumulated during fixed-time period. The above results of the 1994-1995 (Cohort 1) should be expected to be similar to those of 1996-1997 (Cohort 2), except for differences due to random variation. The final model was fitted from Cohort 1 data, and then cross-validated these models on Cohort 2 (Knoke, D. and Burke, P.J., 1980). For example, in Table 3-2, Model ACC-IV is the chosen accident model for Cohort 1, Model ACC-IV-2 for Cohort 2. Both models have the same specifications. It was concluded that the differences in the log-linear results obtained by the two cohorts are no more than might be expected for random variation. (See Table 4-2 and Table 4-3 -- models for car and truck drivers). THE RESULTS This analysis was undertaken to explore the best explanation of observed association between severity and a few specific accident, vehicle, and driver variables. The major procedures included contingency table and loglinear models. The approach was to analyze the data for 10 We focused on the two-way intersection in the current study. The higher order interaction might improve the fit; however, it might be difficult to interpret the results. We note that the chosen models fit well without the higher order interactions in the current study. collapsibility across collision types with respect to severity impacts on the overall crashes, car drivers, and then the truck drivers. The results of collapsibility proved to be negative and we preserved the 10 collision types. CRASH SEVERITY - ACCIDENT LOCATION VARIABLES Overall, collision types and accident locations were associated with an increased likelihood of crash severity in car-semitrailer crashes. Collision types had stronger effect than accident locations. Within collision types, Head-on and angle collisions were the most likely types to result in a severe injury crash. Rear-End Slow and sideswipe collisions were less likely to result in a severe injury crash. Within location, rural driveway was the most likely location to result in a severe injury crash. Thus, we concluded the following variables have stronger impact on crash severity: Accident Location: Collision Type: Rural-Driveway; Head-on, Angle, Rear-End Slow; and sideswipe collisions. DRIVER INJURY - ACCIDENT AND VEHICLE/DRIVER VARIABLES On average, it was found that car drivers were much more often severely injured than truck drivers. (This is not surprising, given the large difference in weight between the two vehicles.) If there was any truck driver injury, it indicated the crashes tended to be more severe accidents. Given the sampling zero, low counts, and perhaps different structures of the vehicles, different combined injury categories were pursued when we analyzed the two subsets of data containing either the injured car driver or the injured truck driver. For car drivers, the dependent variable was the odds of a fatal or A-injury; for the truck driver, the odds of a fatal, A-, B-, or C-injury. Both car and truck drivers had the same model specifications all possible interactions among the independent variables, driver injury, and two-way interactions between driver injury with accident location, collision type, and contributing factors assigned. Note that vehicle maneuver did not have significant impact on the log of the odds. The important variables were collision type, location, and contributing factor assigned. DISCUSSION The car-semitrailer crashes from one of the HSIS States were used to examine factors associated with injury severity. Only those crashes involving two-vehicle accidents were included in this study. Only certain passenger cars and semitrailer trucks were included in this paper. We over-sampled the numbers of particular truck and selected certain collision types given the existing cumulated crashes. In order to study the selected factors associated with severity, a narrower population was used. However, locating the same roadway location within the same time for certain type of trucks was essential to examine the association. Future studies on different truck types, multiple-vehicle car-semitrailer crashes, multiple contributing factors assigned to a driver, specific accident locations such as rural intersection or rural driveway will be helpful to extend the current study, and then determine if the detected effects hold for other populations.
In terms of the analysis, as the sample size increases, the magnitude of X 2 increases. In order to interpret meaningful X 2, the analysis considered more than its numerical value (Reynold, H.T., 1984). The effects and adjusted residuals of each variable were examined. Two cohorts were used to validate the collapsibility and subsequent models to ensure the results were valid. The results of the Cohort 1 and 2 remained the same in the analyses, except for the differences due to random variation. It was concluded the reporting threshold change in 1996 had no significant impact on the current results. REFERENCES Allison, P.D. (1999), Logistic Regression Using the SAS System: Theory and Application, Cary, NC: SAS Institute Inc. Demaris, A. (1992), Logit Modeling Practical Applications, Sage University Paper series on Quantitative Applications in the Social Sciences, 07-086, Beverly Hill and London: Sage Pubns. Duncan, O.D. (1975), Partitioning Polytomous Variables in Multiway Contingency Analysis, Social Science Research, 4, 167-182. Knoke, D. and Burke, P.J. (1980), Log-Linear Model, Sage University Paper series on Quantitative Applications in the Social Sciences, 07-020, Beverly Hill and London: Sage Pubns. Light, R.J., Singer J.D., & Willett J.B. (1990), By Design - Planning Research on Higher Education, Cambridge: Harvard University Press. Reynolds, H.T. (1984), Analysis of Nominal Data, Sage University Paper series on Quantitative Applications in the Social Sciences, 07-007, Beverly Hill and London: Sage Pubns. SAS Institute Inc. (1999), SAS OnlineDoc(TM), Version 8.02, Cary, NC: SAS Institute Inc. SAS Institute Inc. (1993), SAS Technical Report P-243, SAS/STAT Software: The GENMOD Procedure, Release 6.09, Cary, NC: SAS Institute Inc. Upton, G.J.G. (1978), The Analysis of Cross-Tabulated Data, New York: Wiley. Zelterman, D. (1999), Models for Discrete Data, New York: Oxford University Press. CONTACT INFORMATION Li wan Chen LENDIS Corporation 6300 Georgetown Pike, Rm T-211 McLean, VA 22101 Work Phone: 202-493-3466 Email:li_wan.chen@fhwa.dot.gov.
Table 1. Cross-tabulation of Collision type (A) by Crash Severity (S). Cohort 1 Cohort 2 odds on Fatal or A Injury Collision Type Code Fatal or A Injury No or BC Injury Fatal or A Injury No or BC Injury Cohort 1 Cohort 2 Rear-End Slow A14 47 926 63 963 0.051 0.065 Rear-End Turn A15 5 102 6 87 0.049 0.069 Left-Turn A16 37 367 27 304 0.101 0.089 Left-Turn Cross Trfc A17 17 214 29 248 0.079 0.117 Right-Turn A18 6 291 2 210 0.021 0.010 Rgt-Turn Cross Trfc A19 8 105 1 83 0.076 0.012 Head-on A20 32 17 31 36 1.882 0.861 Sideswipe A21 23 1250 34 1332 0.018 0.026 Angle A22 107 897 112 894 0.119 0.125 Backing A23 13 215 8 205 0.060 0.039 Total 295 4384 313 4362 0.067 0.072 Table 2. Log-Linear Models -- Collapsibility for Collision Type (A) on Crash Severity (S). Method A a Method B Collapsing Categories Model b L 2 df L 2 /df p Model c L 2 df L 2 /df p Remain original categories A-I 15.853 10 1.585 0.104 B-I 15.853 10 1.585 0.104 Rear-End Slow, Turn (A14,A15) A-II 15.853 11 1.441 0.147 B-II 15.833 9 1.759 0.070 Left-Turn, Left-Turn Cross Trfc (A16,A17) A-III 15.898 11 1.445 0.145 B-III 14.314 9 1.590 0.112 Left-Turn, Left-Turn Cross Trfc, Angel(A16,A17,A22) A-IV 19.491 12 1.624 0.077 B-IV 14.312 8 1.789 0.074 Right-Turn, Rgt-Turn Cross Trfc (A18,A19) A-V 20.686 11 1.881 0.037 B-V 15.064 9 1.674 0.089 Rear-End and Left-Turn crashes(a14,a15)(a16,a17) B-VI 14.295 8 1.787 0.074 a. Duncan, O.D. (1975), Knoke, D. and Burke P.J. (1980) b. Model Specification: A-I: T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A-II: T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A16*S A17*S A18*S A19*S A20*S A21*S A22*S A23*S A-III:T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A14*S A15*S A18*S A19*S A20*S A21*S A22*S A23*S A-IV: T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A14*S A15*S A18*S A19*S A20*S A21*S A23*S A-V: T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A14*S A15*S A16*S A17*S A20*S A21*S A22*S A23*S c. Model Specification: B-1: T A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 S A14*S A15*S A16*S A17*S A18*S A19*S A20*S A21*S A22*S A23*S B-II: T A14 A16 A18 A19 A20 A21 A22 A23 S A14*S A16*S A17*S A18*S A19*S A20*S A21*S A22*S A23*S B-III: T A14 A15 A16 A18 A19 A20 A21 A22 A23 S A14*S A15*S A16*S A18*S A19*S A20*S A21*S A22*S A23*S B-IV: T A14 A15 A16 A18 A20 A21 A23 S A14*S A15*S A16*S A18*S A20*S A21*S A23*S B-V: T A14 A15 A16 A17 A18 A20 A21 A22 A23 S A14*S A15*S A16*S A17*S A18*S A20*S A21*S A22*S A23*S B-VI: T A14 A16 A18 A19 A20 A21 A22 A23 S A14*S A16*S A18*S A19*S A20*S A21*S A22*S A23*S
Table 3-1. Location (L) by Crash Severity (S) and Collision Type (A) by S. Variable Category Fatal or A Injury No or BC Injury Odds a Ratio a L by S Rural-Section 88 1056 0.083 1.238 Rural-Inters 85 668 0.127 1.891 Rural-Driveway 43 282 0.152 2.266 Rural-Ramp 0 49 0.000 0.000 Rural-Other 5 54 0.093 1.376 Urban-Section 30 1346 0.022 0.331 Urban-Inters 34 606 0.056 0.834 Urban-Driveway 6 90 0.067 0.991 Urban-Ramp 3 159 0.019 0.280 Urban-Other 1 74 0.014 0.201 Total 295 4384 0.067 1.000 A by S Rear-End Slow 47 926 0.051 0.754 Rear-End Turn 5 102 0.049 0.728 Left-Turn 37 367 0.101 1.498 Left-Turn Cross Trfc 17 214 0.079 1.181 Right-Turn 6 291 0.021 0.306 Rgt-Turn Cross Trfc 8 105 0.076 1.132 Head-on 32 17 1.882 27.974 Sideswipe 23 1250 0.018 0.273 Angle 107 897 0.119 1.773 Backing 13 215 0.060 0.899 Total 295 4384 0.067 1.000 a.odds on Killed or A Injury; Ratio = Odds/Total Odds. Table 3-2. Summary of the Models Fit - Location (L), Collision Type (A), and Crash Severity (S). Model Specification L 2 df L 2 /df p ACC-I L,A,L*A,S 49 309.293 6.312 0.000 ACC-II L,A,L*A,S,L*S 41 206.357 5.033 0.000 ACC-III L,A,L*A,S,A*S 40 108.323 2.708 0.000 ACC-IV L,A,L*A,S,L*S,A*S 32 38.120 1.191 0.211 ACC-IV-2 L,A,L*A,S,L*S,A*S 27 36.219 1.341 0.111 Table 3-3. Analysis Of Parameter Estimates on Crash Severity - Reference Group. Parameter df Estimate Standard Error Wald 95% Confidence Limits Chi-Square p S 1 1-1.035 1.259-3.502 1.432 0.680 0.411 L*S 11 1-1.593 1.233-4.010 0.823 1.670 0.196 L*S 12 1-1.175 1.224-3.575 1.224 0.920 0.337 L*S 13 1-0.833 1.232-3.247 1.582 0.460 0.499 L*S 15 1-0.738 1.321-3.328 1.852 0.310 0.577 L*S 21 1-2.698 1.241-5.131-0.265 4.720 0.030 L*S 22 1-1.624 1.229-4.031 0.784 1.750 0.186 L*S 23 1-1.223 1.301-3.772 1.327 0.880 0.347 L*S 24 1-2.180 1.364-4.853 0.494 2.550 0.110 A*S 14 1-0.194 0.332-0.845 0.457 0.340 0.559 A*S 15 1-0.615 0.549-1.691 0.461 1.260 0.262 A*S 16 1 0.065 0.346-0.613 0.743 0.040 0.851 A*S 17 1-0.005 0.398-0.786 0.775 0.000 0.990 A*S 18 1-0.560 0.519-1.577 0.457 1.160 0.281 A*S 19 1-0.064 0.501-1.046 0.918 0.020 0.899 A*S 20 1 3.494 0.441 2.631 4.358 62.920 <.0001 A*S 21 1-0.827 0.373-1.559-0.096 4.910 0.027 A*S 22 1 0.573 0.315-0.044 1.191 3.310 0.069 LR Statistics For Type 3 Analysis. Source Df Chi-Square p L 9 441.16 <.0001 A 9 357.01 <.0001 L*A 72 1686.09 <.0001 S 1 96.55 <.0001 A*S 9 168.24 <.0001 L*S 8 70.2 <.0001
Table 3-4. Analysis Of Parameter Estimates on Crash Severity (S) - Overall. Standard Category S Estimate Anti-log odds Error Wald 95% Confidence Limits Chi-Square p Fatal or A Injury -1.514 0.303-2.108-0.920 24.980 <.0001 Rural-Section Fatal or A Injury 0.293 1.341 1.797 0.305-0.304 0.890 0.930 0.336 No or BC Injury -0.293 0.746 Rural-Inters Fatal or A Injury 0.502 1.652 2.729 0.306-0.098 1.103 2.690 0.101 No or BC Injury -0.502 0.605 Rural-Driveway Fatal or A Injury 0.673 1.961 3.844 0.313 0.060 1.287 4.620 0.032 No or BC Injury -0.673 0.510 Rural-Ramp Fatal or A Injury -3.776 0.023 0.001 2.503-8.682 1.130 2.280 0.131 No or BC Injury 3.776 43.641 Rural-Other Fatal or A Injury 0.721 2.056 4.229 0.390-0.043 1.484 3.420 0.064 No or BC Injury -0.721 0.486 Urban-Section Fatal or A Injury -0.259 0.772 0.596 0.312-0.871 0.353 0.690 0.407 No or BC Injury 0.259 1.296 Urban-Inters Fatal or A Injury 0.278 1.320 1.744 0.315-0.339 0.895 0.780 0.378 No or BC Injury -0.278 0.757 Urban-Driveway Fatal or A Injury 0.478 1.613 2.602 0.371-0.250 1.206 1.660 0.198 No or BC Injury -0.478 0.620 Urban-Ramp Fatal or A Injury 0.000 1.000 1.000 0.000 0.000 0.000.. No or BC Injury 0.000 1.000 Urban-Other Fatal or A Injury 1.090 2.974 8.846 No or BC Injury -1.090 0.336 Rear-End Slow Fatal or A Injury -0.190 0.827 0.683 0.084-0.355-0.026 5.150 0.023 No or BC Injury 0.190 1.210 Rear-End Turn Fatal or A Injury -0.401 0.670 0.448 0.214-0.821 0.019 3.500 0.061 No or BC Injury 0.401 1.493 Left-Turn Fatal or A Injury -0.061 0.941 0.885 0.094-0.245 0.123 0.420 0.516 No or BC Injury 0.061 1.063 Left-Turn Cross Trfc Fatal or A Injury -0.096 0.908 0.825 0.127-0.345 0.153 0.570 0.450 No or BC Injury 0.096 1.101 Right-Turn Fatal or A Injury -0.373 0.688 0.474 0.198-0.761 0.014 3.560 0.059 No or BC Injury 0.373 1.453 Rgt-Turn Cross Trfc Fatal or A Injury -0.125 0.882 0.778 0.186-0.490 0.240 0.450 0.502 No or BC Injury 0.125 1.133 Head-on Fatal or A Injury 1.654 5.227 27.319 0.156 1.349 1.959 112.940 <.0001 No or BC Injury -1.654 0.191 Sideswipe Fatal or A Injury -0.507 0.602 0.363 0.115-0.732-0.281 19.400 <.0001 No or BC Injury 0.507 1.660 Angle Fatal or A Injury 0.193 1.213 1.472 0.068 0.061 0.326 8.180 0.004 No or BC Injury -0.193 0.824 Backing Fatal or A Injury -0.093 0.911 0.830 No or BC Injury 0.093 1.097
Table 4-1. Location (L) by Driver Injury (I), Collision Type (A) by I, Maneuver (M) by I, and Contribution Factors Assigned (P) by I. No, BC Killed or A injury or No, BC Killed or A injury or Vehicle Variable Category Injury Other Odds a Ratio a Vehicle Variable Category Injury Other Odds a Ratio a Car L by I Rural-Section 76 1068 0.071 1.224 Truck L by I Rural-Section 61 1083 0.056 0.998 Rural-Inters 72 681 0.106 1.819 Rural-Inters 84 669 0.126 2.224 Rural-Driveway 38 287 0.132 2.278 Rural-Driveway 27 298 0.091 1.605 Rural-Ramp 0 49 0.000 0.000 Rural-Ramp 0 49 0.000 0.000 Rural-Other 5 54 0.093 1.593 Rural-Other 2 57 0.035 0.622 Urban-Section 26 1350 0.019 0.331 Urban-Section 35 1341 0.026 0.462 Urban-Inters 31 609 0.051 0.876 Urban-Inters 28 612 0.046 0.811 Urban-Driveway 5 91 0.055 0.945 Urban-Driveway 7 89 0.079 1.393 Urban-Ramp 3 159 0.019 0.325 Urban-Ramp 3 159 0.019 0.334 Urban-Other 1 74 0.014 0.233 Urban-Other 3 72 0.042 0.738 Total 257 4422 0.058 1.000 Total 250 4429 0.056 1.000 Car A by I Rear-End Slow 41 932 0.044 0.757 Truck A by I Rear-End Slow 39 934 0.042 0.740 Rear-End Turn 3 104 0.029 0.496 Rear-End Turn 9 98 0.092 1.627 Left-Turn 28 376 0.074 1.281 Left-Turn 24 380 0.063 1.119 Left-Turn Cross Trfc 15 216 0.069 1.195 Left-Turn Cross Trfc 15 216 0.069 1.230 Right-Turn 4 293 0.014 0.235 Right-Turn 12 285 0.042 0.746 Rgt-Turn Cross Trfc 7 106 0.066 1.136 Rgt-Turn Cross Trfc 7 106 0.066 1.170 Head-on 30 19 1.579 27.168 Head-on 19 30 0.633 11.220 Sideswipe 20 1253 0.016 0.275 Sideswipe 25 1248 0.020 0.355 Angle 96 908 0.106 1.819 Angle 98 906 0.108 1.916 Backing 13 215 0.060 1.040 Backing 2 226 0.009 0.157 Total 257 4422 0.058 1.000 Total 250 4429 0.056 1.000 Car M by I Stopping in Road 5 591 0.008 0.146 Truck M by I Stopping in Road 1 145 0.007 0.122 Prkd out of Road 0 7 0.000 0.000 Prkd out of Road 0 2 0.000 0.000 Prkd in Road 0 7 0.000 0.000 Prkd in Road 0 1 0.000 0.000 Going Straight 199 2356 0.084 1.453 Going Straight 202 2283 0.088 1.568 Changing Lanes 4 405 0.010 0.170 Changing Lanes 6 709 0.008 0.150 Passing 4 135 0.030 0.510 Passing 10 119 0.084 1.489 Right Turn 7 197 0.036 0.611 Right Turn 11 342 0.032 0.570 Left Turn 26 354 0.073 1.264 Left Turn 11 336 0.033 0.580 U Turn 4 11 0.364 6.257 U Turn 0 13 0.000 0.000 Backing 0 22 0.000 0.000 Backing 2 206 0.010 0.172 Slowing,stopping 3 220 0.014 0.235 Slowing,stopping 5 196 0.026 0.452 Starting in Road 4 71 0.056 0.969 Starting in Road 1 47 0.021 0.377 Parking 0 1 0.000 0.000 Leaving Prkd Pos 0 13 0.000 0.000 Leaving Prkd Pos 0 4 0.000 0.000 Avoidg Obj in Rd 1 4 0.250 4.302 Avoidg Obj in Rd 0 2 0.000 0.000 Other Veh Manvr 0 28 0.000 0.000 Other Veh Manvr 1 24 0.042 0.738 Total 257 4422 0.058 1.000 Total 250 4429 0.056 1.000 Car P by I Car Driver Only 154 1600 0.096 1.656 Truck P by I Car Driver 152 1602 0.095 1.681 Truck Driver Only 74 2226 0.033 0.572 Truck Driver 78 2222 0.035 0.622 Both Driver 24 423 0.057 0.976 Both Driver 16 431 0.037 0.658 Neither Driver 5 173 0.029 0.497 Neither Driver 4 174 0.023 0.407 Total 257 4422 0.058 1.000 Total 250 4429 0.056 1.000 a. Odds on Killed or A Injury; Ratio = Odds/Total Odds.
Table 4-2. Car -- Summary the Models Fit - Location (L), Collision type (A), Maneuver (M), Contributing Factor Assigned (P), and Driver Injury a (I). Cohort Model Specification b L 2 df L 2 /df p Cohort 1 C-I L M A P, I, L*I 211.147 79 2.673 0.000 C-II L M A P, I, A*I 123.511 78 1.583 0.001 C-III L M A P, I, M*I 265.58 79 3.362 0.000 C-IV L M A P, I, P*I 213.021 84 2.536 0.000 C-V L M A P, I, L*I, A*I 95.5235 70 1.365 0.023 C-VI L M A P, I, L*I, M*I 189.411 71 2.668 0.000 C-VII L M A P, I, L*I, P*I 168.969 76 2.223 0.000 C-VIII L M A P, I,M*I, A*I 117.37 70 1.677 0.000 C-IX L M A P, I,M*I,P*I 203.694 76 2.680 0.000 C-X L M A P, I, A*I, P*I 89.3827 75 1.192 0.123 C-XI L M A P, I, L*I, A*I, M*I 82.0082 62 1.323 0.045 C-XII L M A P, I, L*I, P*I, M*I 150.027 68 2.206 0.000 C-XIII L M A P, I, M*I, A*I, P*I 77.8409 67 1.162 0.172 C-XIV L M A P, I, L*I, A*I, P*I 65.2768 67 0.974 0.537 C-XV L M A P, I, L*I, M*I, A*I, P*I 52.6952 59 0.893 0.706 Cohort 2 C-XIV-2 L M A P, I, L*I, A*I, P*I 62.0407 65 0.954 0.581 a. Driver Injury - (Killed or A Injury) versus (No, BC injury or other) b. L M A P includes main effects (L, M, A, P), two-way interactions (i.e., L*M, P*M, etc.), three-way interactions (i.e., L*M*A, L*M*P, etc.), and four-way interaction (L*M*A*P). Table 4-3. Truck -- Summary the Models Fit - Location (L), Collision type (A), Maneuver (M), Contributing Factor Assigned (P), and Driver Injury a (I). Cohort Model Specification b L 2 df L 2 /df p Cohort 1 T-I L M A P, I, L*I 160.95 73 2.205 0.000 T-II L M A P, I, A*I 146.989 72 2.042 0.000 T-III L M A P, I, M*I 191.301 73 2.621 0.000 T-IV L M A P, I, P*I 212.733 78 2.727 0.000 T-V L M A P, I, L*I, A*I 90.5459 64 1.415 0.016 T-VI L M A P, I, L*I, M*I 139.434 65 2.145 0.000 T-VII L M A P, I, L*I, P*I 133.894 70 1.913 0.000 T-VIII L M A P, I,M*I, A*I 113.262 65 1.742 0.000 T-IX L M A P, I,M*I,P*I 175.966 70 2.514 0.000 T-X L M A P, I, A*I, P*I 119.447 69 1.731 0.000 T-XI L M A P, I, L*I, A*I, M*I 76.1991 57 1.337 0.046 T-XII L M A P, I, L*I, P*I, M*I 120.346 62 1.941 0.000 T-XIII L M A P, I, M*I, A*I, P*I 101.706 62 1.640 0.001 T-XIV L M A P, I, L*I, A*I, P*I 66.8799 61 1.096 0.282 T-XV L M A P, I, L*I, M*I, A*I, P*I 61.3569 54 1.136 0.229 Cohort 2 T-XIV-2 L M A P, I, L*I, A*I, P*I 59.4869 57 1.044 0.385 a. Driver Injury - (Killed or ABC Injury) versus (No injury or other) b. L M A P includes main effects (L, M, A, P), two-way interactions (i.e., L*M, P*M, etc.), three-way interactions (i.e., L*M*A, L*M*Pet.), and four-way interaction (L*M*A*P).