Appendix: Association between SSF and Rollover Risk Estimated from Crash Data

A. Purpose of the Analysis

Our purpose is to describe the relationship between the Static Stability Factor (SSF) and the risk of rollover in single-vehicle crashes given the average mix of road use characteristics nationwide. We know that environmental, road, and driver factors affect rollover risk, and we suspect that vehicles with low SSFs may tend to be used differently than vehicles with high SSFs. (Another way to describe this is to say that SSF may be confounded with road use characteristics.) For example, some vehicles with a low SSF may tend to be used on curved roads or by young drivers, and these may be conditions that increase rollover risk. Therefore, our description of the association between the SSF and rollover risk will be no better than our ability to remove the confounding effects of differences in road use.

B. Data Availability

To compare the performance of different vehicle models, we need a large number of single-vehicle crashes. The National Automotive Sampling System (NASS) provides good data, but NASS is limited to towaway crashes and includes too few cases for this type of analysis. The Fatality Analysis Reporting System (FARS) includes a large number of cases, but the restriction to fatal crashes limits its use for comparisons of rollover propensity. The General Estimates System (GES) includes a large number of cases of all crash severities, and these data will be valuable when used in conjunction with the larger volume of cases available in the state crash files.

The agency routinely obtains crash files from seventeen states as part of its State Data System (SDS). We questioned whether a single state could represent the national experience (given state-to-state differences in road use and reporting practices), so we decided to use as many states as possible. This allowed us to compare the results among states and to combine the results to produce our best national estimate of the relationship between the SSF and rollover risk. Participants in the SDS include nine states that have the Vehicle Identification Number (VIN) on their crash files; we will call them the "VIN states" here. We need the VIN to completely and accurately describe the vehicle, and this is an essential part of our analysis. We eliminated three VIN states: Illinois (because we have not yet obtained the 1996 and 1997 data from this state) and New Mexico and Ohio (because we know that a rollover is recorded in these states only if the police identify it as the first harmful event in the crash). The 1994-1997 calendar year files for the other six VIN states in the SDS (Florida, Maryland, Missouri, North Carolina, Pennsylvania, and Utah) are the basis of our analysis. We used GES to verify and calibrate the results obtained from the six state files, but these six states include 26 times as many cases as GES alone.

C. Determination of the SSF

The main criterion for selecting the vehicles used in this analysis was the availability of a reasonable estimate of the SSF, and our goal was to include as many vehicle models as possible. We started with an existing compilation of all the SSF measurements made by the agency through 1998, but limited the study vehicles to model years 1988 and later. We added measurements provided by the General Motors Corporation (GM) for other vehicles, but we limited these additions to passenger cars and vans because the GM data did not distinguish between two- and four-wheel drive versions of pickup trucks and sport utility vehicles. We used data from vehicles tested with a single passenger when these were available, and from zero- or two-passenger loading when one-passenger loading was not available. A handful of SSF values were imputed, as in the following example: we assigned a late-generation four-wheel drive S-series Blazer (model years 1995 to 1998, for which we had no SSF measurement) the same SSF as the two-wheel drive version because there was no difference in the SSF between the two- and four-wheel drive versions in the earlier generation of that model (model years 1983 to 1994).

The result was a list of a hundred vehicle models (vehicle models tested by the agency, identified by GM, or imputed as described above). The list includes the following number of vehicle models for each of four light vehicle types: 36 cars, 30 sport utility vehicles, 13 vans, and 21 pickup trucks. The number of vehicle models in the study (a hundred) is a nice round number, but this was not by design. Our goal was to include as many models as possible, and one hundred was the number that was possible.

D. Data Processing

We identified vehicles for which we had a SSF value (including corporate cousins of the tested vehicles) in the state and national crash files based on the VIN and with the help of the 1998 version of The Polk Company's PC VINA® software. The list of vehicle models used in the analysis is shown as Tables A-1 through A-4; note that some vehicle groups include more than one vehicle model because the tested vehicles had corporate cousins. We restricted the crash data to single-vehicle events, which we defined to exclude crashes with another motor vehicle in transport or with a nonmotorist (such as a pedestrian or pedalcyclist), animal, or train. We eliminated any vehicle without a driver and all vehicles that were parked, pulling a trailer, designed for certain special or emergency uses (ambulance, fire, police, or military), or on an emergency run at the time of the crash.

All the files we used include variables that describe the conditions of the road and driver, and these are useful for understanding the risk of rollover. A detailed review of the agency's GES and SDS documentation showed that the following information is available for most of the six states and for GES. The name of the variable created from this information is shown in capital letters, in parentheses:

  1. Did the vehicle roll over? (ROLL)

  2. Was it dark when the crash occurred? (DARK)

  3. Was the weather inclement? (STORM)

  4. Did the crash occur in a rural area? (RURAL)

  5. Was the speed limit 50 mph or greater? (FAST)

  6. Did the crash occur on a grade, dip, or summit? (HILL)

  7. Did the crash occur on a curve? (CURVE)

  8. Were there potholes or other bad road conditions? (BADROAD)

  9. Was the road wet or icy or have another bad surface condition? (BADSURF)

  10. Was the driver male? (MALE)

  11. Was the driver under 25 years old? (YOUNG)

  12. Was the driver uninsured? (NOINSURE)

  13. Was drinking or illegal drug use noted for the driver? (DRINK)

  14. How many occupants were in the vehicle? (NUMOCC)

For each state and GES, we calculated the following summary statistics for each of the hundred vehicle groups in the study:

  1. Number of single-vehicle crashes during these four years;

  2. Number of rollovers per single-vehicle crash;

  3. Involvement of the following per single-vehicle crash (as available on each file):
    DARK, STORM, RURAL, FAST, HILL, CURVE, BADROAD, BADSURF,
    MALE, YOUNG, NOINSURE, and DRINK; and

  4. Average number of occupants per vehicle in these crashes.

We used these summary-level data (summarized as counts and averages per vehicle group) as the basis for our analysis. Each summary record, representing a vehicle model group, is a data point in our linear regressions.

E. State-by-state Data Analysis

For each state, we limited the analysis to vehicle groups with at least 25 single-vehicle crashes. This threshold is somewhat arbitrary, but it is the one we used in an earlier analysis of single-vehicle crashes in state data (1). There are two valuable results: (1) there is at least one rollover for each vehicle group included in the model, and (2) there is no vehicle group for which every single-vehicle crash resulted in a rollover. That is, the rollover rate is greater than zero and less than one for every vehicle group we included in the study. We could have had as many as 600 data points (six states, each with up to 100 vehicle groups) for this analysis. We actually had (because of the threshold for inclusion) 481 data points, which represent the experience of 184,726 single-vehicle crashes. A similar restriction on the GES data file produced 60 data points representing the experience of 7,022 vehicles. The number of vehicle groups available for our analysis and the total number of single-vehicle crashes represented by these groups are shown in the first two data rows of Table A-5.

The number of rollovers per single-vehicle crash varies by state (from a low of 0.127 for Missouri to a high of 0.363 for Utah). There are two major reasons for this variation: (1) real differences among the states in road conditions, vehicles, and drivers, and (2) state-to-state reporting differences (and, in particular, the conventions for reporting nonrollover, nontowaway crashes). However, it is encouraging that the average number of rollovers per single-vehicle crash for the study vehicles was 0.198 for the six states combined, which is the same as the proportion estimated from GES for the same vehicles and time period.

We performed a number of stepwise linear regressions (using forward variable selection and a significance level of 0.15 for entry and removal from the model) on the individual states as preparation for an analysis of the six states combined. In each case, we modeled the natural logarithm of the number of rollovers per single-vehicle crash, LN(ROLL), as a function of a linear combination of the road, vehicle, and driver variables available in that state's crash file. We chose this transformation for three reasons: (1) a visual inspection of the data suggested that this form describes the relationship between rollover risk and the SSF better than a simple linear fit, (2) this form was consistent with our understanding of the process (we expected the biggest differences in the number of rollovers per single-vehicle crash to occur at relatively low values of the SSF, with diminishing effects for higher values of the SSF), and (3) this transformation has convenient mathematical properties. The form of the model implies that arithmetic changes in the SSF (for example, an additional 0.01 in the value) are associated with geometric changes in the number of rollovers per single-vehicle crash (about 3 percent fewer rollovers observed per single-vehicle crash for any 0.01 increase in the SSF, before accounting for differences in road use).

We ran stepwise regression models using the option that gives more weight to data points that are based on more observations, so vehicle groups with more crashes count for more in the analysis. Each data point was weighted by the number of single-vehicle crashes it represented, but the weighting was capped at 250. That is, data points based on more than 250 observations were weighted by 250. The weighting threshold is somewhat arbitrary, but it was chosen because it is 10 times the threshold for inclusion in the analysis. The rationale for weighting the data for the regression is that data points based on more observations are more reliable; the rationale for capping the weights is that at some point there are only marginal improvements in our estimates, and we want estimates that fit well over the entire range of the data (that is, for low-SSF and for high-SSF vehicles).

Florida can be used to illustrate our procedure. There are 85 vehicle groups available for our analysis, which represent the experiences of 34,521 vehicles in single-vehicle crashes during 1994-1997. There were 0.208 rollovers per single-vehicle crash in these data. A weighted linear regression of LN(ROLL) as a function of the SSF alone has an R-squared of 0.7074, which means that the SSF alone explains 71 percent of the variability in the data. This suggests that the SSF has great explanatory power for the number of rollovers per single-vehicle crash, but we are concerned that differences among vehicle groups in the mix of road use characteristics may be confounding the relationship. Therefore, we also used more-complex models that explicitly include these potentially confounding factors.

A weighted linear regression using a stepwise approach to include the best of the road use variables alone (that is, without the SSF) produced an equation with an R-squared of 0.5313. A second weighted linear regression using a stepwise approach to include the best of the road use variables plus the SSF produced an equation with an R-squared of 0.9041. The variability unexplained by the first model is:

1 - 0.5313 = 0.4687 (without the SSF),

and the variability unexplained by the second model is:

1 - 0.9041 = 0.0959 (with the SSF).

This means that 80 percent of the variability in the data remaining after the effects of the best of the road use variables are used is eliminated by allowing the SSF to enter the stepwise procedure. This is calculated as:

(0.4687 - 0.0950) / 0.4687 = 0.80.

We consider 80 percent to be the value of the SSF in explaining the number of rollovers per single-vehicle crash.

We used the results of the model to adjust the observed number of rollovers per single-vehicle crash to account for differences among vehicle groups in their road use characteristics in single-vehicle crashes. For each data point, we used the regression results (the coefficients of the explanatory road use variables, FAST, CURVE, MALE, YOUNG, and DRINK) and the typical road use (the observed averages of these road use characteristics for the study vehicles as a group) to estimate what LN(ROLL) would have been if road use for that vehicle group had been the typical road use for all the vehicles in the Florida study. The approach is similar to that described in our July 1991 Technical Assessment Paper. The average adjusted number of rollovers per single-vehicle crash for all the study vehicles in Florida is, by design, 0.208 (that is, the same as the number estimated from the unadjusted data). The line through the adjusted data is described by:

LN(ROLL) = 3.1691 - 3.7935 × SSF.

Exponentiating both sides of the equation produces an estimate that the number of rollovers per single-vehicle crash is approximated by the curve described by:

ROLL = 23.79 × e(-3.7935 × SSF).

This model form has very useful properties.

The equation can be used to estimate the number of rollovers per single-vehicle crash as a function of SSF alone, for the average mix of road use characteristics for the study vehicles in Florida during the years 1994-1997. For example, we can use the statistical model to identify the increase in the SSF that is associated with an estimate of half as many rollovers per single-vehicle crash. Note that our model has the same form as that used to describe radioactive decay as a function of time (with SSF used in place of time as the independent variable). Using the terminology and theory from the physical application, 3.7935 is the decay constant, and the half-life of the process is estimated as:

Half-life = LN(2) / (3.7935)
  = 0.18.

This means that the increase in the SSF that is associated with halving the number of rollovers per single-vehicle crash in Florida is estimated as 0.18. For example, the number of rollovers per single-vehicle crash under average conditions in Florida for the study vehicles as a group is estimated as:

0.40 for a SSF of 1.08

0.20 for a SSF of 1.26, and

0.10 for a SSF of 1.44.

Thus, rollover risk drops by a half when the SSF increases from 1.08 to 1.26, and it drops in half again when the SSF increases from 1.26 to 1.44.

F. Comparison of the State Results

The results for the six individual states and GES are shown in Table A-5. The value of the SSF in explaining rollovers per single-vehicle crash (measured as the decrease in unexplained variability when SSF is allowed to enter the stepwise regression) for the six states ranges from 64 percent for Utah to 80 percent for Florida; the value estimated from GES is 54 percent. The estimated increase in the SSF that is associated with halving the number of rollovers per single-vehicle crash is similar across the six states, ranging from 0.18 (Florida and Missouri) to 0.24 (Pennsylvania and Utah); the value estimated from GES is 0.18.

There are also similarities in which explanatory variables were chosen by the stepwise regression procedure. The best models for the states (the models that include SSF and those road use variables that are most useful in explaining the number of rollovers per single-vehicle crash in each state) include the following variables:

DARK: 2 states,
STORM: 1 state,
RURAL: 2 states (not available in 2 other states),
FAST: 5 states,
HILL: 2 states,
CURVE: 4 states,
BADROAD: 1 state (not available in 2 other states),
BADSURF: 1 state,
MALE: 6 states,
YOUNG: 5 states,
DRINK: 4 states, and
NUMOCC: 2 states (not available in 1 other state).

The similarities among the individual state models suggests that the six states can be combined to form a best estimate of the relationship between the SSF and the number of rollovers per single-vehicle crash if the differences among the states in road use and crash reporting can be addressed. We would not be surprised if a multi-state stepwise regression selected FAST, CURVE, MALE, YOUNG, and DRINK as explanatory variables because these factors are important in the individual state analyses. Note that combining the data from individual states is already done by FARS (a census of traffic fatalities in all states) and by GES (a survey of police-reported crashes in sampled states), and this combination is done without adjustment for differences in reporting practices. Our efforts to model the combined data from the six available VIN states are described below.

G. Combined Six-state Data Analysis

We performed a weighted stepwise linear regression analysis for the six states combined using the 481 data points that represent at least 25 single-vehicle crashes, with the weighting capped at 250. These 481 data points represent the experience of 184,726 single-vehicle crashes in the six-state combined data, including the following number of data points for each of four light vehicle types:

204 for cars,
124 for sport utility vehicles,
45 for vans, and
108 for pickup trucks.

The road use variables considered by the model were those that are available in all six states: DARK, STORM, FAST, HILL, CURVE, BADSURF, MALE, YOUNG, and DRINK.

We modeled LN(ROLL) as a function of these road use variables, and we created five dummy variables (DUMMY_FL, DUMMY_MD, DUMMY_NC, DUMMY_PA, and DUMMY_UT) to capture state-to-state differences. We needed dummy variables to combine the state data because the states have different reporting thresholds and practices, which produce different levels of rollovers per single-vehicle crash even after accounting for differences in road use. We chose Missouri as the baseline state for two reasons. First, Missouri has the lowest rollover rate (both before and after accounting for differences in road use), and this means that the coefficients of all the state dummy variables will be positive; this makes the results a little easier to describe, but it has no analytical implications. And second, there are significant differences between Missouri and each of the other five states in the number of rollovers per single-vehicle crash; this allows all five state dummy variables to enter the model and lets us measure the relative reporting effect of every state.

For example, the dummy variable DUMMY_FL was defined as "one" for each of the 85 Florida data points, and it was defined as "zero" for each of the 396 data point from the other five states. The coefficient of DUMMY_FL estimated by the regression analysis is interpreted as the incremental risk of rollover in Florida (compared to Missouri, the baseline state), after considering differences in road use. The other four dummy variables were handled analogously. All five dummy variables were defined as "zero" for all the Missouri data points.

The best model without SSF has an R-squared of 0.5753, and the best model with SSF has an R-squared of 0.8829. This means that allowing the SSF to enter the model explains 72 percent of the variation that was not explained by the model without SSF, and so we say that the value of the SSF to our model is 72 percent. The stepwise regression procedure with SSF chose three variables that describe the driving situation (DARK, FAST, and CURVE), three variables that describe the driver (MALE, YOUNG, and DRINK), and all five state dummy variables.

We used forward variable selection and a significance level of 0.15 for entry and removal from the model, but only one variable in the best model that included the SSF had a significance level greater than 0.0001 (DARK, at 0.0663). The F-statistic for the model as a whole was 294, and the probability of a value this high by chance alone is less than 0.0001. More details on the fit of the model are included as Table A-6.

The variables FAST, MALE, and YOUNG are unambiguous, and it seems likely that they are consistently reported by all six states (though there are some differences in the rates of missing data). The coding of DARK and CURVE may vary somewhat by state (states may differ in how they code twilight conditions, and states where most roads curve may tend to call a slightly-curved road "straight"). The coding of DRINK probably differs among the states. The state dummy variables describe systematic differences between states, including differences in the reporting threshold.

We used the results of the model to adjust the observed number of rollovers per single-vehicle crash to account for differences among states and vehicle groups in their road use characteristics in single-vehicle crashes. For each data point, we used the regression results to calculate how many rollovers per single-vehicle crash we would have expected if road use for that vehicle group had been the typical road use for all the vehicles in the study. (The effects of the adjustments on individual data points are sometimes large. For example, one pickup truck group had 0.46 rollovers per single-vehicle crash in Florida, in part because drivers of this vehicle in Florida tended to be young. If the vehicle had been driven like the average of all the vehicles in the study, we estimate that there would have been 0.35 rollovers per single-vehicle crash. This second number is what we are calling the "adjusted" rollover risk.)

The average adjusted number of rollovers per single-vehicle crash for all the study vehicles is, by design, 0.198 (that is, it is the number estimated from both the six-state data and GES). The fit of the curve through the adjusted data is described by:

Estimated rollovers per single-vehicle crash = 13.25 × e(-3.7831 × SSF).

This is the curve determined from the observed number of rollovers per single-vehicle crash, the results of the weighted regression model, and with an average of 0.198 rollovers per single-vehicle crash for all the vehicles used in the study. Figure A-1 shows the adjusted value of the rollover risk for each vehicle group averaged over all six states and the curve that describes the pattern of rollover risk as a function of the SSF. Our national estimate of the number of rollovers per single-vehicle crash declines by half for any increase of 0.21 in the SSF.

H. Discussion

The observed relationship between the SSF and the number of rollovers per single-vehicle crash is confounded by (1) the relationship between the SSF and road use factors that directly affect the risk of rollover and (2) state-to-state differences in reporting practices, including the reporting threshold. We attempted to correct for these biases in order to isolate the effect of the SSF on rollover risk, and the curve through the adjusted data is our best estimate of the relationship between the SSF and the risk of rollover. The fit of the model (an R-squared of 0.88), the significance of the SSF in the model (the probability of a greater value of the t statistic is less than 0.0001), the value of the SSF in this model (a 72 percent reduction in the R-squared compared to the best model without the SSF), and the implications from the model (rollovers decrease by half for any increase of 0.21 in the SSF) suggest a strong relationship between the SSF and rollover risk. However, this (in common with all statistical models) is a simplification of a complex process.

There are important factors that were not included in the model because they are not available on the state data files. Some of the unmeasured factors that may influence rollover risk include driver skill (including attitudes, habits, and experience) and after-market changes to the vehicle's SSF (including those caused by differences in tire inflation, vehicle loading, and wheel size). None of these factors was explicitly included in the analysis, but some of them may be included through their association with other, measured variables. For example, differences in driver skill as a function of vehicle group are captured to the extent that driver skill is a function of age (as measured by YOUNG).

Statistical models are a method for dealing with uncertainty. The results can suggest an underlying process, but they do not (except in the most trivial cases) produce deterministic predictions. For example, Figure A-1 shows some scatter around the fitted curve. This may reflect omitted variables, the effect of having only a few vehicle groups at each level of the SSF, or the effects of natural statistical variability (reflecting, in part, sample size limitations). We can put this unexplained variability in perspective, and we will use Florida for illustrative purposes.

Figure A-2 shows the Florida data adjusted to the typical road use for all vehicles in the study. (The amount of scatter in the Florida data appears similar to that for the average of the six states shown in Figure A-1.) The natural variability in the data is suggested by how much the rollover risk for a single vehicle group varies from year-to-year. Figure A-3 shows the number of rollovers per single-vehicle crash (calculated directly from the Florida data, without any adjustments for confounding factors) for each vehicle group for two calendar year groups: 1994-1995 versus 1996-1997. For this purpose, the data were limited to vehicle groups that had at least 25 single-vehicles crashes in both time periods. The line fit to these data (weighting each vehicle group by the number of single-vehicle crashes in Florida during these four years, with the weighting capped at 250) has an R-squared of 0.89 and the equation:

Rollover risk in 1996-1997 = 0.0111 + 0.946 × Rollover risk in 1994-1995.

That is, our model of rollover risk as a function of SSF across vehicle groups seems to fit the data about as well as a model of year-to-year changes for each vehicle group, which seems like a reasonably good fit for such a complex process.

 
Table A-1: The SSF for Passenger Cars
 
Vehicle Group Make / Model Model Years SSF
1 Dodge Neon, Plymouth Neon 95-98 1.44
2 Ford Crown Victoria 92-97 1.42
3 Ford Escort 91-96 1.38
4 Ford Escort, Mercury Tracer 97-98 1.37
5 Ford Mustang 88-93 1.38
6 Ford Probe 93-97 1.41
7 Ford Taurus, Mercury Sable 88-95 1.45
8 Lincoln Town Car 90-96 1.44
9 Buick Century, Chevrolet Celebrity, Oldsmobile Cutlass Ciera / Ciera, Pontiac 6000 88-96 1.38
10 Buick Regal, Pontiac Grand Prix 88-96 1.41
11 Chevrolet Lumina 95-98 1.34
12 Buick Lesabre, Pontiac Bonneville 92-96 1.39
13 Buick Park Avenue, Oldsmobile 98 91-96 1.38
14 Buick Skylark / Somerset, Oldsmobile Cutlass Calais / Calais, Pontiac Grand Am 88-91 1.35
15 Buick Skylark, Oldsmobile Achieva, Pontiac Grand Am 92-97 1.38
16 Chevrolet Camaro, Pontiac Firebird 88-92 1.53
17 Chevrolet Camaro, Pontiac Firebird 93-98 1.50
18 Buick Roadmaster, Chevrolet Caprice 91-96 1.40
19 Buick Skyhawk, Chevrolet Cavalier, Pontiac Sunbird 88-94 1.32
20 Chevrolet Corsica 88-96 1.30
21 Chevrolet Geo Metro, Suzuki Swift 89-94 1.32
22 Chevrolet Geo Metro, Suzuki Swift 95-98 1.29
23 Saturn SL 90-95 1.39
24 Saturn SL 96-98 1.35
25 Chevrolet Geo Prizm 89-92 1.38
26 Honda Civic 92-95 1.48
27 Honda Civic 96-98 1.43
28 Honda Accord 90-93 1.47
29 Mazda Protégé 95-98 1.40
30 Nissan Maxima 89-94 1.44
31 Nissan Sentra 91-94 1.46
32 Nissan Sentra 95-98 1.40
33 Toyota Camry 92-96 1.46
34 Toyota Corolla 89-92 1.36
35 Toyota Tercel 91-94 1.41
36 Toyota Tercel 95-98 1.39

 
Table A-2: The SSF for SUVs
 
Vehicle Group Make / Model Model Years Drive Wheels SSF
37 Dodge Ramcharger 88-93 4 1.13
38 Ford Bronco 88-96 4 1.13
39 Ford Bronco II 88-90 2 1.04
40 Ford Bronco II 88-90 4 1.04
41 Ford Explorer 91-94 2 1.07
42 Ford Explorer 91-94 4 1.08
43 Ford Explorer 95-98 2 1.06
44 Ford Explorer 95-98 4 1.06
45 Chevrolet S-10 Blazer, GMC S-1500 Jimmy 88-94 2 1.10
46 Chevrolet S-10 Blazer, GMC S-1500 Jimmy 88-94 4 1.10
47 Chevrolet Blazer, GMC Jimmy 95-98 2 1.09
48 Chevrolet Blazer, GMC Jimmy 95-98 4 1.09
49 Chevrolet V10/K10/K1500 Blazer 88-91 4 1.09
50 Chevrolet K1500 Blazer / Tahoe, GMC Yukon 92-98 4 1.12
51 Chevrolet V1500/V2500 Suburban, GMC V1500/V2500 Suburban 88-91 4 1.10
52 Chevrolet K1500/K2500 Suburban, GMC K1500/K2500 Suburban 92-98 4 1.08
53 Chevrolet Geo Tracker, Suzuki Sidekick 89-98 4 1.13
54 Honda CR-V 97-98 4 1.19
55 Honda Passport, Isuzu Rodeo 91-97 4 1.06
56 Isuzu Trooper 88-91 4 1.02
57 Isuzu Trooper 92-94 4 1.07
58 Jeep Cherokee 88-97 4 1.08
59 Acura SLX, Isuzu Trooper 95-98 4 1.09
60 Jeep Grand Cherokee 93-98 4 1.07
61 Jeep Wrangler 88-96 4 1.20
62 Nissan Pathfinder 88-95 4 1.07
63 Nissan Pathfinder 96-98 4 1.10
64 Suzuki Samurai 88-95 4 1.09
65 Toyota 4Runner 88-96 4 1.00
66 Toyota 4Runner 97-98 4 1.06

 
Table A-3: The SSF for Vans
 
Vehicle Group Make / Model Model Years Drive Wheels SSF
67 Dodge Caravan / Grand Caravan, Plymouth Voyager / Grand Voyager 88-95 2 1.21
68 Chrysler Town & Country, Dodge Caravan / Grand Caravan, Plymouth Voyager / Grand Voyager 96-98 2 1.23
69 Dodge B-150 Ram Wagon 88-98 2 1.09
70 Ford Aerostar 88-98 2 1.10
71 Ford E-150 Clubwagon 88-91 2 1.11
72 Ford E-150 Clubwagon 92-97 2 1.11
73 Ford Windstar 95-98 2 1.24
74 Chevrolet Astro, GMC Safari 88-98 2 1.12
75 Chevrolet Lumina APV, Oldsmobile Silhouette, Pontiac Transport 90-96 2 1.12
76 Chevrolet Venture, Oldsmobile Silhouette, Pontiac Transport 97-98 2 1.18
77 Chevrolet G10/G20 Sportsvan, GMC G1500/G2500 Rally van 88-95 2 1.08
78 Mazda MPV 89-97 2 1.17
79 Toyota Previa 91-97 2 1.23

 
Table A-4: The SSF for Pickup Trucks
 
Vehicle Group Make / Model Model Years Drive Wheels SSF
80 Dodge Dakota 97-98 2 1.25
81 Dodge Ram 1500 94-98 2 1.22
82 Dodge D-150 Ram 88-93 2 1.28
83 Ford F-150 88-96 2 1.19
84 Ford F-150 88-96 4 1.15
85 Ford F-150 97-98 2 1.18
86 Ford Ranger 88-92 2 1.13
87 Ford Ranger 88-92 4 1.03
88 Ford Ranger, Mazda B-series 93-97 2 1.17
89 Ford Ranger, Mazda B-series 93-97 4 1.07
90 Chevrolet C-1500, GMC C-1500 / Sierra 88-98 2 1.22
91 Chevrolet K-1500, GMC K-1500 / Sierra 88-98 4 1.14
92 Chevrolet S-10, GMC S-15 / Sonoma 88-93 2 1.19
93 Chevrolet S-10, GMC S-15 / Sonoma 88-93 4 1.19
94 Chevrolet S-10, GMC S-15 / Sonoma, Isuzu Hombre 94-98 2 1.14
95 Chevrolet S-10, GMC S-15 / Sonoma 94-98 4 1.14
96 Nissan Pickup 88-97 2 1.20
97 Nissan Pickup 88-97 4 1.11
98 Toyota Pickup 89-94 2 1.23
99 Toyota Pickup 89-94 4 1.07
100 Toyota Tacoma 95-98 2 1.26

 
Table A-5:
Rollovers per Single-Vehicle (SV) Crash as a Function of the SSF and Road Use Variables
 
  FL MD MO NC PA UT Six

States

 GES
Vehicle groups for study 85 81 82 86 86 61 481 60
Single-vehicle crashes 34,521 17,683 31,517 45,440 48,519 7,046 184,726 7,022
Rollovers per SV crash 0.208 0.159 0.127 0.177 0.246 0.363 0.198 0.198
 
R-squared for models of LN(ROLL) with:                
                 
SSF only 0.7074 0.6072 0.7266 0.5304 0.7281 0.7606 0.5386 0.4456
SSF and state             0.7334  
                 
Road use only 0.5313 0.6550 0.5520 0.5479 0.6878 0.5461   0.4147
Road use and state             0.5753  
                 
SSF plus road use 0.9041 0.8818 0.8559 0.8945 0.8879 0.8548   0.7332
SSF, road use, and state             0.8829  
                 
Value of SSF 80% 66% 68% 77% 64% 68% 72% 54%
                 
Best model of ROLL                
                 
Intercept 23.79 8.28 15.15 13.53 8.33 11.39 13.25 5.84
Coefficient of SSF -3.7935 -3.1414 -3.8627 -3.4328 -2.8494 -2.8784 -3.3731 -2.6943
Standard error of coefficient of SSF 0.1729 0.2552 0.2141 0.1798 0.1488 0.2391 0.0761 0.3192
                 
Increase in SSF to halve rollovers per SV crash 0.18 0.22 0.18 0.20 0.24 0.24 0.21 0.18

Table A-6:
Fit of the Model of Rollovers per Single-Vehicle Crash
as a Function of the SSF and Road Use Variables

R-square = 0.88290867 C(p) = 10.21256387

  DF Sum of Squares Mean Square F Prob>F
           
Regression 12 27480.16301362 2290.01358447 294.07 0.0001
Error 468 3644.41878744 7.78721963    
Total 480 31124.58180106      
           
Variable Parameter
Estimate		 Standard
Error		 Type II
Sum of Squares		 F Prob>F
           
INTERCEP 0.98462872 0.19748866 193.57224437 24.86 0.0001
SSF -3.37314841 0.07612591 15289.32722322 1963.39 0.0001
DARK -0.38680987 0.21016386 26.37918835 3.39 0.0663
FAST 1.52493695 0.1991692 456.50110043 58.62 0.0001
CURVE 1.55970317 0.25046223 301.98254463 38.78 0.0001
MALE -1.33399065 0.10621334 1228.37181405 157.74 0.0001
YOUNG 0.86034711 0.09977145 579.05158823 74.36 0.0001
DRINK 1.73507462 0.27938756 300.33406907 38.57 0.0001
DUMMY_FL 1.17092992 0.07322547 1991.22295614 255.7 0.0001
DUMMY_MD 0.64541483 0.09276482 376.9586446 48.41 0.0001
DUMMY_NC 0.50232907 0.03749136 1397.96646995 179.52 0.0001
DUMMY_PA 1.1724727 0.06537935 2504.41755183 321.61 0.0001
DUMMY_UT 0.83176783 0.05431222 1826.38170253 234.54 0.0001

Figure A-1

Figure A-2

Figure A-3

1. As described in our July 1991, Technical Assessment Paper: Relationship between Rollover and Vehicle Factors.