Index | Table of contents | Technical Report | Executive Summary | Background | Rear Window Defrogger and Wiper Information | State Crash Data | Analysis Databases | Analysis Method | Hypotheses | Conclusions | Appendix A
Analysis method
To detect if rear window defoggers are effective, we considered and tested several different hypotheses. The first is that rear window defoggers reduce relevant crashes all the time. In other words, just the presence of rear window defoggers reduces backing up and changing lanes crashes. This hypothesis is probably unrealistic since rear window defoggers only improve rearward vision under certain conditions: when drivers turn them on because there is condensation, frost, ice, and/or snow on the back window. Nevertheless, this hypothesis was tested. (In part, this hypothesis had to be included in each model for methodological reasons, as will be explained later on.)
The second hypothesis is that rear window defoggers reduce relevant crashes when they are used. There is no way to determine if the rear window defogger was in use prior to the crash on the analysis databases, but we surmise that they are most likely used if any one or more of the following adverse conditions occurred: snowing or raining, during the earlier part of the morning, or during winter.
A third hypothesis is that rear window defoggers have independent (and additive) effects of reducing relevant crashes under the three individual conditions when they are most likely used: raining or snowing, during early morning, or during the winter. This hypothesis suggests the overall effect of rear window defoggers is the sum of the effects when it is raining or snowing, during early morning, and during the winter.
The fourth hypothesis is that the more adverse the conditions, the more effective the defoggers are at reducing relevant crashes but that the effect of each type of adverse condition is equal. In other words, when it is raining, morning, and winter, the effect of defoggers is three times as large as when just one of these conditions is present. This hypothesis is very similar to the third hypothesis in that is assumes that the effect is additive, but it differs in that it assumes each type of adverse condition has the same effect.
Logistic regression was used to estimate the effect of defoggers on the probability that the crash was relevant (as opposed to being a control group crash), while controlling for other factors. Estimating the impact of defoggers in reducing relevant crashes could be confounded by factors related to the driver, environment, vehicle, crash or other circumstances. To accurately estimate the impact of rear window defoggers, variables were included in the logistic regression to control for those factors, other than defoggers, which could influence the proportion of relevant crashes. For example, if rear window defoggers are in newer cars, or are more likely to be driven by older drivers than by other segments of the driving population, then driver and vehicle characteristics could confound estimating the impact of rear window defoggers. As a result, the age and sex of the driver, whether or not the crash occurred during adverse weather conditions (while raining or snowing when rear window defoggers are more likely to be used), whether or not the crash occurred during the morning or winter (also when rear window defoggers are more likely to be used), the age of the vehicle, vehicle make-model, and calendar year of the data were chosen for inclusion in the logistic regression model.
The following regression model was run on the Florida data set to test our second hypothesis – defoggers reduce relevant crashes in conditions when they are most likely to be used:
MODEL CLBKSTOP =
DEF_USED DEF USED ADWEA WINTER MORN VEHAGE VEHAGE2 CY86 CY87 CY88 CY89 CY90 CY91 CY92 CY93 CY94 CY95 CY96 CY97 CY98 DRVMALE M14_30 M30_50 M50_70 M70+ F14_30 F30_50 F50_70 F70+ CAVALIER1 ESCORT1…TERCEL;
CLBKSTOP is a flag that indicates whether the crash-involved car was changing lanes or backing (failures) or stopped (successes). All records where the crash-involved car was changing lanes or backing have CLBKSTOP = 1. All records where the crash-involved car was stopped have CLBKSTOP =2. ²
DEF is the percentage of rear window defoggers for that make-model in that model year. It is a continuous variable with values from 0 to 100.
DEF_USED is an interaction variable that expresses the probability that the rear window defoggers were most likely being used prior to the crash. It has the value of DEF if it is snowing or raining, during the earlier part of the morning or during winter. DEF_USED = DEF * USED (defined below) . For example, if 1989 Ford Taurus (89.7 percent had rear window defoggers) had a collision when it was raining, then DEF = 89.7 and DEF_USED = 89.7. DEF_USED has the value of zero if it is unlikely that the rear window defogger was in use. DEF_USED = 0 when it is not snowing, not raining, not during the earlier part of the morning and not during winter even if the car is equipped with rear window defoggers. For example, if a 1989 Ford Taurus had a crash that occurred on a bright, sunny afternoon in May, then DEF_USED = 0. DEF_USED also equals zero when the car does not have rear window defogger even if it is snowing or raining, during the early morning or during winter.² SAS/STAT â User’s Guide, Version 6, Fourth Edition, Volume 2, SAS Institute, Cary, NC, 1989, pp.1071-1126. The LOGISTIC procedure in SAS prefers values of 1 for failures and 2 for successes.
USED indicate if the conditions when rear window defoggers are most likely being used. It has the value one if it is snowing or raining, during the earlier part of the morning or during winter. It equals zero, otherwise. Specifically, USED = 1 if ADWEA = 1 or MORN = 1 or WINTER = 1 (defined below).
ADWEA has the value 1 if the crash occurred when it was raining or foggy, 0 otherwise.
WINTER has the value 1 if the crash occurred during January thru April or November or December, 0 if it occurred in May-October.
MORN has the value 1 if the crash occurred during 6:00 am to 9:59 am.
The model included both a linear and non-linear variable to account for vehicle age. The linear variable (VEHAGE) is age of the vehicle when the crash occurred (CY - MY). The non-linear variable (VEHAGE2) is VEHAGE * VEHAGE.
All the “CY” variables are indicator variables for calendar year, they have the value 1 if true otherwise the value of 0. For example, CY86 has value 1 if the calendar year is 1986, 0 otherwise.
The model includes one dichotomous and eight continuous variables to express driver age and gender. Kahane in the Vehicle Weight, Fatality Risk and Crash Compatibility of Model Year 1991-99 Passenger Cars and Light Trucks ³; used this approach. The dichotomous variable is DRVMALE. It has the value 1 if the driver is male and 0 if the driver is female.
“Driver age is expressed as a 4-piece linear variable, separately for males and females (eight variables in all): four connected straight-line segments, one from age 14 to 30, another from 30 to 50, another from 50 to 70, and the last from 70 and up. The eight variables are:
M14_30 = 30 – DRVAGE for male drivers age 14-30, otherwise it is 0 for male drivers age 30+ and all female drivers.
M30_50 = 50-DRVAGE for male drivers age 30-50; = 20 for male drivers age 14-30; or =0 for male drivers age 50+ and for all female drivers.
M50_70 = DRVAGE –50 for male drivers age 50-70; = 20 for male drivers70 +; =0 for male drivers age 14-50 and all female drivers.
³Kahane, C.J., Vehicle Weight, Fatality Risk and Crash Compatibility of Model Year 1991-99 Passenger Cars and Light Trucks, NHTSA Technical Report No. DOT HS 809 662, Washington, 2003, pp. 67-74.
M70+ = DRVAGE –70 for male drivers age 70+; =0 for male drivers age 14-70 and all female drivers.
F14_30 = 30 – DRVAGE for female drivers age 14-30, otherwise it is 0 for female drivers age 30+ and all male drivers.
F30_50 = 50-DRVAGE for female drivers age 30-50; = 20 for female drivers age 14-30; or =0 for female drivers age 50+ and for all male drivers.
F50_70 = DRVAGE –50 for female drivers age 50-70; = 20 for female drivers70 +; =0 for female drivers age 14-50 and all male drivers.
F70+ = DRVAGE –70 for female drivers age 70+; =0 for female drivers age 14-70 and all male drivers.
For example, a 40-year-old male driver would have M30-50 = 10, and the other variables set to zero. A 25-year-old male driver would have M30_50 = 20, M14_30 = 5, and the others set to zero. Conversely, a 60-year-old female driver would have F50_70 = 10 and the others set to zero. A 75-year-old female driver would have F50_70 = 20, F70+ = 5, and the others set to zero.
The rationale for defining the variables that way is that it treats 50 years as the baseline age. Each year that a driver is younger than 50 has some effect (usually increasing) on fatality risk, and each year that a driver is older that 50 has another effect (also usually increasing).4;” Given any specific age and gender, there is exactly one combination of the nine variables that will indicate a driver of that age and gender. These variables allow different linear relationships between age and crash risk in different age/gender groups.
Indicator variables for each make model were included in the model. These indicator variables are needed because some make-models are driven differently than others. For specific make-models, there may be two or more indicator variables included in the model depending on whether or not the car had a major redesign. For example, the Chevrolet Cavalier has two indicator variables: CAVALIER1 and CAVALIER2. The Chevrolet Cavalier was redesigned in model year 1995. So CAVALIER1 has the value 1 if the car was a 1983-1994 model year Chevrolet Cavalier, 0 otherwise and CAVALIER2 has the value 1 if the car was a 1995-2000 model year Cavalier, 0 otherwise. Similar indicator variables were made for all the other cars included in the model. The reference car was the 1975-1978 Volkswagen Rabbit.
4Kahane, C.J., Vehicle Weight, Fatality Risk and Crash Compatibility of Model Year 1991-99 Passenger Cars and Light Trucks, NHTSA Technical Report No. DOT HS 809 662, Washington, 2003, pp. 69-70.