Gender, Safety Features, and Injury Severity: An Analysis of Vehicle Crash Outcomes Using FARS 2021 Data
Anjelica Martinez
Introduction
For decades, crash safety research and automotive engineering have relied on gender-biased data. The standard crash test dummy used in U.S. regulatory testing represents the height and weight of an average mid-sized male, and many vehicle safety systems (such as seatbelts and airbags) were originally designed around these male body dimensions (Bose et al., 2011; Sato et al., 2020). As a result, women may not receive the same level of protection, even when using safety equipment correctly. Prior research has reported that female occupants face higher injury risk in similar crash conditions, suggesting that design assumptions may not translate equally across genders.
Much of the work documenting these disparities comes from European researchers, particularly Astrid Linder, whose studies examine how male-centric crash testing affects injury outcomes. However, there is limited research applying the same level of scrutiny to U.S. data. Since vehicle fleets, regulations, and demographics differ between the U.S. and Europe, it is important to evaluate whether gender disparities appear in American crash outcomes as well.
This project uses the 2021 Fatality Analysis Reporting System (FARS) to investigate whether male and female drivers experience different levels of injury severity in fatal crashes. The research question guiding the analysis is:
Do female drivers experience higher injury severity than male drivers after accounting for seatbelt use and airbag deployment?
Based on prior work, I hypothesize that female drivers will show higher injury severity, but that the magnitude of the gender difference will decrease once safety equipment use is taken into account.
About the Dataset
This project uses data from the Fatality Analysis Reporting System (FARS), a nationwide census of all fatal motor vehicle crashes in the United States. FARS is maintained by the National Highway Traffic Safety Administration (NHTSA) and compiled by the National Center for Statistics and Analysis (NCSA). Each state and U.S. territory has trained FARS analysts who collect and verify crash data locally before submitting standardized case files to NHTSA.
FARS integrates information from multiple official sources for every crash, including Police Accident Reports, medical examiner and death certificate records, vehicle registration and VIN data, driver licensing files, and hospital or EMS documentation. The dataset is widely used in transportation safety research due to its national coverage and detailed documentation of driver, vehicle, and crash-level factors.
For this project, I use the 2021 FARS dataset, which is the most recent complete year of data available and contains tens of thousands of individual driver records.
Variables of Interest
age - Continuous variable representing the driver’s age
in years. Reported values range from 0 to 98, with 99 or 9999 coded as
missing or unknown.
gender - Categorical variable indicating the driver’s
sex as recorded in the crash report (1 = Male, 2 = Female). Records
labeled “Unknown” or “Not Reported” were excluded.
seatbelt_use – Categorical variable representing
restraint use at the time of the crash, based on FARS codes. Recoded as
Used (shoulder/lap belt, child restraint, etc.), Not Used (no
restraint), or Unknown.
airbag_deployment - Categorical variable describing
whether any airbag deployed in the vehicle. Recoded as Deployed, Not
Deployed, or Unknown based on system status at the time of impact.
vehicle_type – Categorical variable derived from the
FARS BODY_TYP codes. Recoded into six groups: Car,
Medium/Heavy Truck, Pickup/Light Truck, SUV/Crossover, and
Van/Minivan.
injury_severity – Ordinal variable representing the
level of injury sustained by the driver, ranging from 0 to 4, where:
0 = No injury,
1 = Possible injury,
2 = Minor injury,
3 = Serious injury
4 = Fatal injury
This scale reflects increasing levels of severity as defined in the FARS KABCO injury classification system.
Causal Framework (DAG Explanation)
The DAG represents the hypothesized relationships among the key variables in this analysis. Gender is treated as the main explanatory variable, with a potential direct effect on injury severity and indirect effects that operate through safety behaviors such as seatbelt use and airbag deployment. These safety behaviors are modeled as mediators because they can vary by gender and have well-established effects on crash outcomes.
Age and vehicle type are included as contextual variables that influence both safety behavior and injury severity. Older drivers, for example, tend to have higher seatbelt compliance and are more likely to drive larger or heavier vehicles, both of which reduce injury risk. Vehicle type also affects the likelihood of airbag deployment and the amount of crash protection available to the occupant.
By accounting for age and vehicle type, the model reduces confounding and isolates the portion of injury severity differences that may be associated with gender rather than differences in behavior or vehicle characteristics. This framework clarifies which variables should be adjusted for in the regression models and why they are necessary for estimating gender differences in crash injury severity.
gender_dag <- dagitty("
dag {
age [pos=\"3,1\"]
gender [pos=\"1,2\"]
seatbelt_use [pos=\"2,2\"]
airbag_deployment [pos=\"3,2\"]
vehicle_type [pos=\"2,1.5\"]
injury_severity [pos=\"4,2\"]
age -> injury_severity
age -> vehicle_type
airbag_deployment -> injury_severity
gender -> airbag_deployment
gender -> injury_severity
gender -> seatbelt_use
gender -> vehicle_type
seatbelt_use -> airbag_deployment
seatbelt_use -> injury_severity
vehicle_type -> injury_severity
}
")
plot(gender_dag)
Descriptive Statistics
For this analysis, the dataset was restricted to drivers only, excluding passengers and other non-driver occupants who do not directly influence vehicle control or safety equipment use. I also limited the sample to standard road vehicles (cars, SUVs, pickups, and vans) to maintain consistency in crash dynamics and safety system design. Motorcycle, ATV, and off-road vehicle cases were removed because they follow different injury mechanisms and safety equipment rules.
In addition, I focused on drivers recorded as male or female, removing cases coded as unknown or unreported. After applying these filters, the dataset decreased from 52,813 total occupants to 46,084 drivers, providing a more accurate and comparable sample for examining gender differences in crash injury severity.
nrow(df)## [1] 52813df_clean <- df |>
filter(
restraint_used != "Unknown",
air_bag != "Unknown",
!is.na(gender),
body_type != "Other/Unknown"
)
df_clean <- df_clean |>
mutate(
gender = factor(gender, levels = c("Female", "Male")),
restraint_used = factor(restraint_used, levels = c("Not Used", "Used")),
air_bag = factor(air_bag, levels = c("Deployed", "Not Deployed"))
)
nrow(df_clean)## [1] 46084Demographics
Age
The average age of drivers in the sample was 43 years (SD = 18.3), with ages ranging from 12 to 99. This distribution reflects a typical adult driving population and is consistent with the dataset’s focus on standard road vehicles rather than ATVs or recreational units, which often involve younger occupants. The wide age range indicates substantial variation among drivers, which is important since age can influence both driving behavior and injury risk.
df_clean |>
summarize(
n = n(),
mean_age = mean(age, na.rm = TRUE),
sd_age = sd(age, na.rm = TRUE),
min_age = min(age, na.rm = TRUE),
max_age = max(age, na.rm = TRUE)
)## # A tibble: 1 × 5
## n mean_age sd_age min_age max_age
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 46084 43.0 18.3 12 99Gender
Approximately 71% of drivers were male and 29% were female, which is consistent with national crash statistics showing that men are generally overrepresented in fatal crashes. This pattern is often attributed to men driving more miles and engaging in higher-risk driving behaviors overall (Insurance Institute for Highway Safety \[IIHS\], 2023). Despite the imbalance, the female subsample is still large enough to support reliable comparisons in injury severity between genders.
df_clean |>
tabyl(gender)## gender n percent
## Female 13362 0.2899488
## Male 32722 0.7100512Safety Equipment Use
Seatbelt Use
Most drivers in the dataset were wearing a seatbelt at the time of the crash (about 74%), while roughly 26% were unrestrained. Although this reflects the general trend of high seatbelt usage in the United States, the proportion of unbelted drivers remains substantial. Because seatbelt use is one of the strongest predictors of injury severity, this split is important for understanding differences in crash outcomes.
df_clean |>
tabyl(restraint_used)## restraint_used n percent
## Not Used 11953 0.2593742
## Used 34131 0.7406258Airbag Deployment
Airbags deployed in approximately 55% of crashes and did not deploy in about 45% of cases. This distribution is expected, since airbags are engineered to activate primarily during moderate to severe frontal impacts, while seatbelts provide protection across nearly all crash configurations. The deployment pattern helps contextualize injury severity differences, as airbag activation typically corresponds to higher-energy collisions.
df_clean |>
tabyl(air_bag)## air_bag n percent
## Deployed 25356 0.5502127
## Not Deployed 20728 0.4497873Vehicle Type
Most drivers were operating passenger cars (about 44%), followed by SUVs and crossovers (approximately 22%) and pickup or light trucks (around 20%). Medium and heavy trucks accounted for about 10%, while vans and minivans made up the remaining 4%. Overall, this distribution reflects the makeup of everyday traffic on U.S. roads, with the majority of crashes involving standard passenger vehicles.
df_clean |>
tabyl(body_type)## body_type n percent
## Car 20167 0.43761392
## Medium/Heavy Truck 4632 0.10051211
## Pickup/Light Truck 9182 0.19924486
## SUV/Crossover 10171 0.22070567
## Van/Minivan 1932 0.04192344Injury Severity
Injury outcomes ranged from no injury to fatal, with fatal injuries representing the largest category at about 39% of all cases. No injury outcomes were the next most common (32%), followed by minor injuries (11%), serious injuries (9%), and possible injuries (8%). Fewer than 1% of records had missing injury severity information. This distribution is expected in a dataset focused on police-reported crashes, where severe and fatal outcomes are more likely to be documented and included in FARS.
df_clean |>
tabyl(injury_severity_fac)## injury_severity_fac n percent valid_percent
## Fatal 18060 0.391893065 0.39412522
## Minor 5012 0.108757920 0.10937739
## No injury 14889 0.323083934 0.32492416
## Possible 3729 0.080917455 0.08137835
## Serious 4133 0.089684055 0.09019488
## <NA> 261 0.005663571 NACross tabulations
Seatbelt Use by Gender
Seatbelt use differed noticeably between male and female drivers. About 79% of female drivers were restrained at the time of the crash compared to 72% of male drivers. Conversely, 28% of men were unrestrained versus 21% of women. This pattern is consistent with national research showing that women tend to have higher seatbelt compliance rates than men (Insurance Institute for Highway Safety \[IIHS\], 2023). These behavioral differences are important because they can contribute to observed disparities in injury severity.
df_clean |>
tabyl(gender, restraint_used) |>
adorn_percentages("row") |>
adorn_totals("row") |>
adorn_title("combined")## gender/restraint_used Not Used Used
## Female 0.2057327 0.7942673
## Male 0.2812787 0.7187213
## Total 0.4870113 1.5129887# Summarize the data by gender and restraint use
seatbelt_summary <- df_clean %>%
count(gender, restraint_used) %>%
group_by(gender) %>%
mutate(percent = n / sum(n))
# Create the bar chart
ggplot(seatbelt_summary, aes(x = gender, y = percent, fill = restraint_used)) +
geom_col(position = "fill", width = 0.7) +
scale_y_continuous(labels = percent_format()) +
scale_fill_manual(values = c("#A7C7E7", "#4A90E2"),
name = "Seatbelt Use",
labels = c("Not Used", "Used")) +
labs(
title = "Seatbelt Use by Gender",
x = "Gender",
y = "Percentage of Drivers"
) +
theme_minimal(base_size = 10) +
theme(
plot.title = element_text(hjust = 0.5, face = "bold"),
legend.position = "right"
)
Injury Severity by Gender
Injury severity patterns showed small but noticeable differences between male and female drivers. Female drivers had slightly lower fatality rates (38%) compared to males (40%), but they experienced higher proportions of minor and possible injuries. Male drivers, on the other hand, had a larger share of “no injury” outcomes. These differences suggest that while fatality rates are similar across genders, women may be more likely to sustain non-fatal injuries in crashes.
df_clean |>
tabyl(gender, injury_severity_fac) |>
adorn_percentages("row") |>
adorn_totals("row") |>
adorn_title("combined")## gender/injury_severity_fac Fatal Minor No injury Possible Serious
## Female 0.3814549 0.1240832 0.2876066 0.09556953 0.10582248
## Male 0.3961555 0.1024998 0.3375711 0.07493429 0.08309394
## Total 0.7776104 0.2265831 0.6251777 0.17050382 0.18891642
## NA_
## 0.005463254
## 0.005745370
## 0.011208624Model Fitting and Hypothesis Testing
To examine whether gender differences in injury severity persist after accounting for safety behavior and other contextual factors, I estimated a series of four regression models. Each model adds an additional layer of information, allowing me to see how the gender effect changes as seatbelt use, airbag deployment, age, and vehicle type are included. This step-by-step approach clarifies whether observed gender differences are due to gender itself or to differences in behavior, vehicle characteristics, or crash circumstances.
df_clean <- df |>
filter(
restraint_used != "Unknown",
air_bag != "Unknown",
!is.na(gender),
body_type != "Other/Unknown"
)
df_clean <- df_clean |>
mutate(
gender = factor(gender, levels = c("Female", "Male")),
restraint_used = factor(restraint_used, levels = c("Not Used", "Used")),
air_bag = factor(air_bag, levels = c("Deployed", "Not Deployed"))
)Model 1: Baseline Gender Differences in Injury Severity
The first model tested whether gender alone predicts injury severity. On average, male drivers had slightly lower injury severity scores than female drivers (b = −0.07, 95% CI \[−0.11, −0.04\], p < .001). The intercept (2.20) reflects the mean injury severity for female drivers, and the negative coefficient indicates a small but statistically significant difference for males.
However, the effect size is extremely small (R² = 0.00036), meaning gender by itself explains virtually none of the variation in injury severity. This suggests that other factors such as restraint use, airbag deployment, and vehicle characteristics likely account for much more of the observed differences in crash outcomes.
injury_gender_mdl <- lm(injury_severity ~ gender, df_clean)
injury_gender_mdl##
## Call:
## lm(formula = injury_severity ~ gender, data = df_clean)
##
## Coefficients:
## (Intercept) genderMale
## 2.19904 -0.07298summary(injury_gender_mdl)##
## Call:
## lm(formula = injury_severity ~ gender, data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.199 -2.126 -0.126 1.874 1.874
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.19904 0.01509 145.749 < 0.0000000000000002 ***
## genderMale -0.07298 0.01791 -4.076 0.0000459 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.739 on 45821 degrees of freedom
## (261 observations deleted due to missingness)
## Multiple R-squared: 0.0003624, Adjusted R-squared: 0.0003406
## F-statistic: 16.61 on 1 and 45821 DF, p-value: 0.0000459confint(injury_gender_mdl)## 2.5 % 97.5 %
## (Intercept) 2.1694645 2.22860913
## genderMale -0.1080801 -0.03788797Model 2: Controlling for Restraint Use and Airbag Deployment
The second model tested whether gender differences in injury severity persisted after accounting for seatbelt use and airbag deployment. Male drivers continued to show slightly lower injury severity than female drivers (b = −0.05, 95% CI \[−0.07, −0.02\], p = .001), but the effect remained very small.
Both safety variables were strong predictors of injury outcomes. Seatbelt use had the largest protective effect (b = −1.55, p < .001), and airbag non-deployment was also associated with lower injury severity (b = −1.40, p < .001), reflecting the fact that airbags tend to deploy in more severe crashes.
This model explained 36% of the variance in injury severity (R² = .36), a major improvement over the gender-only model (R² = .0004). Once seatbelts and airbags were included, the remaining gender difference was minimal, suggesting that behavioral and situational factors (rather than inherent biological differences) account for most of the observed disparity.
gender_safety_mdl <- lm(injury_severity ~ gender + restraint_used + air_bag, df_clean, na.action = na.exclude)
gender_safety_mdl##
## Call:
## lm(formula = injury_severity ~ gender + restraint_used + air_bag,
## data = df_clean, na.action = na.exclude)
##
## Coefficients:
## (Intercept) genderMale restraint_usedUsed
## 3.95620 -0.04638 -1.55306
## air_bagNot Deployed
## -1.39545summary(gender_safety_mdl)##
## Call:
## lm(formula = injury_severity ~ gender + restraint_used + air_bag,
## data = df_clean, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9562 -0.9613 0.0387 1.4856 3.0387
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.95620 0.01717 230.445 < 0.0000000000000002 ***
## genderMale -0.04638 0.01446 -3.208 0.00134 **
## restraint_usedUsed -1.55306 0.01506 -103.142 < 0.0000000000000002 ***
## air_bagNot Deployed -1.39545 0.01330 -104.931 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.392 on 45819 degrees of freedom
## (261 observations deleted due to missingness)
## Multiple R-squared: 0.3596, Adjusted R-squared: 0.3595
## F-statistic: 8575 on 3 and 45819 DF, p-value: < 0.00000000000000022confint(gender_safety_mdl)## 2.5 % 97.5 %
## (Intercept) 3.92255587 3.98985355
## genderMale -0.07472319 -0.01804328
## restraint_usedUsed -1.58257507 -1.52354935
## air_bagNot Deployed -1.42151098 -1.36937988Model 3: Interaction Between Gender and Airbag Deployment
The third model tested whether the effect of airbag deployment on injury severity differed by gender, while controlling for seatbelt use, vehicle type, and age. The model was highly significant (F(12, 45,759) = 2,422, p < .001) and explained 38.8% of the variance in injury severity, the highest explanatory power of all models estimated in this analysis.
A significant interaction emerged between gender and airbag deployment (b = 0.27, 95% CI \[0.22, 0.33\], p < .001). This indicates that the relationship between airbag deployment and injury severity varies slightly by gender. In practical terms, airbags were slightly less protective for men when not deployed, although when airbags did deploy, both genders experienced similar reductions in injury severity.
Once again, seatbelt use remained the strongest predictor of injury severity (b = −1.58, p < .001), followed by airbag deployment (b = −1.48, p < .001). Vehicle type also played a role: drivers of medium or heavy trucks had notably lower injury severity, whereas drivers of cars, SUVs, and vans showed comparatively higher injury levels. Age was another significant predictor (p < .001), with older drivers facing increasing injury severity as age rose.
gender_safety_int_mdl <- lm(injury_severity ~ gender * air_bag + restraint_used + body_type + ns(age, 4), data = df_clean)
gender_safety_int_mdl##
## Call:
## lm(formula = injury_severity ~ gender * air_bag + restraint_used +
## body_type + ns(age, 4), data = df_clean)
##
## Coefficients:
## (Intercept) genderMale
## 3.92502 -0.09186
## air_bagNot Deployed restraint_usedUsed
## -1.48143 -1.57948
## body_typeMedium/Heavy Truck body_typePickup/Light Truck
## -0.53977 -0.24927
## body_typeSUV/Crossover body_typeVan/Minivan
## -0.22106 -0.26841
## ns(age, 4)1 ns(age, 4)2
## 0.10553 0.35462
## ns(age, 4)3 ns(age, 4)4
## 0.98596 1.50149
## genderMale:air_bagNot Deployed
## 0.27362summary(gender_safety_int_mdl)##
## Call:
## lm(formula = injury_severity ~ gender * air_bag + restraint_used +
## body_type + ns(age, 4), data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5395 -0.9650 -0.0975 1.1395 3.6366
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 3.92502 0.04589 85.531
## genderMale -0.09186 0.01861 -4.936
## air_bagNot Deployed -1.48143 0.02448 -60.519
## restraint_usedUsed -1.57948 0.01489 -106.067
## body_typeMedium/Heavy Truck -0.53977 0.02505 -21.550
## body_typePickup/Light Truck -0.24927 0.01791 -13.918
## body_typeSUV/Crossover -0.22106 0.01680 -13.155
## body_typeVan/Minivan -0.26841 0.03284 -8.173
## ns(age, 4)1 0.10553 0.04017 2.627
## ns(age, 4)2 0.35462 0.04324 8.202
## ns(age, 4)3 0.98596 0.09902 9.958
## ns(age, 4)4 1.50149 0.06349 23.649
## genderMale:air_bagNot Deployed 0.27362 0.02915 9.386
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## genderMale 0.000000801874905407 ***
## air_bagNot Deployed < 0.0000000000000002 ***
## restraint_usedUsed < 0.0000000000000002 ***
## body_typeMedium/Heavy Truck < 0.0000000000000002 ***
## body_typePickup/Light Truck < 0.0000000000000002 ***
## body_typeSUV/Crossover < 0.0000000000000002 ***
## body_typeVan/Minivan 0.000000000000000308 ***
## ns(age, 4)1 0.00863 **
## ns(age, 4)2 0.000000000000000243 ***
## ns(age, 4)3 < 0.0000000000000002 ***
## ns(age, 4)4 < 0.0000000000000002 ***
## genderMale:air_bagNot Deployed < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.361 on 45759 degrees of freedom
## (312 observations deleted due to missingness)
## Multiple R-squared: 0.3884, Adjusted R-squared: 0.3883
## F-statistic: 2422 on 12 and 45759 DF, p-value: < 0.00000000000000022confint(gender_safety_int_mdl)## 2.5 % 97.5 %
## (Intercept) 3.83507677 4.0149667
## genderMale -0.12834327 -0.0553824
## air_bagNot Deployed -1.52940836 -1.4334514
## restraint_usedUsed -1.60866761 -1.5502932
## body_typeMedium/Heavy Truck -0.58885874 -0.4906741
## body_typePickup/Light Truck -0.28436842 -0.2141640
## body_typeSUV/Crossover -0.25399819 -0.1881253
## body_typeVan/Minivan -0.33277173 -0.2040385
## ns(age, 4)1 0.02678248 0.1842687
## ns(age, 4)2 0.26987500 0.4393699
## ns(age, 4)3 0.79188867 1.1800328
## ns(age, 4)4 1.37704743 1.6259372
## genderMale:air_bagNot Deployed 0.21648681 0.3307596df_stack <- df_clean |>
filter(!is.na(injury_severity_fac), !is.na(air_bag), !is.na(gender)) |>
count(gender, air_bag, injury_severity_fac) |>
group_by(gender, air_bag) |>
mutate(p = n / sum(n))
ggplot(df_stack, aes(x = air_bag, y = p, fill = injury_severity_fac)) +
geom_col(width = 0.8, color = "white", linewidth = 0.2) +
facet_wrap(~ gender) +
scale_y_continuous(labels = scales::percent) +
scale_fill_manual(
name = "Injury Severity",
values = c(
"No injury" = "#A7C7E7", # light blue
"Possible" = "#7FB3D5",
"Minor" = "#5499C7",
"Serious" = "#2E86C1",
"Fatal" = "#003f5c" # darkest blue
)
) +
labs(
title = "Distribution of Injury Severity by Airbag Deployment and Gender",
x = "Airbag Deployment",
y = "Percent within Group"
) +
theme_minimal(base_size = 10) +
theme(
plot.title = element_text(size = 10, face = "bold"),
strip.text = element_text(face = "bold"),
panel.grid.minor = element_blank(),
legend.position = "right"
)
Model 4: Adjusting for Age-Related Vulnerability
he final model incorporated age (using natural splines), gender, seatbelt use, airbag deployment, and vehicle body type to account for how these factors jointly influence injury severity. After adjusting for these variables, gender was no longer a significant predictor of injury severity (b = 0.01, p = .34). This indicates that the gender differences observed in earlier models were fully explained by differences in safety behavior, vehicle characteristics, and age, not by gender itself.
As in prior models, seatbelt use remained the strongest protective factor (b = −1.58, p < .001), followed by airbag deployment (b = −1.29, p < .001). Vehicle type also continued to matter: drivers of medium or heavy trucks showed significantly lower injury severity than those in smaller passenger vehicles, likely due to the added structural protection and higher vehicle mass. Age was again a significant predictor (p < .001), with injury severity increasing steadily among older drivers.
This model explained approximately 38.7% of the variance in injury severity (R² = .39), making it the best-fitting model overall. Taken together, the results suggest that injury risk is shaped primarily by safety equipment use, vehicle design, and age, while gender itself contributes little once these contextual factors are accounted for. This supports the conclusion that gender gaps in crash outcomes reflect differences in circumstances and behaviors, rather than inherent biological vulnerability.
fac_vars <- c("gender","restraint_used","air_bag","body_type")
df_use <- df_clean %>%
filter(!is.na(age)) %>%
drop_na(all_of(fac_vars)) %>%
droplevels()
sapply(df_use[fac_vars], function(x) c(n_levels = nlevels(x), counts = paste(table(x), collapse=",")))## gender restraint_used air_bag
## n_levels "2" "2" "2"
## counts "13344,32685" "11937,34092" "25325,20704"
## body_type
## n_levels "0"
## counts "20145,4628,9172,10155,1929"age_mdl <- lm(injury_severity ~ gender + restraint_used + air_bag + body_type + ns(age, df = 4),
data = df_clean)
age_mdl##
## Call:
## lm(formula = injury_severity ~ gender + restraint_used + air_bag +
## body_type + ns(age, df = 4), data = df_clean)
##
## Coefficients:
## (Intercept) genderMale
## 3.84913 0.01406
## restraint_usedUsed air_bagNot Deployed
## -1.57812 -1.29132
## body_typeMedium/Heavy Truck body_typePickup/Light Truck
## -0.50138 -0.24489
## body_typeSUV/Crossover body_typeVan/Minivan
## -0.22211 -0.26584
## ns(age, df = 4)1 ns(age, df = 4)2
## 0.10655 0.36084
## ns(age, df = 4)3 ns(age, df = 4)4
## 0.99270 1.50313summary(age_mdl)##
## Call:
## lm(formula = injury_severity ~ gender + restraint_used + air_bag +
## body_type + ns(age, df = 4), data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.518 -0.983 -0.089 1.142 3.518
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.84913 0.04522 85.129 < 0.0000000000000002
## genderMale 0.01406 0.01482 0.949 0.34252
## restraint_usedUsed -1.57812 0.01490 -105.880 < 0.0000000000000002
## air_bagNot Deployed -1.29132 0.01376 -93.848 < 0.0000000000000002
## body_typeMedium/Heavy Truck -0.50138 0.02473 -20.271 < 0.0000000000000002
## body_typePickup/Light Truck -0.24489 0.01792 -13.665 < 0.0000000000000002
## body_typeSUV/Crossover -0.22211 0.01682 -13.205 < 0.0000000000000002
## body_typeVan/Minivan -0.26584 0.03287 -8.088 0.000000000000000624
## ns(age, df = 4)1 0.10655 0.04021 2.650 0.00806
## ns(age, df = 4)2 0.36084 0.04327 8.338 < 0.0000000000000002
## ns(age, df = 4)3 0.99270 0.09911 10.016 < 0.0000000000000002
## ns(age, df = 4)4 1.50313 0.06355 23.652 < 0.0000000000000002
##
## (Intercept) ***
## genderMale
## restraint_usedUsed ***
## air_bagNot Deployed ***
## body_typeMedium/Heavy Truck ***
## body_typePickup/Light Truck ***
## body_typeSUV/Crossover ***
## body_typeVan/Minivan ***
## ns(age, df = 4)1 **
## ns(age, df = 4)2 ***
## ns(age, df = 4)3 ***
## ns(age, df = 4)4 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.362 on 45760 degrees of freedom
## (312 observations deleted due to missingness)
## Multiple R-squared: 0.3873, Adjusted R-squared: 0.3871
## F-statistic: 2629 on 11 and 45760 DF, p-value: < 0.00000000000000022confint(age_mdl)## 2.5 % 97.5 %
## (Intercept) 3.76050863 3.93775295
## genderMale -0.01497503 0.04310029
## restraint_usedUsed -1.60732898 -1.54890178
## air_bagNot Deployed -1.31828447 -1.26434609
## body_typeMedium/Heavy Truck -0.54985609 -0.45289712
## body_typePickup/Light Truck -0.28000974 -0.20976239
## body_typeSUV/Crossover -0.25507421 -0.18914013
## body_typeVan/Minivan -0.33026313 -0.20141195
## ns(age, df = 4)1 0.02773080 0.18536625
## ns(age, df = 4)2 0.27602350 0.44565968
## ns(age, df = 4)3 0.79845180 1.18695494
## ns(age, df = 4)4 1.37857192 1.62769755newdat <- expand.grid(
age = seq(min(df_clean$age, na.rm=TRUE), max(df_clean$age, na.rm=TRUE), length.out=200),
gender = "Female", restraint_used = "Used", air_bag = "Deployed", body_type = "Car"
)
pred <- predict(gender_safety_int_mdl, newdata = newdat, se.fit = TRUE)
newdat$fit <- pred$fit
newdat$lo <- pred$fit - 1.96*pred$se.fit
newdat$hi <- pred$fit + 1.96*pred$se.fit
ggplot(newdat, aes(age, fit)) +
geom_ribbon(aes(ymin = lo, ymax = hi), alpha = .15) +
geom_line(size = 1) +
labs(title = "Predicted Injury Severity by Age (holding other factors constant)",
x = "Age", y = "Predicted injury severity") +
theme_minimal()## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Diagnostics and Model Evaluation
To assess the fit of the final linear regression model, I examined
the four standard diagnostic plots produced by the plot()
function. Because injury severity is an ordinal variable with only five
possible values, some violations of linear model assumptions were
expected. Even so, the diagnostics overall indicate that the model
performs adequately for the purposes of this analysis.
1. Residuals vs Fitted
The residuals form several horizontal bands rather than a continuous
cloud, which is expected given the discrete injury severity scale. The
smoothing line is mostly flat with only mild curvature, suggesting no
major violation of the linearity assumption. In this context, the fitted
relationship appears sufficiently linear to justify the use of OLS.
2. Q–Q Plot
The Q–Q plot shows clear deviations from the 45-degree line, especially
in the tails, indicating non-normality of residuals. This pattern
reflects the bounded and ordinal nature of the outcome rather than a
misspecified model. Although the residuals are not normally distributed,
the deviations are not severe enough to undermine the interpretation of
the regression results, particularly since the course requires the use
of a linear model.
3. Scale–Location Plot
The Scale–Location plot indicates mild heteroscedasticity, with residual
variance changing across fitted values. This variation again mirrors the
discrete outcome structure rather than a structural problem in the
model. There is no strong funnel shape or evidence of unstable variance
that would threaten the reliability of the estimates.
4. Residuals vs Leverage
Most observations have low leverage, and none approach Cook’s distance
thresholds. This means that no individual case is exerting undue
influence on the regression results. The coefficients appear stable and
are not driven by outliers or extreme cases.
Overall Evaluation
Across the four diagnostics, the model shows minor departures from
normality and homoscedasticity, both of which are expected when modeling
an ordinal outcome with linear regression. These issues do not point to
a fundamental misfit. The linearity assumption holds reasonably well,
and there are no influential outliers. Given these conditions, the model
is appropriate for testing the research hypothesis. The R-squared value
indicates that the model explains a substantial portion of the variance
in injury severity after accounting for gender, safety behavior, vehicle
type, and age.
plot(age_mdl)
Conclusion
The results of this analysis show that gender is not a strong or consistent predictor of injury severity once seatbelt use, airbag deployment, vehicle type, and age are taken into account. Although the simpler models suggested slightly higher injury severity among female drivers, these differences disappeared in the fully adjusted model, where gender was no longer statistically significant. This indicates that the initial gender gap is largely explained by differences in safety behavior, vehicle choice, and age rather than gender itself.
Across all models, seatbelt use and airbag deployment emerged as the strongest predictors of reduced injury severity. Vehicle type and age also played meaningful roles: drivers of smaller vehicles and older adults consistently showed higher injury severity on average. The interaction model suggested that airbags may operate slightly differently across genders, but these differences were small and not consistent across specifications. The ordered logistic model (more appropriate for an ordinal outcome) did detect a statistically significant gender effect, but the effect size was extremely small and not practically meaningful.
In relation to the original hypothesis, the findings offer limited direct support. This dataset does not show a substantial gender disparity in injury severity once key contextual factors are controlled for. However, the results remain aligned with broader concerns in the literature regarding gender bias in vehicle safety design. If women are more likely to drive smaller vehicles, sit closer to the steering wheel, or rely on restraint systems designed around male body standards, these structural issues can still create gendered patterns in real-world crash outcomes, even if the statistical effect of gender appears small in this dataset.
Overall, these findings highlight the importance of continuing to push for gender-inclusive crash testing and vehicle design standards, while also reinforcing that safety behaviors such as seatbelt use remain the most powerful and consistent predictors of reduced injury severity.
Limitations
While this analysis provides meaningful insight into gender differences in crash injury severity, several limitations should be noted. First, the injury severity measure in FARS is ordinal and not continuous, yet the course requirements necessitated the use of linear regression. Although supplementary ordered logistic regression produced similar conclusions, linear models cannot fully capture the structure of ordinal outcomes. Second, the dataset includes only police-reported crashes, which tend to overrepresent severe and fatal cases and underrepresent minor crashes, potentially influencing the distribution of injury outcomes.
Additionally, FARS does not directly measure biomechanical differences or the design limitations of safety systems, which are central concerns in the gender-bias literature. Variables such as seating position, crash direction, impact speed, and occupant stature were not available for this project and may contribute to real-world gender disparities. Finally, some variables contained “unknown” or missing categories (particularly in restraint use and airbag deployment) which may introduce measurement error.
Despite these limitations, the models were able to explain a substantial portion of injury severity variation and provide a reliable assessment of how gender relates to crash outcomes within the scope of the available data.
Policy Implications
Although gender was not a strong predictor of injury severity in the adjusted models, the findings still reinforce concerns about how current vehicle safety standards may overlook female occupants. Seatbelt use and airbag deployment were consistently the strongest predictors of reduced injury severity, highlighting the importance of designing these systems to protect a broader range of body sizes, seating positions, and crash patterns. Improving gender-inclusive crash testing, particularly through the standardized use of female crash test dummies and updated anthropometric models, could help reduce injury disparities that stem from outdated design assumptions rather than biological differences. Additionally, public safety campaigns aimed at increasing seatbelt compliance among male drivers may further reduce gender gaps in observed injury outcomes.
Future Research
Future studies should incorporate more detailed biomechanical and crash-configuration variables that are not available in FARS, such as occupant height and weight, seating distance, crash direction, and impact speed. These factors may help identify whether subtle gender differences in injury risk emerge under specific crash conditions. Research using newer or more comprehensive datasets could also explore whether vehicle design changes over time reduce gender-related disparities. Finally, linking FARS data with hospital-based injury metrics could provide a richer understanding of how safety systems perform across different demographic groups.
References
Academic Sources
Bose, D., Segui-Gomez, M., & Crandell, J. R. (2011). Vulnerability of female drivers involved in motor vehicle crashes: An analysis of us population at risk. American Journal of Public Health, 101(12), 2368 - 2373. doi:10.2105/AJPH.2011.300275
Linder, A., & Svensson, M. Y. (2019). Road safety: The average male as a norm in vehicle occupant crash safety assessment. Interdisciplinary Science Reviews, 44(2), 140–153. https://doi.org/10.1080/03080188.2019.1603870
Sato, F., Brolin, K., Svensson, M., & Linder, A. (2020). Towards occupant protections for both men and women. In M. Di Nicolantonio, E. Rossi, & T. Alexander (Ed.), Advances in additive manufacturing, modeling systems and 3D prototyping. 975, pp. 603-615. Washington: Springer Nature Switzerland. doi:10.1007/978-3-030-20216-3
Institutional / Government Sources
Insurance Institute for Highway Safety. (2023). Fatality facts: Males and females. IIHS. https://www.iihs.org/topics/fatality-statistics/detail/males-and-females
Insurance Institute for Highway Safety. (2023). Seat belts. IIHS. https://www.iihs.org/research-areas/seat-belts
National Highway Traffic Safety Administration. (2023). Fatality Analysis Reporting System (FARS), 2019–2021 \[Data set\]. U.S. Department of Transportation. https://www.nhtsa.gov/research-data/fatality-analysis-reporting-system-fars
Appendix
Additional exploratory and robustness models are included in the appendix (Models 5–9). These did not substantially alter the main conclusions.
Model 5: Gender Differences in the Protective Effect of Restraint Use
This model tested whether the protective effect of seatbelt use differs by gender, while also accounting for airbag deployment. On average, male drivers without restraints had slightly higher injury severity than females (b = 0.05, p = .076), though this difference was not statistically significant. Seatbelt use remained a strong predictor of lower injury severity (b = −1.46, p < .001), and airbag non-deployment was also associated with reduced severity (b = −1.39, p < .001).
The interaction between gender and restraint use was significant (b = −0.13, 95% CI \[−0.20, −0.06\], p < .001), indicating that seatbelts provided a slightly stronger protective effect for males than for females. This suggests that while both genders benefit substantially from seatbelt use, the reduction in injury severity is somewhat greater among male drivers. The model explained 36% of the variance in injury severity (R² = .36), showing that most differences in crash outcomes are driven by safety equipment rather than gender alone.
gender_diffs_mdl <- lm(injury_severity ~ gender * restraint_used + air_bag, data = df_clean, na.action = na.exclude)
gender_diffs_mdl##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used + air_bag,
## data = df_clean, na.action = na.exclude)
##
## Coefficients:
## (Intercept) genderMale
## 3.87884 0.05374
## restraint_usedUsed air_bagNot Deployed
## -1.45600 -1.39446
## genderMale:restraint_usedUsed
## -0.12940summary(gender_diffs_mdl)##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used + air_bag,
## data = df_clean, na.action = na.exclude)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9326 -0.9527 0.0473 1.4619 3.0473
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.87884 0.02679 144.780 < 0.0000000000000002
## genderMale 0.05374 0.03029 1.774 0.076085
## restraint_usedUsed -1.45600 0.02988 -48.733 < 0.0000000000000002
## air_bagNot Deployed -1.39446 0.01330 -104.852 < 0.0000000000000002
## genderMale:restraint_usedUsed -0.12940 0.03441 -3.761 0.000169
##
## (Intercept) ***
## genderMale .
## restraint_usedUsed ***
## air_bagNot Deployed ***
## genderMale:restraint_usedUsed ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.392 on 45818 degrees of freedom
## (261 observations deleted due to missingness)
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3597
## F-statistic: 6437 on 4 and 45818 DF, p-value: < 0.00000000000000022confint(gender_diffs_mdl)## 2.5 % 97.5 %
## (Intercept) 3.826327050 3.93134997
## genderMale -0.005637585 0.11310812
## restraint_usedUsed -1.514561403 -1.39744263
## air_bagNot Deployed -1.420530275 -1.36839661
## genderMale:restraint_usedUsed -0.196839103 -0.06196719Model 6: Accounting for Vehicle Body Type
This model added vehicle body type as a control variable to examine whether the relationship between gender and injury severity changes once differences in vehicle size and structure are accounted for. After including body type, gender was no longer a significant predictor of injury severity (b = 0.01, p = .34). This means that once you control for what kind of vehicle someone was driving, the small gender difference seen earlier disappears.
As expected, seatbelt use (b = −1.53, p < .001) and airbag non-deployment (b = −1.31, p < .001) remained strong predictors of reduced injury severity. Vehicle type also played a meaningful role: drivers of medium or heavy trucks had the lowest average injury severity, while car, SUV, and van drivers experienced slightly higher injury levels. The model explained about 36.6% of the variance in injury severity (R² = .37), showing that differences in safety outcomes are better explained by vehicle type and safety device use rather than by gender.
car_safety <- lm(injury_severity ~ gender + restraint_used + air_bag + body_type, data = df_clean)
summary(car_safety)##
## Call:
## lm(formula = injury_severity ~ gender + restraint_used + air_bag +
## body_type, data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0070 -0.9832 -0.0070 1.4891 3.3188
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.99260 0.01824 218.946 < 0.0000000000000002
## genderMale 0.01442 0.01506 0.957 0.338
## restraint_usedUsed -1.52767 0.01509 -101.227 < 0.0000000000000002
## air_bagNot Deployed -1.30986 0.01397 -93.755 < 0.0000000000000002
## body_typeMedium/Heavy Truck -0.47388 0.02470 -19.185 < 0.0000000000000002
## body_typePickup/Light Truck -0.20143 0.01803 -11.174 < 0.0000000000000002
## body_typeSUV/Crossover -0.18625 0.01697 -10.978 < 0.0000000000000002
## body_typeVan/Minivan -0.18941 0.03321 -5.703 0.0000000118
##
## (Intercept) ***
## genderMale
## restraint_usedUsed ***
## air_bagNot Deployed ***
## body_typeMedium/Heavy Truck ***
## body_typePickup/Light Truck ***
## body_typeSUV/Crossover ***
## body_typeVan/Minivan ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.386 on 45815 degrees of freedom
## (261 observations deleted due to missingness)
## Multiple R-squared: 0.3656, Adjusted R-squared: 0.3655
## F-statistic: 3771 on 7 and 45815 DF, p-value: < 0.00000000000000022confint(car_safety)## 2.5 % 97.5 %
## (Intercept) 3.95685715 4.02834107
## genderMale -0.01510617 0.04394129
## restraint_usedUsed -1.55725392 -1.49809451
## air_bagNot Deployed -1.33724604 -1.28247863
## body_typeMedium/Heavy Truck -0.52229745 -0.42546840
## body_typePickup/Light Truck -0.23676523 -0.16609751
## body_typeSUV/Crossover -0.21950018 -0.15299357
## body_typeVan/Minivan -0.25450281 -0.12431116Model 7: Interaction Between Gender and Seatbelt Use
This model tested whether the protective effect of seatbelt use differs by gender, while controlling for airbag deployment, vehicle type, and age. The overall model was significant (F(12, 45,759) = 2,411, p < .001) and explained about 38.7% of the variance in injury severity, similar to the previous airbag interaction model.
Results showed a small but significant interaction between gender and seatbelt use (b = −0.08, 95% CI \[−0.15, −0.01\], p = .017). This indicates that seatbelts were slightly more protective for male drivers compared to female drivers. In other words, while seatbelt use greatly reduced injury severity for both groups, the reduction was marginally larger among men.
Main effects remained consistent with earlier models: seatbelt use (b = −1.52, p < .001) and airbag deployment (b = −1.29, p < .001) were the strongest predictors of lower injury severity. Vehicle type and age were also significant, with older drivers and those in smaller vehicles experiencing higher severity on average.
Together, these results suggest that seatbelts remain the most critical safety factor for all drivers, but small gender-based differences in how effectively they reduce injury severity may exist, potentially reflecting differences in body size, seating position, or how seatbelts fit across occupants.
seatbelt_int_mdl <- lm(injury_severity ~ gender * restraint_used + air_bag +
body_type + ns(age, 4), data = df_clean)
seatbelt_int_mdl##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used + air_bag +
## body_type + ns(age, 4), data = df_clean)
##
## Coefficients:
## (Intercept) genderMale
## 3.80100 0.07627
## restraint_usedUsed air_bagNot Deployed
## -1.51762 -1.29142
## body_typeMedium/Heavy Truck body_typePickup/Light Truck
## -0.49744 -0.24520
## body_typeSUV/Crossover body_typeVan/Minivan
## -0.22259 -0.26583
## ns(age, 4)1 ns(age, 4)2
## 0.10716 0.36030
## ns(age, 4)3 ns(age, 4)4
## 0.99321 1.50313
## genderMale:restraint_usedUsed
## -0.08096summary(seatbelt_int_mdl)##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used + air_bag +
## body_type + ns(age, 4), data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5313 -0.9794 -0.0896 1.1354 3.5205
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.80100 0.04947 76.829 < 0.0000000000000002
## genderMale 0.07627 0.02989 2.552 0.0107
## restraint_usedUsed -1.51762 0.02931 -51.771 < 0.0000000000000002
## air_bagNot Deployed -1.29142 0.01376 -93.859 < 0.0000000000000002
## body_typeMedium/Heavy Truck -0.49744 0.02479 -20.069 < 0.0000000000000002
## body_typePickup/Light Truck -0.24520 0.01792 -13.683 < 0.0000000000000002
## body_typeSUV/Crossover -0.22259 0.01682 -13.234 < 0.0000000000000002
## body_typeVan/Minivan -0.26583 0.03287 -8.088 0.000000000000000623
## ns(age, 4)1 0.10716 0.04021 2.665 0.0077
## ns(age, 4)2 0.36030 0.04327 8.326 < 0.0000000000000002
## ns(age, 4)3 0.99321 0.09910 10.022 < 0.0000000000000002
## ns(age, 4)4 1.50313 0.06355 23.653 < 0.0000000000000002
## genderMale:restraint_usedUsed -0.08096 0.03379 -2.396 0.0166
##
## (Intercept) ***
## genderMale *
## restraint_usedUsed ***
## air_bagNot Deployed ***
## body_typeMedium/Heavy Truck ***
## body_typePickup/Light Truck ***
## body_typeSUV/Crossover ***
## body_typeVan/Minivan ***
## ns(age, 4)1 **
## ns(age, 4)2 ***
## ns(age, 4)3 ***
## ns(age, 4)4 ***
## genderMale:restraint_usedUsed *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.362 on 45759 degrees of freedom
## (312 observations deleted due to missingness)
## Multiple R-squared: 0.3873, Adjusted R-squared: 0.3872
## F-statistic: 2411 on 12 and 45759 DF, p-value: < 0.00000000000000022confint(seatbelt_int_mdl)## 2.5 % 97.5 %
## (Intercept) 3.70402938 3.89796673
## genderMale 0.01768705 0.13484697
## restraint_usedUsed -1.57508072 -1.46016838
## air_bagNot Deployed -1.31838341 -1.26444757
## body_typeMedium/Heavy Truck -0.54602825 -0.44886120
## body_typePickup/Light Truck -0.28032494 -0.21007933
## body_typeSUV/Crossover -0.25556255 -0.18962705
## body_typeVan/Minivan -0.33024780 -0.20140330
## ns(age, 4)1 0.02834399 0.18597443
## ns(age, 4)2 0.27548777 0.44511745
## ns(age, 4)3 0.79897254 1.18745645
## ns(age, 4)4 1.37857322 1.62768594
## genderMale:restraint_usedUsed -0.14718513 -0.01474293Model 8: Interaction Between Gender, Restraint Use, and Airbag Deployment
This final expanded model tested whether the combined effects of seatbelt use and airbag deployment on injury severity differ by gender, while also controlling for vehicle type and age. The model came out highly significant (F(15, 45,756) = 2,215, p < .001) and explained about 42% of the variance in injury severity (R² = .42), the highest explanatory power of all models tested.
The three-way interaction between gender, seatbelt use, and airbag deployment was not statistically significant (b = 0.09, p = .19), which means the combined protective effects of seatbelts and airbags operated similarly for male and female drivers. The two-way interaction between seatbelt use and airbag deployment, however, was highly significant (b = −1.59, p < .001), confirming that injury severity was lowest when both restraints were used together, consistent with well-established crash safety findings.
Main effects stayed strong across all predictors: seatbelt use (b = −1.03, p < .001) and airbag deployment (b = −0.18, p = .002) were both associated with substantially reduced injury severity. Vehicle type and age also remained significant, with older occupants and those in smaller vehicles experiencing more severe injuries.
In short, this model shows that the combination of seatbelts and airbags provides the greatest protection for all drivers, regardless of gender. While earlier models showed slight gender-based differences in how individual safety features perform, the full interaction model suggests that when both systems work together, protection is consistent across men and women.
int_all_mdl <- lm(injury_severity ~ gender * restraint_used * air_bag + body_type + ns(age, 4),
data = df_clean)
int_all_mdl##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used * air_bag +
## body_type + ns(age, 4), data = df_clean)
##
## Coefficients:
## (Intercept)
## 3.489824
## genderMale
## -0.020650
## restraint_usedUsed
## -1.027268
## air_bagNot Deployed
## -0.180063
## body_typeMedium/Heavy Truck
## -0.441822
## body_typePickup/Light Truck
## -0.302764
## body_typeSUV/Crossover
## -0.247130
## body_typeVan/Minivan
## -0.285331
## ns(age, 4)1
## 0.136072
## ns(age, 4)2
## 0.381386
## ns(age, 4)3
## 1.007063
## ns(age, 4)4
## 1.398390
## genderMale:restraint_usedUsed
## -0.006089
## genderMale:air_bagNot Deployed
## 0.055517
## restraint_usedUsed:air_bagNot Deployed
## -1.588899
## genderMale:restraint_usedUsed:air_bagNot Deployed
## 0.093207summary(int_all_mdl)##
## Call:
## lm(formula = injury_severity ~ gender * restraint_used * air_bag +
## body_type + ns(age, 4), data = df_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3094 -0.8140 -0.0487 0.7947 3.6675
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 3.489824 0.050469 69.148
## genderMale -0.020650 0.034220 -0.603
## restraint_usedUsed -1.027268 0.033981 -30.231
## air_bagNot Deployed -0.180063 0.057386 -3.138
## body_typeMedium/Heavy Truck -0.441822 0.024509 -18.027
## body_typePickup/Light Truck -0.302764 0.017464 -17.337
## body_typeSUV/Crossover -0.247130 0.016365 -15.101
## body_typeVan/Minivan -0.285331 0.031966 -8.926
## ns(age, 4)1 0.136072 0.039109 3.479
## ns(age, 4)2 0.381386 0.042089 9.061
## ns(age, 4)3 1.007063 0.096378 10.449
## ns(age, 4)4 1.398390 0.061834 22.615
## genderMale:restraint_usedUsed -0.006089 0.040024 -0.152
## genderMale:air_bagNot Deployed 0.055517 0.064353 0.863
## restraint_usedUsed:air_bagNot Deployed -1.588899 0.063103 -25.180
## genderMale:restraint_usedUsed:air_bagNot Deployed 0.093207 0.071720 1.300
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## genderMale 0.546213
## restraint_usedUsed < 0.0000000000000002 ***
## air_bagNot Deployed 0.001704 **
## body_typeMedium/Heavy Truck < 0.0000000000000002 ***
## body_typePickup/Light Truck < 0.0000000000000002 ***
## body_typeSUV/Crossover < 0.0000000000000002 ***
## body_typeVan/Minivan < 0.0000000000000002 ***
## ns(age, 4)1 0.000503 ***
## ns(age, 4)2 < 0.0000000000000002 ***
## ns(age, 4)3 < 0.0000000000000002 ***
## ns(age, 4)4 < 0.0000000000000002 ***
## genderMale:restraint_usedUsed 0.879092
## genderMale:air_bagNot Deployed 0.388308
## restraint_usedUsed:air_bagNot Deployed < 0.0000000000000002 ***
## genderMale:restraint_usedUsed:air_bagNot Deployed 0.193744
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.324 on 45756 degrees of freedom
## (312 observations deleted due to missingness)
## Multiple R-squared: 0.4207, Adjusted R-squared: 0.4205
## F-statistic: 2215 on 15 and 45756 DF, p-value: < 0.00000000000000022confint(int_all_mdl)## 2.5 % 97.5 %
## (Intercept) 3.39090357 3.58874437
## genderMale -0.08772101 0.04642133
## restraint_usedUsed -1.09387095 -0.96066575
## air_bagNot Deployed -0.29254093 -0.06758487
## body_typeMedium/Heavy Truck -0.48985983 -0.39378364
## body_typePickup/Light Truck -0.33699390 -0.26853459
## body_typeSUV/Crossover -0.27920565 -0.21505521
## body_typeVan/Minivan -0.34798502 -0.22267627
## ns(age, 4)1 0.05941721 0.21272744
## ns(age, 4)2 0.29889012 0.46388215
## ns(age, 4)3 0.81816054 1.19596525
## ns(age, 4)4 1.27719343 1.51958579
## genderMale:restraint_usedUsed -0.08453721 0.07236004
## genderMale:air_bagNot Deployed -0.07061537 0.18164935
## restraint_usedUsed:air_bagNot Deployed -1.71258153 -1.46521741
## genderMale:restraint_usedUsed:air_bagNot Deployed -0.04736463 0.23377836Model 9: Ordered Logistic Regression (Robustness Check)
To account for the fact that injury severity is an ordered scale rather than a truly continuous measure, I ran an ordered logistic regression using gender, seatbelt use, and airbag deployment as predictors.
Seatbelt use came out as the strongest protective factor (β = 1.86, t = 75.75, p < .001), showing that drivers wearing seatbelts were much more likely to have less severe injuries.
Male drivers showed slightly lower odds of being in a higher injury severity category (β = -0.04, t = -2.19, p = .03), and crashes where airbags did not deploy were linked to lower injury severity (β = 0.60, t = 32.73, p < .001).
Overall, the ordered logit results tell the same story as the linear regression: once seatbelt and airbag use are accounted for, gender differences in injury severity are small but statistically significant.
ordered_model <- polr(as.factor(injury_severity_fac) ~ gender + restraint_used + air_bag, data = df_clean, Hess = TRUE)
summary(ordered_model)## Call:
## polr(formula = as.factor(injury_severity_fac) ~ gender + restraint_used +
## air_bag, data = df_clean, Hess = TRUE)
##
## Coefficients:
## Value Std. Error t value
## genderMale -0.04281 0.01957 -2.187
## restraint_usedUsed 1.86047 0.02456 75.750
## air_bagNot Deployed 0.59793 0.01827 32.730
##
## Intercepts:
## Value Std. Error t value
## Fatal|Minor 1.2187 0.0270 45.2137
## Minor|No injury 1.7879 0.0281 63.7263
## No injury|Possible 3.5225 0.0308 114.3749
## Possible|Serious 4.2508 0.0325 130.7839
##
## Residual Deviance: 119180.75
## AIC: 119194.75
## (261 observations deleted due to missingness)