Accident dataset

Traffic Accident Victims in France in 1958

Bertin (1983) used these data to illustrate the cross-classification of data by numerous variables, each of which could have various types and could be assigned to various visual attributes.

For modeling and visualization purposes, the data can be treated as a 4-way table using loglinear models and mosaic displays, or as a frequency-weighted data frame using a binomial response for result ("Died" vs. "Injured") and plots of predicted probabilities. data

data(Accident)

Format

A data frame in frequency form (comprising a 5 x 2 x 4 x 2 table) with 80 observations on the following 5 variables.

• age: an ordered factor with levels 0-9 < 10-19 < 20-29 < 30-49 < 50+
• result: a factor with levels Died Injured
• mode: mode of transportation, a factor with levels 4-Wheeled Bicycle Motorcycle Pedestrian
• gender: a factor with levels Female Male
• Freq: a numeric vector

Details

age is an ordered factor, but arguably, mode should be treated as ordered, with levels Pedestrian < Bicycle < Motorcycle < 4-Wheeled

as Bertin does. This affects the parameterization in models, so we don't do this directly in the data frame.

Source

Bertin (1983), p. 30; original data from the Ministere des Travaux Publics

References

Bertin, J. (1983), Semiology of Graphics, University of Wisconsin Press.

Examples

# examples
data(Accident)
head(Accident)

# for graphs, reorder mode
Accident$mode <- ordered(Accident$mode,
   levels=levels(Accident$mode)[c(4,2,3,1)])

# Bertin's table
accident_tab <- xtabs(Freq ~ gender + mode + age + result, data=Accident)
structable(mode + gender ~ age + result, data=accident_tab)

## Loglinear models
## ----------------

# mutual independence
acc.mod0 <- glm(Freq ~ age + result + mode + gender, 
                data=Accident, 
                family=poisson)
LRstats(acc.mod0)

mosaic(acc.mod0, ~mode + age + gender + result)

# result as a response
acc.mod1 <- glm(Freq ~ age*mode*gender + result, 
                data=Accident, 
                family=poisson)
LRstats(acc.mod1)

mosaic(acc.mod1, ~mode + age + gender + result, 
    labeling_args = list(abbreviate = c(gender=1, result=4)))

# allow two-way association of result with each explanatory variable
acc.mod2 <- glm(Freq ~ age*mode*gender + result*(age+mode+gender), 
                data=Accident, 
                family=poisson)
LRstats(acc.mod2)
mosaic(acc.mod2, ~mode + age + gender + result, 
    labeling_args = list(abbreviate = c(gender=1, result=4)))

acc.mods <- glmlist(acc.mod0, acc.mod1, acc.mod2)
LRstats(acc.mods)

## Binomial (logistic regression) models for result
## ------------------------------------------------
library(car)  # for Anova()
acc.bin1 <- glm(result=='Died' ~ age + mode + gender, 
    weights=Freq, data=Accident, family=binomial)
Anova(acc.bin1)

acc.bin2 <- glm(result=='Died' ~ (age + mode + gender)^2, 
    weights=Freq, data=Accident, family=binomial)
Anova(acc.bin2)

acc.bin3 <- glm(result=='Died' ~ (age + mode + gender)^3, 
    weights=Freq, data=Accident, family=binomial)
Anova(acc.bin3)

# compare models
anova(acc.bin1, acc.bin2, acc.bin3, test="Chisq")

# visualize probability of death with effect plots
## Not run:

library(effects)
plot(allEffects(acc.bin1), ylab='Pr (Died)')

plot(allEffects(acc.bin2), ylab='Pr (Died)')
## End(Not run)


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