R: Survival in the Donner Party

Donner

R Documentation

Survival in the Donner Party

Description

This data frame contains information on the members of the Donner Party, a group of people who attempted to migrate to California in 1846. They were trapped by an early blizzard on the eastern side of the Sierra Nevada mountains, and before they could be rescued, nearly half of the party had died.

What factors affected who lived and who died?

Usage

data(Donner)

Format

A data frame with 90 observations on the following 5 variables.

family: family name, a factor with 10 levels
age: age of person, a numeric vector
sex: a factor with levels Female Male
survived: a numeric vector, 0 or 1
death: date of death for those who died before rescue, a POSIXct

Details

This data frame uses the person's name as row labels. family reflects a recoding of the last names of individuals to reduce the number of factor levels. The main families in the Donner party were: Donner, Graves, Breen and Reed. The families of Murphy, Foster and Pike are grouped as 'MurFosPik', those of Fosdick and Wolfinger are coded as 'FosdWolf', and all others as 'Other'.

survived is the response variable. What kind of models should be used here?

Source

D. K. Grayson, 1990, "Donner party deaths: A demographic assessment", J. Anthropological Research, 46, 223-242.

Johnson, K. (1996). Unfortunate Emigrants: Narratives of the Donner Party. Logan, UT: Utah State University Press. Additions, and dates of death from http://user.xmission.com/~octa/DonnerParty/Roster.htm.

References

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis, (2nd ed), Duxbury.

Friendly, M. and Meyer, D. (2016). Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data. Boca Raton, FL: Chapman & Hall/CRC. http://ddar.datavis.ca.

Examples

# conditional density plots
op <- par(mfrow=c(1,2), cex.lab=1.5)
cdplot(factor(survived) ~ age, 
       subset=sex=='Male', 
       data=Donner, 
       main="Donner party: Males", 
       ylevels=2:1, 
       ylab="Survived", 
       yaxlabels=c("yes", "no"))
with(Donner, rug(jitter(age[sex=="Male"]), 
                 col="white", quiet=TRUE))

cdplot(factor(survived) ~ age, 
       subset=sex=='Female', 
       data=Donner, 
       main="Donner party: Females", 
       ylevels=2:1, 
       ylab="Survived", 
       yaxlabels=c("yes", "no"))
with(Donner, rug(jitter(age[sex=="Female"]), 
                 col="white", quiet=TRUE))
par(op)


# fit some models
(mod1 <- glm(survived ~ age + sex, data=Donner, family=binomial))
(mod2 <- glm(survived ~ age * sex, data=Donner, family=binomial))
anova(mod2, test="Chisq")

(mod3 <- glm(survived ~ poly(age,2) * sex, data=Donner, family=binomial))
anova(mod3, test="Chisq")
LRstats(glmlist(mod1, mod2, mod3))

# plot fitted probabilities from mod2 and mod3
# idea from: http://www.ling.upenn.edu/~joseff/rstudy/summer2010_ggplot2_intro.html
library(ggplot2)

# separate linear fits on age for M/F
ggplot(Donner, aes(age, survived, color = sex)) +
  geom_point(position = position_jitter(height = 0.02, width = 0)) +
  stat_smooth(method = "glm", 
              method.args = list(family = binomial), 
              formula = y ~ x,
              alpha = 0.2, 
              size=2, 
              aes(fill = sex))

# separate quadratics
ggplot(Donner, aes(age, survived, color = sex)) +
  geom_point(position = position_jitter(height = 0.02, width = 0)) +
  stat_smooth(method = "glm", 
              method.args = list(family = binomial), 
              formula = y ~ poly(x,2),
              alpha = 0.2, 
              size=2, 
              aes(fill = sex))