Example 1 - using the Titanic survivors data set
Let’s start by exploring the likelihood of surviving the Titanic disaster based on passenger economic status (class), sex, and age group.
Get and prepare data
from the datasets package.
df <- datasets::Titanic |>
as_tibble() |>
# convert counts to observations
filter(n > 0) |>
uncount(weights = n) |>
# convert categorical variables to factors.
# we specify an order for levels in Class and Survival, otherwise ordering
# in descending order of frequency
mutate(
Class = Class |>
fct(levels = c('1st', '2nd', '3rd', 'Crew')),
Sex = Sex |>
fct_infreq(),
Age = Age |>
fct_infreq(),
Survived = Survived |>
fct(levels = c('No', 'Yes'))
)
# preview the data
df |> glimpse()
#> Rows: 2,201
#> Columns: 4
#> $ Class <fct> 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3rd, 3…
#> $ Sex <fct> Male, Male, Male, Male, Male, Male, Male, Male, Male, Male, M…
#> $ Age <fct> Child, Child, Child, Child, Child, Child, Child, Child, Child…
#> $ Survived <fct> No, No, No, No, No, No, No, No, No, No, No, No, No, No, No, N…We now have a tibble of data containing four columns:
Survived- our outcome variable describing whether the passenger survivedYesor diedNo,Class- the passenger class, either1st,2nd,3rdorCrew,Sex- the gender of the passenger, eitherMaleorFemale,Age- whether the passenger was anAdultorChild.
We next conduct a logistic regression of survival (as a binary
factor: ‘yes’ and ‘no’) against the characteristics of passenger class,
sex and age group. For this we use the Generalised Linear Model function
(glm) from the stats package, specifying:
the family as ‘binomial’, and
the formula as survival being a function of
Class,SexandAge.
# conduct a logistic regression of survival against the other variables
lr <- glm(
data = df,
family = 'binomial',
formula = Survived ~ Class + Sex + Age
)
# preview the model as a tidy table
lr |>
tidy() |>
glimpse()
#> Rows: 6
#> Columns: 5
#> $ term <chr> "(Intercept)", "Class2nd", "Class3rd", "ClassCrew", "SexFema…
#> $ estimate <dbl> -0.3762229, -1.0180950, -1.7777622, -0.8576762, 2.4200603, 1…
#> $ std.error <dbl> 0.1361769, 0.1959969, 0.1715657, 0.1573387, 0.1404093, 0.244…
#> $ statistic <dbl> -2.762751, -5.194443, -10.361993, -5.451147, 17.235750, 4.35…
#> $ p.value <dbl> 5.731642e-03, 2.053331e-07, 3.691891e-25, 5.004592e-08, 1.43…Finally, we can plot the Odds Ratio of survival using the
plot_or function.
This plot makes it clear that:
Children were 2.89 times more likely to survive than Adults,
Passengers in
2nd,3rdclass as well asCrewwere all less likely to survive than those in1stclass,Women were 11.25 times more likely to survive than men.
Note on plot features
The primary components of an Odds-Ratio plot are dots, whiskers and the line of no effect.
The dot represents the point estimate for the Odds-Ratio, which indicates how much more likely the event is than the comparator event.
The width of the whiskers represents the 95% Confidence Interval, a range of values the point estimate (the dot) is likely to fall within if the study were to be repeated, with a probability of 95%.
The line of no effect is set at a value of 1. Events whose confidence intervals touch or cross this line are considered to show no difference in likelihood than the comparator event.
The size of the dots is proportional to the number of observations.
In the above, the size of the Adult square is much larger
than the Child square, because there were 20 times more
adults on the ship than children. This feature can help contextualise
the findings from OR plots.
Change base font size
To increase the size of the font you can extend the returned plot
using the theme
function from ggplot2. Here we set the base size of all
fonts in the plot to size 16.
Specify the breaks
Odds Ratio (OR) plots produced by plotor are displayed
using a log10 x-axis.
By default ten breaks are shown, however, this can be altered by
extending the scale_x_log10
function from ggplot2. Here we provide a manual list of
breaks to use:
Change the dot and whisker colours
There are three types of colours used for the dots and whiskers in the OR plot, depending on their category.
Significantrefers to dots where their results indicate a significant finding because their 95% confidence intervals do not touch or cross the value 1 - the line of no effect.Comparatorrefers to the level of a factor in the model against which the Odds Ratios are calculated.Not significantrefers to dots where their results do not indicate a significant finding because their confidence intervals touch or cross the line of no effect.
The colours for these points can be changed by extending the output
using scale_colour_manual
function from ggplot2 with a named vector specifying colour
values for the three types of colours:
plot_or(glm_model_results = lr) +
scale_colour_manual(values = c(
'Significant' = '#44bd32',
'Comparator' = '#8c7ae6',
'Not significant' = '#e84118')
)
Change the title, subtitle and add a caption
plotor uses the dependent variable as the title of the
plot by default with a subtitle indicating this it is an Odds Ratio plot
with a 95% confidence interval.
The plot can be customised with your own title, subtitle and add a
caption by extending the labs
function of ggplot2.
plot_or(glm_model_results = lr) +
labs(
title = 'Passenger survival from the Titanic disaster',
subtitle = 'Odds Ratio of survival by Class, Age and Gender',
caption = 'Data source: Dawson, Robert J. MacG. (1995), The ‘Unusual Episode’ Data Revisited. Journal of Statistics Education, 3. doi:10.1080/10691898.1995.11910499'
)
