The code outlined below demonstrates a few simple ways of visualising the relationship between two ordinal variables. Ordinal variables are ordered factors in R - a variable with a number of levels arranged in a hierarchy. For the purposes of this, we will be looking at a 5-level measure of Deprivation and a 5-level measure of Self-Rated Health.

You could present this information in a series of tables, or as a contingency table which shows the frequency distribution of the two variables in a matrix format.

Instead, it might be easier to express (or quickly assess) the relationship between the variables using one/all of these four plots:

  1. Heatmap
  2. Mosaic Plot
  3. Proportional Stacked Bar Chart
  4. River Plot

Getting Started

Packages

Before we start creating plots, we need to install and load the following packages. We’re mostly using ggplot2, but also some add-ons. You should use install.packages("pkg") before loading them from the library.

library(tidyverse)
library(ggmosaic)
library(viridis)
library(ggalluvial)

Data

We also need to create a dummy dataset to make the visualisation.

I’m creating a tibble with the following variables:

  • ID: to identify individuals
  • group: a subset of the population
  • health: 5-levels, ordered from 1 = Very Good to 5 = Very Poor
  • deprivation: 5-levels, ordered from 1 = Least Deprived to 5 = Most Deprived

Note that I’m also specifying the distribution of the levels so that they don’t come out as equally distributed (and result in a pretty boring visualisation).

mockup <- as_tibble(
  list(
        ID = c(1:5000),
        group = as.factor(sample(0:1, 5000, prob = c(0.7, 0.3), replace = TRUE)),
        health = as.factor(sample(1:5,
                             5000, prob = c(0.25, 0.21, 0.10, 0.05, 0.03), replace = TRUE)), 
        deprivation = as.factor(sample(1:5,
                                   5000, prob = c(0.22, 0.17, 0.14, 0.14, 0.10), replace = TRUE))
        )
      )
head(mockup)
## # A tibble: 6 x 4
##      ID group health deprivation
##   <int> <fct> <fct>  <fct>      
## 1     1 0     2      3          
## 2     2 0     2      1          
## 3     3 0     1      1          
## 4     4 0     3      3          
## 5     5 0     3      5          
## 6     6 1     2      1

Plots

Option 1: Heatmap

A heatmap shows the magnitude or frequency of an observation as colour in 2D. It works essentially like a contingency table but rather than showing the raw numbers, you can see the colour variation.

For comparison here’s a very simple contingency table.

my_table <- mockup %>% 
  group_by(deprivation, health) %>% 
  tally() %>% 
  spread(key = health, value = n)
print.data.frame(my_table)
##   deprivation   1   2   3   4  5
## 1           1 562 456 243 111 76
## 2           2 452 343 150  96 45
## 3           3 391 289 124  80 60
## 4           4 352 298 121  70 45
## 5           5 270 190  95  49 32

And here’s how we build the heatmap plot. I’ve re-oriented the x axis label and reversed the order displayed for the y axis so that it’s equivalent to the contingency table output. Which do you think is easier to understand?

ggplot(mockup, aes(deprivation, health)) + 
  scale_fill_viridis() +
  geom_bin2d() +
  scale_x_discrete(name = "Deprivation Quintile",
                   position = "top") +
  scale_y_discrete(name = "Self-Rated Health",
                   limits = rev(levels(mockup$health))) +
  labs(title = "Self-Rated Health by UKIMD Quintile",
       subtitle = "Deprivation: 1 = Least Deprived | Health: 1 = Very Good",
       caption = "Plot by @WillBall12") +
  theme_minimal() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank())

Option 2: Mosaic Plot

A mosaic plot is very similar to a heatmap, except that the frequency of an observation (e.g. response is Deprivation group 1 & Health group 1) is proportional to the area of a tile, rather than by colour. Colour in this instance distinguishes the self-rated health response.

ggplot(data = mockup) +
  geom_mosaic(aes(x = product(health, deprivation), fill = health),
              na.rm=TRUE) + 
  labs(x = "Deprivation Quintile", 
       y = "Proportion", 
       title="Self-Rated Health by Deprivation Quintile",
       subtitle = "Left - Right = (1) Least Deprived - (5) Most Deprived",
       caption = "Plot by @WillBall12") +
  scale_fill_manual(values=c("#440145FF", "#404788FF", "#238A8DFF", "#55C667FF", "#FDE725FF"), 
                    name="Self-Rated Health",
                    breaks=c("1", "2", "3", "4", "5"),
                    labels=c("1 - Very Good", "2", "3", "4", "5 - Very Poor")) +
  theme_minimal() +
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank())

Option 3: Proportional Stacked Bar Chart

This might be a more familiar and common visualisation but it does a nice job of quickly presenting how levels of a category are distributed. I think it’s preferable to providing a table of percentages.

ggplot(mockup,
       aes(y = reorder(deprivation, desc(deprivation)))) +
  geom_bar(aes(fill = health),
           position = position_fill(reverse = TRUE)) +
  scale_fill_manual(values=c("#440145FF", "#404788FF", "#238A8DFF", "#55C667FF", "#FDE725FF"), 
                    name="Self-Rated Health",
                    breaks=c("1", "2", "3", "4", "5"),
                    labels=c("Very Good", "Good", "Fair", "Poor", "Very Poor")) +
  labs(title = "Proportion of Self-Rated Health Response by Deprivation Quintile",
       subtitle = "Deprivation: 1 = Least Deprived - 5 = Most Deprived",
       x = "Proportion",
       y = "Deprivation Quintile",
       caption = "Plot by @WillBall12") +
  theme_minimal() +
  theme(legend.position = "bottom",
        panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank())

This plot is also quite well suited to comparing these distributions on a subset. Remember the group variable? You can create the plot below by adding + facet_grid(group~.) to the end of the code.

Option 4: River/Alluvial/Sankey Plot

River plots are normally used to show ‘flow’ through a process but it’s possible to adapt them to to show how two categorical variables relate to each other.

Before we can produce the plot, it’s necessary to create a frequency table of all the variables of interest. Below you’ll see that each row is now a unique combination of the levels.

For instance we can see how many people who are in the ‘0’ group subset, with ‘Very Good’ health, living in the least deprived areas.

mockup_freq <- mockup %>%
  dplyr::count(health, deprivation) %>%
  mutate(proptot = prop.table(n))
head(mockup_freq)
## # A tibble: 6 x 4
##   health deprivation     n proptot
##   <fct>  <fct>       <int>   <dbl>
## 1 1      1             562  0.112 
## 2 1      2             452  0.0904
## 3 1      3             391  0.0782
## 4 1      4             352  0.0704
## 5 1      5             270  0.054 
## 6 2      1             456  0.0912

Here’s how we make the riverplot itself. It uses the geom_alluvium() and geom_stratum() function which is an extension to ggplot2 from the ggalluvial package.

ggplot(as.data.frame(mockup_freq),
       aes(y = proptot, axis1 = deprivation, 
           axis2 = health)) +
  geom_alluvium(aes(fill = deprivation), 
                width = 1/12) +
  geom_stratum(width = 1/12, 
               fill = "black", 
               colour = "grey") +
  geom_label(stat = "stratum",
             infer.label = TRUE) +
  scale_x_discrete(limits = c("deprivation", "health"),
                   expand = c(.05, .05),
                   labels = c("Deprivation\nQuintile", "Self-Rated\nHealth")) +
  ggtitle("'Flow' of Self-Rated Health from Deprivation Quintile") +
  scale_fill_manual(values=c("#440145FF", "#404788FF", "#238A8DFF", "#55C667FF", "#FDE725FF"), 
                    name="Deprivation Quintile",
                    breaks=c("1", "2", "3", "4", "5"),
                    labels=c("1 - Least Deprived", "2", "3", "4", "5 - Most Deprived")) +
  theme_minimal() +
  theme(legend.position = "right",
        panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank()) +
  labs(y = "Proportion of total",
       subtitle = "Deprivation Quintile (1 = Least Deprived) | Self-Rated Health (1 = Very Good)",
       caption = "Plot by @WillBall12")

Further Reading

That’s a quick introduction to just 4 ways that you could present this type of information. I’m sure there are many others and quite possibly some of them will be simpler and/or neater than what I have come up with.

ggplot2

For more information about ggplot2 in general you can’t go wrong with the ‘Data Visualisation’ and ‘Graphics for Communication’ sections from R for Data Science

ggalluvial

The code for my alluvial/riverplot was adapted from this tutorial produced by Jason Corey Brunson