16  Mosaic plots

Graphs in this chapter use fmggp2::theme_titanic(), modeled on Titanic (1997), using the Vallejo Titanic Colors paint set: a hull black background, a yellow hull stripe frame and title, a canvas plot area with deck planking grid lines, antifouling red, faded yellow, stone, and wood deck marks, and a Big Caslon title.


Requirements:

✅ at least two categorical variables

16.1 Description

A mosaic plot is similar to a stacked bar graph, but instead of only relying on height and color to display the relative amount for each value, mosaic plots also use width.

Mosaic plot legends should be positioned on top or bottom and justified horizontally to preserve shape and improve readability.

We can build mosaic plots using the ggmosaic package.

16.2 Set up

PACKAGES:

Install packages.

show/hide 
# pak::pak("haleyjeppson/ggmosaic")
library(ggmosaic)
library(ggplot2)
library(dplyr) # for tibble() and data manipulation

DATA:

Titanic (1997) stayed in theaters for months, and plenty of fans (especially teenagers) went back to see it again and again.

We’ll simulate 500 moviegoers in three linked steps. First, sample() decides each fan’s age_group. Next, each age group gets its own chances of seeing the movie once, twice, or three or more times (viewings). Finally, the more times a fan saw the movie, the more likely they were to buy the soundtrack (soundtrack). For each fan, runif() draws a number between 0 and 1 and compares it to the chance for that fan’s number of viewings. Setting the seed with set.seed() means you’ll get the same 500 fans every time you run the code below.

show/hide 
set.seed(1997) # same 500 fans every time the code runs
titanic_fans <- tibble(
  fan_id = 1:500, # 500 different fans, one row each
  age_group = sample(
    c("Teen", "Adult"), 500, # each fan is a teen or an adult
    replace = TRUE, # groups repeat across fans
    prob = c(0.4, 0.6) # a few more adults than teens
    )
  ) |>
  mutate(
    viewings = if_else(age_group == "Teen",
      sample(c("Once", "Twice", "3+ times"), n(), replace = TRUE,
        prob = c(0.35, 0.35, 0.30)), # teens go back to the theater more often
      sample(c("Once", "Twice", "3+ times"), n(), replace = TRUE,
        prob = c(0.70, 0.22, 0.08)) # most adults see it once
      ),
    soundtrack = if_else(
      runif(n()) < c(Once = 0.25, Twice = 0.50, `3+ times` = 0.80)[viewings], # more viewings, more likely to buy
      "Yes", "No"),
    age_group = factor(age_group, levels = c("Teen", "Adult")),
    viewings = factor(viewings, levels = c("Once", "Twice", "3+ times")), # fewest to most viewings
    soundtrack = factor(soundtrack, levels = c("No", "Yes"))
    )
glimpse(titanic_fans)
#> Rows: 500
#> Columns: 4
#> $ fan_id     <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10…
#> $ age_group  <fct> Adult, Teen, Teen, Teen, Adul…
#> $ viewings   <fct> Twice, 3+ times, 3+ times, Tw…
#> $ soundtrack <fct> Yes, No, Yes, Yes, No, Yes, N…

16.3 Distribution

A mosaic plot draws a two way table as a set of rectangles, and each rectangle’s width and height are probabilities. Because we built the dependence between age and viewings into the simulation, we know what those widths and heights should be. Below we’ll move from the fans, to a picture, to the formula.

COUNT IT:

Start with the first eight fans.

show/hide 
head(titanic_fans, 8)

All five teens in this group saw the movie more than once, while two of the three adults saw it only once. The table below counts every combination of age group and viewings, then converts the counts to proportions within each age group.

show/hide 
titanic_fans |>
  count(age_group, viewings) |>
  group_by(age_group) |>
  mutate(share = round(n / sum(n), 2)) |>
  ungroup()

Teens split almost evenly across one, two, and three or more viewings, while about two thirds of adults saw the movie once.

DRAW IT:

The mosaic plot below draws the table above. The width of each column is the share of fans in that age group (adults take up more width because there are more of them). The height of each tile is the share of that age group with each number of viewings.

The second mosaic shuffles viewings with sample(), which keeps the same counts but breaks the link between age and viewings. Without the link, the tiles line up into nearly straight rows: every age group has the same mix of viewings.

show/hide 
ggplot(data = titanic_fans) +
  ggmosaic::geom_mosaic(aes(x = product(viewings, age_group),
                            fill = viewings)) +
  scale_x_productlist("Age group") +
  scale_y_productlist("Viewings") +
  labs(title = "Simulated", fill = "Viewings") +
  theme(legend.position = "bottom", panel.grid.major = element_blank())

titanic_fans |>
  mutate(viewings = sample(viewings)) |>
  ggplot() +
  ggmosaic::geom_mosaic(aes(x = product(viewings, age_group),
                            fill = viewings)) +
  scale_x_productlist("Age group") +
  scale_y_productlist("Viewings") +
  labs(title = "Shuffled", fill = "Viewings") +
  theme(legend.position = "bottom", panel.grid.major = element_blank())

NAME IT:

Each tile’s area is a joint probability, which we can split into a width times a height:

\[ P(\text{age}, \text{viewings}) = \underbrace{P(\text{age})}_{\text{width}} \times \underbrace{P(\text{viewings} \mid \text{age})}_{\text{height}} \]

The simulation sets the widths with \(P(\text{Teen}) = 0.4\) and \(P(\text{Adult}) = 0.6\), and the heights with a different conditional distribution for each age group: \((0.35, 0.35, 0.30)\) for teens and \((0.70, 0.22, 0.08)\) for adults.

When two variables are independent, \(P(\text{viewings} \mid \text{age}) = P(\text{viewings})\), so every column has the same heights. That’s what the shuffled mosaic shows. The more the tiles in one column are out of line with the tiles in the next, the stronger the relationship. Try giving adults the same viewing probabilities as teens and the first mosaic will look like the second.

16.4 Grammar

CODE:

  • Create labels with labs()

  • Initialize the graph with ggplot() and provide data

  • Map the product() of viewings and age_group to the x axis

  • Map age_group to fill

  • geom_mosaic() names the axes after the variables, so set the axis titles with scale_x_productlist() and scale_y_productlist()

  • Remove the grid lines and move the legend to the bottom with theme(legend.position = "bottom", panel.grid.major = element_blank())

show/hide 
labs_mosaic <- labs(
      title = "Titanic",
      caption = "Simulated data",
      subtitle = "500 moviegoers in 1998",
      fill = "Age group")
ggp2_mosaic <- ggplot(data = titanic_fans) +
   ggmosaic::geom_mosaic(mapping =
          aes(x = product(viewings, age_group),
              fill = age_group)) +
    scale_x_productlist("Age group") +
    scale_y_productlist("Times seen in theaters") +
    theme(legend.position = "bottom",
          panel.grid.major = element_blank())
ggp2_mosaic +
    labs_mosaic

GRAPH:

16.4.1 Details

We’ve re-written the labels for the mosaic plot (ggp2_mosaic) to illustrate what’s happening in the aes() of geom_mosaic().

It’s a good idea to adjust the fig-height and fig-width of your graph

The table below displays the counts for each combined response. As we can see, the counts are represented by height and width in the graph.

viewings Teen Adult
3+ times 62 26
Twice 60 85
Once 62 205

16.5 More info

I recommend reading the ggmosaic vignette, particularly the sections on ordering and conditioning.

16.5.1 Two variables

viewings No Yes
3+ times 15 73
Twice 75 70
Once 202 65

Below is another example of a two-variable mosaic plot, mapping the product() variables as viewings and soundtrack, and the fill variable as soundtrack.

Once again we can see the counts for each category in the cross-tabulation:

show/hide 
# build 2-variable mosaic plot
labs_mosaic_2var <- labs(
  title = "Titanic",
  caption = "Simulated data",
  subtitle = "2-Variable plot",
  fill = "soundtrack")

ggp2_mosaic_2var <- ggplot(data = titanic_fans) +
  geom_mosaic(aes(
    x = product(viewings, soundtrack),
    fill = soundtrack)) +
  scale_x_productlist("Bought the soundtrack?") +
  scale_y_productlist("Times seen in theaters") +
  theme(legend.position = "bottom",
        panel.grid.major = element_blank())

ggp2_mosaic_2var +
    labs_mosaic_2var

For conditional variables, we map the product() variable as viewings and the fill variable as viewings, but include a conds variable (as product(soundtrack)).

show/hide 
# build conditional mosaic plot
labs_mosaic_cond <- labs(
  title = "Titanic",
  caption = "Simulated data",
  subtitle = "Conditional plot",
  fill = "viewings")
ggp2_mosaic_cond <- ggplot(data = titanic_fans) +
  geom_mosaic(aes(
    x = product(viewings), # product variable
    fill = viewings,
    conds = product(soundtrack))) + # conditional variable
  scale_x_productlist("Bought the soundtrack?") +
  scale_y_productlist("Times seen in theaters") +
  theme(legend.position = "bottom",
        panel.grid.major = element_blank())

ggp2_mosaic_cond +
    labs_mosaic_cond

16.5.2 Facets

Another option for including a conditioning variable is including facets. In the example below we use soundtrack in both x and fill (remember to wrap soundtrack in product()).

The divider argument lets us control how the tiles are split (vertically and horizontally). Below are the two vertical orientation options for the divider argument.

The two horizontal orientation options make the axis text harder to read, so these need to be manipulated manually.