🏵 Visualizing Categorical Data

Feb 10, 2023

Introduction

To recall, a categorical variable is one for which the possible measured or assigned values consist of a discrete set of categories, which may be ordered or unordered. Some typical examples are:

Gender, with categories “Male,” “Female.”
Marital status, with categories “Never married,” “Married,” “Separated,” “Divorced,” “Widowed.”
Fielding position (in ~~baseball~~ cricket), with categories “Slips,”Cover “,”Mid-off “Deep Fine Leg”, “Close-in”, “Deep”…
Side effects (in a pharmacological study), with categories “None,” “Skin rash,” “Sleep disorder,” “Anxiety,” . . ..
Political attitude, with categories “Left,” “Center,” “Right.”
Party preference (in India), with categories “BJP” “Congress,” “AAP,” “TMC.”…
Treatment outcome, with categories “no improvement,” “some improvement,” or “marked improvement.”
Age, with categories “0–9,” “10–19,” “20–29,” “30–39,” . . . .
Number of children, with categories 0, 1, 2, . . . .

As these examples suggest, categorical variables differ in the number of categories: we often distinguish binary variables (or dichotomous variables) such as Gender from those with more than two categories (called polytomous variables).

Categorical Data

From the {vcd package} vignette:

The first thing you need to know is that categorical data can be represented in three different forms in R, and it is sometimes necessary to convert from one form to another, for carrying out statistical tests, fitting models or visualizing the results.

Case Data
Frequency Data
Cross-Tabular Count Data

Let us first see examples of each.

Case Form

Containing individual observations with one or more categorical factors, used as classifying variables. The total number of observations is nrow(X), and the number of variables is ncol(X).

names(Arthritis)

## [1] "ID"        "Treatment" "Sex"       "Age"       "Improved"

class(Arthritis)

## [1] "data.frame"

glimpse(Arthritis)

## Rows: 84
## Columns: 5
## $ ID        <int> 57, 46, 77, 17, 36, 23, 75, 39, 33, 55, 30, 5, 63, 83, 66, 4…
## $ Treatment <fct> Treated, Treated, Treated, Treated, Treated, Treated, Treate…
## $ Sex       <fct> Male, Male, Male, Male, Male, Male, Male, Male, Male, Male, …
## $ Age       <int> 27, 29, 30, 32, 46, 58, 59, 59, 63, 63, 64, 64, 69, 70, 23, …
## $ Improved  <ord> Some, None, None, Marked, Marked, Marked, None, Marked, None…

From Michael Friendly Discrete Data Analysis and Visualization :

In many circumstances, data is recorded on each individual or experimental unit. Data in this form is called case data, or data in case form.

Table 1: Arthritis Treatments and Effects (first 6 entries)
ID	Treatment	Sex	Age	Improved
57	Treated	Male	27	Some
46	Treated	Male	29	None
77	Treated	Male	30	None
17	Treated	Male	32	Marked
36	Treated	Male	46	Marked
23	Treated	Male	58	Marked

The Arthritis data set has three factors and two integer* variables. One of the three factors Improved is an ordered factor.

ID
Treatment: a factor; Placebo or Treated
Sex: a factor, M / F
Age: integer
Improved: Ordinal factor; None < Some < Marked

Frequency Data

Data in frequency form has already been tabulated, by counting over the (combinations of ) categories of the table variables. When the data are in case form, we can always trace any observation back to its individual identifier or data record, since each row is a unique observation or case; the reverse is rarely possible.

Frequency Data is usually a data frame, with columns of categorical variables and at least one column containing frequency or count information.

str(GSS)

## 'data.frame':	6 obs. of  3 variables:
##  $ sex  : Factor w/ 2 levels "female","male": 1 2 1 2 1 2
##  $ party: Factor w/ 3 levels "dem","indep",..: 1 1 2 2 3 3
##  $ count: num  279 165 73 47 225 191

GSS %>% 
  kbl(caption = "General Social Survey",centering = TRUE) %>%
  kable_classic_2(html_font = "Cambria", full_width = F,)

Table 2: General Social Survey
sex	party	count
female	dem	279
male	dem	165
female	indep	73
male	indep	47
female	rep	225
male	rep	191

Respondents in the GSS survey were classified by sex and party identification.

Table form

Table Form Data can be a matrix, array or table object, whose elements are the frequencies in an n-way table. The variable names (factors) and their levels are given by dimnames(X).

HairEyeColor
class(HairEyeColor)

## , , Sex = Male
## 
##        Eye
## Hair    Brown Blue Hazel Green
##   Black    32   11    10     3
##   Brown    53   50    25    15
##   Red      10   10     7     7
##   Blond     3   30     5     8
## 
## , , Sex = Female
## 
##        Eye
## Hair    Brown Blue Hazel Green
##   Black    36    9     5     2
##   Brown    66   34    29    14
##   Red      16    7     7     7
##   Blond     4   64     5     8
## 
## [1] "table"

HairEyeColor is a “two-way” table, consisting of two tables, one for Sex = Female and the other for Sex = Male. The total number of observations is sum(X). The number of dimensions of the table is length(dimnames(X)), and the table sizes are given by sapply(dimnames(X), length). The data looks like a n-dimensional cube and needs n-way tables to represent.

sum(HairEyeColor)
dimnames(HairEyeColor)
sapply(dimnames(HairEyeColor), length)

## [1] 592
## $Hair
## [1] "Black" "Brown" "Red"   "Blond"
## 
## $Eye
## [1] "Brown" "Blue"  "Hazel" "Green"
## 
## $Sex
## [1] "Male"   "Female"
## 
## Hair  Eye  Sex 
##    4    4    2

We may need to convert the (multiple) tables into a data frame:

## Convert the two tables into a data frame
HairEyeColor %>% 
  as_tibble() %>% # Convert
  head() %>% # Take first few rows to show
  kbl(caption = "Hair Eye and Color (First 6 Entries)") %>% 
  kable_classic_2(html_font = "Cambria", full_width = F)

Table 3: Hair Eye and Color (First 6 Entries)
Hair	Eye	Sex	n
Black	Brown	Male	32
Brown	Brown	Male	53
Red	Brown	Male	10
Blond	Brown	Male	3
Black	Blue	Male	11
Brown	Blue	Male	50

What sort of Plots can we make for Categorical Data?

We have already seen bar plots, which allow us to plot counts of categorical data. However, if there are a large number* of categorical variables or if the categorical variables have many levels, the bar plot is not adequate.

From Michael Friendly:

The familiar techniques for displaying raw data are often disappointing when applied to categorical data. The simple scatterplot, for example, widely used to show the relation between quantitative response and predictors, when applied to discrete variables, gives a display of the category combinations, with all identical values overplotted, and no representation of their frequency.

Instead, frequencies of categorical variables are often best represented graphically using areas rather than as position along a scale. Using the visual attribute:

\[\pmb{area \sim frequency}\]

allows creating novel graphical displays of frequency data for special circumstances.

Let us not look at some sample plots that embody this “area-frequency* principle.

Mosaic Plots

A mosaic plot is basically an area-proportional visualization of (typically observed) frequencies, consisting of tiles (corresponding to the cells) created by vertically and horizontally splitting a rectangle recursively. Thus, the area of each tile is proportional to the corresponding cell entry given the dimensions of previous splits.

The vcd::mosaic() function needs the data in contingency table form. We will use vcd::structable() function to construct one:

art <- vcd::structable(~ Treatment + Improved, data = Arthritis)
art

##           Improved None Some Marked
## Treatment                          
## Placebo              29    7      7
## Treated              13    7     21

vcd::mosaic(art, gp = shading_max)

### Or
### vcd::mosaic(structable(~ Treatment + Improved, data = Arthritis), gp = shading_max, split_vertical = TRUE)

Balloon Plots

housetasks <- read.delim(
  system.file("demo-data/housetasks.txt", package = "ggpubr"),
  row.names = 1
  )
head(housetasks, 4)

##            Wife Alternating Husband Jointly
## Laundry     156          14       2       4
## Main_meal   124          20       5       4
## Dinner       77          11       7      13
## Breakfeast   82          36      15       7

ggballoonplot(housetasks, fill = "value")+
  scale_fill_viridis_c(option = "C")

df <- as.data.frame(HairEyeColor)
ggballoonplot(df, x = "Hair", y = "Eye", size = "Freq",
              fill = "Freq", facet.by = "Sex",
              ggtheme = theme_bw()) +
  scale_fill_viridis_c(option = "C")

Plots for Likert Data

In many business situations, we perform surveys to get Likert scale data, where several respondents rate a product or a service on a scale of Very much like, somewhat like, neutral, Dislike and Very much dislike. Such data may look for example as follows:

data(efc)
head(efc, 20)

##    c12hour e15relat e16sex e17age e42dep c82cop1 c83cop2 c84cop3 c85cop4
## 1       16        2      2     83      3       3       2       2       2
## 2      148        2      2     88      3       3       3       3       3
## 3       70        1      2     82      3       2       2       1       4
## 4      168        1      2     67      4       4       1       3       1
## 5      168        2      2     84      4       3       2       1       2
## 6       16        2      2     85      4       2       2       3       3
## 7      161        1      1     74      4       4       2       4       1
## 8      110        4      2     87      4       3       2       2       1
## 9       28        2      2     79      4       3       2       3       2
## 10      40        2      2     83      4       3       2       1       2
## 11     100        1      1     68      4       3       4       4       4
## 12      25        8      2     97      3       3       3       3       1
## 13      25        2      2     80      4       3       2       2       2
## 14      24        1      2     75      3       3       2       4       4
## 15      56        2      2     82      3       2       3       3       3
## 16      20        2      2     89      3       4       2       1       3
## 17      25        1      1     80      1       3       2       1       2
## 18     126        1      1     72      3       4       2       1       2
## 19     168        2      1     94      3       3       2       1       2
## 20     118        1      1     79      4       3       2       4       2
##    c86cop5 c87cop6 c88cop7 c89cop8 c90cop9 c160age c161sex c172code c175empl
## 1        1       1       2       3       3      56       2        2        1
## 2        4       1       3       2       2      54       2        2        1
## 3        1       1       1       4       3      80       1        1        0
## 4        1       1       1       2       4      69       1        2        0
## 5        2       2       1       4       4      47       2        2        0
## 6        3       2       2       1       1      56       1        2        1
## 7        1       2       4       1       4      61       2        2        0
## 8        1       1       2       3       3      67       2        2        0
## 9        2       1       3       1       3      59       2       NA        0
## 10       1       1       1       1       3      49       2        2        0
## 11       4       4       4       1       1      66       2        2        0
## 12       3       1       4       3       1      47       2        2        1
## 13       2       1       2       4       4      58       2        3        0
## 14       1       1       2       4       4      75       1        1        0
## 15       2       2       1       1       1      49       2        3        1
## 16       3       1       2       1       3      56       2        2        0
## 17       1       1       2       4       4      75       2        2        0
## 18       1       1       2       3       3      70       2        2        0
## 19       2       1       3       1       4      52       1        3        1
## 20       1       3       3       2       2      48       2        3        1
##    barthtot neg_c_7 pos_v_4 quol_5 resttotn tot_sc_e n4pstu nur_pst
## 1        75      12      12     14        0        4      0      NA
## 2        75      20      11     10        4        0      0      NA
## 3        35      11      13      7        0        1      2       2
## 4         0      10      15     12        2        0      3       3
## 5        25      12      15     19        2        1      2       2
## 6        60      19       9      8        1        3      2       2
## 7         5      15      13     20        0        0      3       3
## 8        35      11      14     20        0        1      1       1
## 9        15      15      13      8        0        2      3       3
## 10        0      10      13     15        1        1      3       3
## 11       25      28       9      1        1        1      3       3
## 12       85      18       8     19        1        1      1       1
## 13       15      13      14     12        0        3      3       3
## 14       70      18      14      8        0        0      1       1
## 15       NA      16       9      8        3        3      0      NA
## 16        0      13      14      6        0        2      0      NA
## 17       95      11      15     16        0        2      0      NA
## 18       55      11      13     14        0        0      2       2
## 19       55      13      13     15        3        1      1       1
## 20       45      17      12     10        0        7      2       2

efc is a German data set from a European study on family care of older people. Following a common protocol, data were collected from national samples of approximately 1,000 family carers (i.e. caregivers) per country and clustered into comparable subgroups to facilitate cross-national analysis. One of the research questions in this EUROFAM study was:

What are the main difficulties carers experience accessing the services used? What prevents carers from accessing unused supports that they need? What causes them to stop using still-needed services?

We will select the variables from the efc data set that related to coping (on part of care-givers) and plot their responses after inspecting them:

efc %>% select(dplyr::contains("cop")) %>% str()

## 'data.frame':	908 obs. of  9 variables:
##  $ c82cop1: num  3 3 2 4 3 2 4 3 3 3 ...
##   ..- attr(*, "label")= chr "do you feel you cope well as caregiver?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "never" "sometimes" "often" "always"
##  $ c83cop2: num  2 3 2 1 2 2 2 2 2 2 ...
##   ..- attr(*, "label")= chr "do you find caregiving too demanding?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c84cop3: num  2 3 1 3 1 3 4 2 3 1 ...
##   ..- attr(*, "label")= chr "does caregiving cause difficulties in your relationship with your friends?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c85cop4: num  2 3 4 1 2 3 1 1 2 2 ...
##   ..- attr(*, "label")= chr "does caregiving have negative effect on your physical health?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c86cop5: num  1 4 1 1 2 3 1 1 2 1 ...
##   ..- attr(*, "label")= chr "does caregiving cause difficulties in your relationship with your family?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c87cop6: num  1 1 1 1 2 2 2 1 1 1 ...
##   ..- attr(*, "label")= chr "does caregiving cause financial difficulties?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c88cop7: num  2 3 1 1 1 2 4 2 3 1 ...
##   ..- attr(*, "label")= chr "do you feel trapped in your role as caregiver?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "Never" "Sometimes" "Often" "Always"
##  $ c89cop8: num  3 2 4 2 4 1 1 3 1 1 ...
##   ..- attr(*, "label")= chr "do you feel supported by friends/neighbours?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "never" "sometimes" "often" "always"
##  $ c90cop9: num  3 2 3 4 4 1 4 3 3 3 ...
##   ..- attr(*, "label")= chr "do you feel caregiving worthwhile?"
##   ..- attr(*, "labels")= Named num [1:4] 1 2 3 4
##   .. ..- attr(*, "names")= chr [1:4] "never" "sometimes" "often" "always"

The coping related variables have responses on the Likert Scale (1,2,3,4) which correspong to (never, sometimes, often, always), and each variable also has a label defining each variable. We can plot this data using the plot_likert function from package sjPlot:

efc %>% select(dplyr::contains("cop")) %>% 
  sjPlot::plot_likert(title = "Caregiver Survey from EUROFAM")

So there we are with Categorical data ! There are a few other plots with this type of data, which are useful in very specialized circumstances. One example of this is the agreement plot which captures the agreement between two (sets) of evaluators, on ratings given on a shared ordinal scale to a set of items. An example from the field of medical diagnosis is the opinions of two specialists on a common set of patients.

We can also do what is called “Correspondence Analysis” with Categorical Data, but that topic must remain for an advanced course.

Conclusion

How are these bar plots different from histograms? Why don’t “regular” plots simply work for Categorical data? Discuss!

References

Using the strcplot command from vcd, https://cran.r-project.org/web/packages/vcd/vignettes/strucplot.pdf
Creating Frequency Tables with vcd, https://cran.r-project.org/web/packages/vcdExtra/vignettes/A_creating.html
Creating mosaic plots with vcd, https://cran.r-project.org/web/packages/vcdExtra/vignettes/D_mosaics.html