4 Categorical data

Code

# load libraries
library(tidyverse)
library(kableExtra)
library(faraway)
library(scales)

# add obesity and diabetes status to diabetes faraway data
inch2m <- 2.54/100
pound2kg <- 0.45
data_diabetes <- diabetes %>%
  mutate(height  = height * inch2m, height = round(height, 2)) %>% 
  mutate(waist = waist * inch2m) %>%  
  mutate(weight = weight * pound2kg, weight = round(weight, 2)) %>%
  mutate(BMI = weight / height^2, BMI = round(BMI, 2)) %>% 
  mutate(obese= cut(BMI, breaks = c(0, 29.9, 100), labels = c("No", "Yes"))) %>% 
  mutate(diabetic = ifelse(glyhb > 7, "Yes", "No"), diabetic = factor(diabetic, levels = c("No", "Yes"))) %>%
  na.omit()

Categorical data can be summarized by counting the number of observations of each category and summarizing in a frequency table or graphically in a bar chart. Alternatively we can calculate the proportions or percentages of each category.

flowchart TD
  A(Categorical data) --> B(Numerical summary)
  B(Numerical summary) --> D(Table of frequencies <br/> Proportions <br/> Percentages <br/> ...)
  A(Categorical data) --> C(Graphical summary)
  C(Graphical summary) --> E(Bar charts <br/> Pie chart <br/> Mosaic plot <br/> ...)

Figure 4.1: Example of numerical summaries and graphical visualization applicable to categorical data

Given the diabetes data set we have some categorical data type such as obesity or diabetes status (yes/no), gender (male/female) and location (Buckingham/Louisa) to name few. Taking obesity status as an example, we can:

ask how many study participants we have in each category? I.e. how many suffer from obesity (\(BMI \ge 30\)) and how many have \(BMI < 30\)?
visualize these descriptive statistics as counts or percentages in a bar chart or a pie chart.

4.1 Frequency table

Let’s focus on 130 study participants for which no missing data was observed, i.e. complete case analysis. An example frequency table summarizing study participants by their BMI status is shown below.

Code

# count frequencies, percentages and proportions
table.summary <- data_diabetes %>%
  group_by(obese) %>%
  tally() %>%
  mutate("percent (%)" = n/sum(n)*100) %>%
  mutate("proportion" = n/sum(n))

# show table
kable(table.summary, digits = 1) %>% 
  kable_styling(full_width = TRUE)

obese	n	percent (%)	proportion
No	72	55.4	0.6
Yes	58	44.6	0.4

Table 4.1: Frequency table showing the number, percentages and proportions of study participants with BMI \(\ge\) 30 and with BMI < 30

4.2 Bar chart & pie chart

To visualize the frequencies (or percentages or proportions) we can use bar chart or a pie chart.

Code

# set a custom ggplot theme
font.size <- 30
my.ggtheme <- theme(axis.title = element_text(size = font.size), 
        axis.text = element_text(size = font.size), 
        legend.text = element_text(size = font.size), 
        legend.title = element_blank(), 
        axis.title.y = element_text(angle = 0))

# use ggplot to draw a bar chart
data_diabetes %>%
  ggplot(aes(x = obese, fill = obese)) +
  geom_bar(width = 0.5) +
  scale_fill_brewer(palette = "Paired") + 
  theme_bw() +
  my.ggtheme

# draw pie chart
data_diabetes %>%
  ggplot(aes(x="", y = obese, fill = obese)) +
  geom_bar(width = 1, stat = "identity") +
  theme_bw() +
  coord_polar("y", start=0) +
  scale_fill_brewer(palette="Paired") +
  xlab("") +
  ylab("") + 
  my.ggtheme

4.3 Summary table: 2 categorical variables

When we are interested in how one categorical variable is related to another categorical variable, we can use a summary table. For instance, we can look at the relationship between obesity (yes/no) and diabetes (yes/no).

Code

data_diabetes %>%
  group_by(obese) %>%
  dplyr::summarize(Total=n(), `Diabetic` = sum(gender=="male")) %>% 
  mutate(`Diabetic (%)` = round(`Diabetic` * 100 / Total, 2)) %>%
  kable() %>%
  kable_styling(full_width = TRUE)

obese	Total	Diabetic	Diabetic (%)
No	72	39	54.17
Yes	58	18	31.03

Table 4.2: Summary table showing relation between obesity and diabesis status among study participants

4.4 Contingency table: 2 categorical variables

Shows the multivariate frequency distribution of variables

Code

# use table() function to create contingency table
table.con <- table(data_diabetes$obese, data_diabetes$diabetic)
table.con <- addmargins(table.con)
rownames(table.con) <- c("Non-obese", "Obese", "Sum")
colnames(table.con) <- c("Non-diabetic", "Diabetic", "Sum")

table.con %>%
  kable(row.names = TRUE) %>%
  kable_styling(full_width = TRUE) %>%
  column_spec(4, bold = T) %>%
  row_spec(3, bold = T)

	Non-diabetic	Diabetic	Sum
Non-obese	57	15	72
Obese	43	15	58
Sum	100	30	130

Table 4.3: Contigency table (or cross table) showing multivariate frequency of obesity and diabesis status among study participants

4.5 Bar chart: 2 categorical variables

Bar charts can be used to visualize two and more categorical variables, e.g. by using stacking, side-by-side bars or colors.

Code

data_diabetes %>% 
  ggplot(aes(x=obese, fill=diabetic)) + 
  geom_bar() + 
  theme_bw() + 
  xlab("obese") + 
  ylab("count (diabetic)") +
  scale_fill_brewer(palette = "Paired") + 
  my.ggtheme
  
# another way of using bar charts: side by side bars
data_diabetes %>% 
  ggplot(aes(x=obese, fill=diabetic)) + 
  geom_bar(position = "dodge") + 
  theme_bw() + 
  xlab("obese") + 
  ylab("count (diabetic)") +
  scale_fill_brewer(palette = "Paired") + 
  my.ggtheme

# another way of using bar charts: showing fractions instead of counts
data_diabetes %>% 
  ggplot(aes(x=obese, fill=diabetic)) + 
  geom_bar(position = "fill") + 
  theme_bw() + 
  xlab("obese") + 
  ylab("fraction (diabetic)") +
  scale_fill_brewer(palette = "Paired") + 
  my.ggtheme

Code

# calculate number of diabetic participants 
# by among participants with BMI >=30 and stratified by gender
data_plot <- data_diabetes %>%
  select(gender, obese, diabetic) %>%
  group_by(obese, diabetic, gender) %>%
  tally() %>%
  filter(diabetic == "Yes") #%>%
  #print()

# bar plot (stacked)
data_plot %>% 
  ggplot(aes(x=obese, y=n, fill = gender)) + 
  geom_bar(stat = "identity") + 
  theme_bw() + 
  xlab("obese") +
  ylab("count (diabetic)") + 
  scale_fill_brewer(palette = "Set2") + 
  my.ggtheme

# bar plot (side-by-side)
data_plot %>% 
  ggplot(aes(x=obese, y=n, fill = gender)) + 
  geom_bar(stat = "identity", position = "dodge") + 
  theme_bw() + 
  xlab("obese") +
  ylab("count (diabetic)") + 
  scale_fill_brewer(palette = "Set2") + 
  scale_y_continuous(breaks = pretty_breaks()) + 
  my.ggtheme

4.6 Mosaic plot

Mosaic plots display contingency tables

Code

library(ggmosaic)
 ggplot(data = data_diabetes) +
  geom_mosaic(aes(x = product(obese), fill=diabetic)) + 
  theme_bw() + 
  scale_fill_brewer(palette = "Paired")

Figure 4.5: Mosaic plot showing contigency table of obesity and diabetic status among study participants

Code

 ggplot(data = data_diabetes) +
  geom_mosaic(aes(x = product(obese, gender), fill=diabetic)) + 
  theme_bw() + 
   scale_fill_brewer(palette = "Set2")

Figure 4.6: Mosaic plot showing contigency table of obesity and diabetic status among study participants stratified by gender