Continuous Data (2 of 2)

Aug 8, 2023

Exploring Univariate Continuous Data using `ggplot2` and `ggpubr`

THIS CHAPTER demonstrates the use of the popular ggplot2 and ggpubr packages to further explore univariate, continuous data.

ggplot2: In the ggplot2 package for instance, the function geom_boxplot() produces box plots, geom_violin() creates violin plots, and geom_histogram() and geom_density() generate histograms and density plots, respectively. The related ggbeeswarm package can be used for creating bee swarm plots.
ggpubr: The ggpubr package in R augments ggplot2 by offering tools for creating publication-ready plots. It enables simplified plotting with easy-to-use functions like gghistogram(), ggdensity(), ggboxplot(), ggviolin, and makes it easy to merge multiple plots with ggarrange(), and provides specialized themes for a polished look. Essentially, ggpubr merges ggplot2’s extensive customization with the ease of creating visually appealing and informative plots.
Data: Suppose we run the following code to prepare the mtcars data for subsequent analysis and save it in a tibble called tb.

# Load the required libraries, suppressing annoying startup messages
library(tibble) 
suppressPackageStartupMessages(library(dplyr))
# Read the mtcars dataset into a tibble called tb
data(mtcars)
tb <- as_tibble(mtcars)
# Convert relevant columns into factor variables
tb$cyl <- as.factor(tb$cyl) # cyl = {4,6,8}, number of cylinders
tb$am <- as.factor(tb$am) # am = {0,1}, 0:automatic, 1: manual transmission
tb$vs <- as.factor(tb$vs) # vs = {0,1}, v-shaped engine, 0:no, 1:yes
tb$gear <- as.factor(tb$gear) # gear = {3,4,5}, number of gears
# Directly access the data columns of tb, without tb$mpg
attach(tb)

We load the ggplot2, dplyr and ggthemes packages. The package ggthemes allows us to use a variety of themes.

library(dplyr)
library(ggthemes)
suppressPackageStartupMessages(library(ggplot2))

Let’s take a closer look at some of the most effective ways of Visualizing Univariate Continuous Data using ggplot2 and related packages, including

Bee Swarm plots using ggbeeswarm
Histograms using ggplot2 and ggpubr
PDF and CDF Density plots using ggplot2 and ggpubr
Box plots using ggplot2 and ggpubr
Violin plots using ggplot2 and ggpubr
Quantile-Quantile (Q-Q) Plots using ggplot2

Note that it is inconvenient to create Stem-and-Leaf plots using ggplot2.

Bee Swarm plot using `ggbeeswarm`

The bee swarm plot is an alternative to the box plot, where each point is plotted in a manner that avoids overlap.
We use the ggbeeswarm package on the mpg column of the tb tibble.

library(ggplot2)
library(ggbeeswarm) # Necessary for geom_beeswarm() 
ggplot(tb, 
       aes(x = 1, 
           y = mpg)) +
  geom_beeswarm() +
  labs(title = "Bee Swarm plot of Miles Per Gallon (mpg)",
       y = "Miles Per Gallon (mpg)") +
  theme_minimal()

Discussion:

Initially, we declare our dataset and the aesthetic mappings, defining how variables in the data are visually represented. For the bee swarm plot, we only need a y aesthetic, which is mpg. We set the x aesthetic to 1 as a placeholder, because bee swarm plots require an x aesthetic, but we only have one variable.
Following that, we append a bee swarm plot using the geom_beeswarm() function.
We use the labs() function to label the plot.
We then adopt a minimalist theme by using theme_minimal() to give our plot a sleek and simple look.

Histogram using `ggplot2`

The following code creates a histogram using the ggplot2 package. Here, we pre-specify the bin width and the resulting number of bins in the histogram depend on the range of the data.

ggplot(tb, 
       aes(x = mpg)) +
  geom_histogram(binwidth = 4, 
                 fill = "gold", 
                 color = "black") +
  theme_minimal() +
  labs(title = "Histogram of Mileage, using package `ggplot2` (setting binwidth = 4)", 
       x = "Miles Per Gallon (mpg)", y = "Frequency")

Discussion:

The code ggplot(tb, aes(x = mpg)) initializes a plot using the tb data frame, mapping the mpg column to the x-axis.
The histogram is created with geom_histogram(), using an adjustable binwidth = 4. Given this bin width, the resulting number of bins in the histogram depend on the range of mpg.
The binwidth argument specifies the width of the bins in the histogram, and we have chosen 4 as an arbitrary width.
We use fill and color to set the bar colors to be gold with a black border.
A clean appearance is achieved with theme_minimal(), and titles and labels are added using labs(). [1]

We could alternately set the number of bins in the histogram, instead of specifying the bin width. In this case, the bin-width gets calculated depending on the range of the data and the specified number of bins.

ggplot(tb, 
       aes(x = mpg)) +
  geom_histogram(bins = 8, 
                 fill = "gold", 
                 color = "black") +
  theme_minimal() +
  labs(title = "Histogram of Mileage, using package `ggplot2` (setting bins = 8)", 
       x = "Miles Per Gallon (mpg)", y = "Frequency")

Discussion:

We instruct R to create a histogram having 8 bins of equal width, by setting bins = 8 ingeom_histogram()`
The width of each bin is adjusted by dividing the range of mpg by the number of specified bins.

Alternately, we can specify custom bin ranges in a histogram. In this this approach, we supply a vector of breakpoints which defines the range of each bin. For example, the following code defines histogram bins with ranges of 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, 35-40, for the mpg variable

ggplot(tb, 
       aes(x = mpg)) +
  geom_histogram(breaks = seq(5, 40, by = 5), 
                 fill = "gold", 
                 color = "black") +
  theme_minimal() +
  labs(title = "Histogram of Mileage, using package `ggplot2` (setting breaks of 5)", 
       x = "Miles Per Gallon (mpg)", y = "Frequency")

Discussion:

ggplot(tb, aes(x = mpg)) initializes a ggplot object with the tb data frame and sets the mpg column as the x-axis variable.
geom_histogram() adds a histogram layer, in which breaks = seq(5, 40, by = 5) specifies bin edges using a sequence that starts at 5, ends at 40, and increases by 5 units. This results in bins like [5,10), [10,15), and so on.

Histogram using `ggpubr`

Recreating a histogram with binwidth of 4, using package ggpubr:

library(ggpubr)
gghistogram(tb, 
            x = "mpg", 
            binwidth = 4,
            add = "mean", 
            rug = TRUE, 
            color = "black" ,
            fill = "lightpink",
            title = "Histogram of Mileage, using package `ggpubr` (setting binwidth = 4) "
)

Discussion:

Here, we’re invoking the gghistogram() function from ggpubr to craft a histogram. The data source is specified as tb, and the variable of interest is mpg.
x = "mpg": This denotes the variable from tb we’re visualizing.
binwidth = 4: Each bin in the histogram will span a range of 4 units of mpg.
add = "mean": Superimposes the mean of mpg on the histogram.
rug = TRUE: Includes a rug plot at the base, which displays individual data points.
color = "black": The outline of the bars will be in black.
fill = "lightpink": Bars in the histogram will be filled with a light pink shade.
title =: Gives a descriptive title to the histogram.
In sum, we’re visualizing the distribution of the mpg variable from the tb dataset as a light pink histogram, emphasized with black borders, with a bin width of 4 units. We’ve also marked the mean value and showcased individual data points as a rug plot beneath the histogram.

Recreating a histogram with 8 bins, using package ggpubr:

library(ggpubr)
gghistogram(tb, 
            x = "mpg", 
            bins = 8,
            add = "mean", 
            rug = TRUE, 
            color = "black" ,
            fill = "lightpink",
            title = "Histogram of Mileage, using package `ggpubr` (setting bins = 8) "
)

Discussion:

In essence, the difference is that this code visualizes the mpg data from the tb dataset as a histogram with 8 bins, set using bins = 8.

Probability Density Function (PDF) plot using `ggplot2`

Recall that this type of plot shows the distribution of a single variable, and the area under the curve represents the probability of an observation falling within a particular range of values. The following code generates it using ggplot2:

ggplot(tb, 
       aes(x = mpg)) +
  geom_density(fill = "gold") +
  theme_minimal() +
  labs(title = "Probability Density Function of Miles Per Gallon (mpg)", 
       x = "Miles Per Gallon (mpg)", y = "density")

Discussion:

We designate our data source and the aesthetic mappings using the ggplot() function. The aesthetic mapping for x is mpg.
Subsequently, we append a density plot to our plot by using the geom_density() function. We fill the area under the curve by setting fill to “gold”.

PDF using `ggpubr`

The following R code creates a PDF of the mpg variable in the tb dataset, using the ggdensity() function from the ggpubr package.

library(ggpubr)
ggdensity(tb, 
            x = "mpg", 
            add = "mean", 
            rug = TRUE, 
            color = "black" ,
            fill = "lightpink",
            title = "PDF of Miles Per Gallon (mpg), using ggpubr::ggdensity()",
            xlab = "Mileage (mpg)",
            ylab = "Probability Density Function (PDF)"
)

Discussion:

The ggdensity() function from ggpubr package, is utilized here to visualize a probability density function (PDF) of the mpg variable from the tb dataset.
x = "mpg": This specifies the column mpg from the tb dataset as the variable we aim to visualize.
add = "mean": This argument ensures that a line or marker is added to the plot, indicating the mean value of the mpg data.
rug = TRUE: By setting this to TRUE, a rug plot is added at the bottom, showcasing individual data points.
color = "black": This defines the border color of the density plot as black.
fill = "lightpink": This fills the interior of the density plot with a light pink color.
title = ... : This provides a descriptive title to our plot, aiding in clarity and understanding.

Cumulative Distribution Function (CDF) Plot using `ggplot2`

The following code generates a CDF using ggplot2:

# Load required library
library(ggplot2)
# Create a CDF plot
ggplot(tb, aes(x = mpg)) +
  stat_ecdf(geom = "line", color = "blue") +
  labs(x = "Miles Per Gallon (mpg)", y = "CDF", 
       title = "Cumulative Distribution Function (CDF) of Mileage (mpg)") +
  theme_minimal()

Discussion:

Here, we’re initiating a plot using the ggplot() function, specifying tb as our data source and the mpg column as the variable of interest. `
We employ the stat_ecdf() function to represent the empirical cumulative distribution function (CDF) of the mpg data. The geom = "line" argument means the CDF will be displayed as a continuous line, and color = "blue" ensures this line is blue.
The labs() function is used to define axis labels and a plot title, enhancing readability.
By invoking theme_minimal(), we apply a clean and straightforward theme to our plot, which removes extraneous details and emphasizes content.
To sum up, this code creates a plot depicting the cumulative distribution function (CDF) of the mpg data from the tb dataset.

Boxplots using `ggplot2`

The following code generates a boxplot using ggplot2:

ggplot(tb, 
       aes(y = mpg)) +
  geom_boxplot(fill = "gold") +
  theme_minimal() +
  coord_flip() +
  labs(title = "Boxplot of Mileage (mpg)", 
       y = "Miles Per Gallon (mpg)")

Discussion:

ggplot(tb, aes(y = mpg)): Initializes a ggplot2 plot using tb with mpg as the y-axis.
geom_boxplot(fill = "gold"): Adds a gold-filled boxplot layer.
theme_minimal(): Applies a clean, minimalistic theme to the plot.
coord_flip(): Flips the plot to display a horizontal boxplot.
labs(...): Sets the plot title to “Boxplot of Mileage (mpg)” and labels the x-axis as “Miles Per Gallon (mpg)”.
In summary, this code creates a horizontal boxplot of the mpg values from the tb data frame, with the boxes filled in gold color, presented with a minimalistic theme, and labeled appropriately.

Boxplot using `ggpubr`

The following code recreates the boxplot using the ggboxplot() function from the ggpubr package.

library(ggpubr)
ggboxplot(tb, 
          y = "mpg", 
          orientation = "horizontal",
          rug = TRUE, 
          color = "black" ,
          fill = "lightpink",
          add = "jitter",
          title = "Boxplot of Mileage (mpg), using ggpubr::ggboxplot()"
)

Discussion:

ggboxplot(tb, y = "mpg"): Creates a boxplot of mpg values from the tb data frame.
orientation = "horizontal": Sets the boxplot to display horizontally.
rug = TRUE: Shows a rug plot indicating the density of data points.
color = "black": Sets the boxplot’s border color to black.
fill = "lightpink": Colors the inside of the boxes light pink.
add = "jitter": Adds jittered points to the boxplot for clearer data visualization.
title = ..": Sets the plot’s title.

Violin plot using `ggplot2`

The following code generates a violin plot using ggplot2, adding a boxplot to the violin plot:

ggplot(tb, aes(x = "", y = mpg)) +
  geom_violin(fill = "gold") +
  geom_boxplot(fill = "skyblue", width = 0.2) +
  labs(x = "", y = "Miles Per Gallon (mpg)", 
       title = "Violin Plot with Boxplot of Miles Per Gallon (mpg)") +
  coord_flip() +
  theme_minimal()

Discussion:

geom_violin() generates the violin plot
geom_boxplot() embeds a box plot within it

Violin plot using `ggpubr`

The following code recreates the violin plot using the ggviolin() function from the ggpubr package.

library(ggpubr)
ggviolin(tb, 
         y = "mpg", 
         orientation = "horizontal",
         rug = TRUE, 
         color = "black" ,
         fill = "lightpink",
         add = "boxplot", add.params = list(fill = "lightblue"),
         title = "Violin plot of Miles Per Gallon (mpg), using ggpubr::ggviolin()"
)

Discussion:

tb: This refers to the dataset we’re using. The dataset should have a variable named “mpg” as we’ve specified it in the next parameter.
y = "mpg": This indicates that we want the “mpg” variable (Miles Per Gallon) from the tb dataset to be plotted on the y-axis.
orientation = "horizontal": This parameter sets the orientation of the violin plot to be horizontal.
rug = TRUE: This adds a “rug” to the plot, which essentially places small vertical bars (or ticks) at the actual data points along the axis.
color = "black": The edge color of the violin plot is set to black.
fill = "lightpink": This sets the main color inside the violin plot to light pink.
add = "boxplot": This specifies that a boxplot should be added inside the violin plot. A boxplot provides a summary of the distribution, showing the median, quartiles, and potential outliers.
add.params = list(fill = "lightblue"): This further customizes the added boxplot by setting its fill color to light blue.
title = "Violin plot of Miles Per Gallon (mpg), using ggpubr::ggviolin()": This sets the title of the plot.
In summary, the code generates a horizontal violin plot for the “mpg” variable from the tb dataset. The violin plot showcases the distribution of the “mpg” variable, colored in light pink with a light blue boxplot added inside. The rug adds an additional layer of visualization, showing the actual data points along the axis.

Quantile-Quantile (Q-Q) Plots using `ggplot2`

Recall that a Q-Q plot is a graphical method for comparing two probability distributions by plotting their quantiles against each other. The following code generates a Quantile-Quantile (Q-Q) plot using ggplot2,

ggplot(tb, 
       aes(sample = mpg)) +
  stat_qq() +
  stat_qq_line() +
  labs(x = "Theoretical Quantiles", y = "Sample Quantiles", 
       title = "Q-Q Plot of Miles Per Gallon (mpg)") +
  theme_minimal()

Discussion:

ggplot(tb, aes(sample = mpg)) : Here, we initiate a ggplot graphic using the tb dataset and set the aesthetic (aes) to the “mpg” variable. In the context of the stat_qq() function (which we’ll come to shortly), the sample aesthetic specifies the data variable for which we want to create the Q-Q plot.
stat_qq() : This function adds the Q-Q plot points to the graphic. The x-axis of this plot represents the quantiles from a theoretical distribution (often the standard normal distribution), and the y-axis represents the quantiles from our sample data (“mpg”).
stat_qq_line() : This function adds a reference line to the Q-Q plot, which represents the expected line if the sample comes from the specified distribution (again, often the standard normal distribution). If our data points lie roughly on this line, it suggests that the data follows the theoretical distribution.
In summary, this code produces a Q-Q plot for the “mpg” variable from the tb dataset. The plot compares the quantiles of “mpg” against the quantiles of a theoretical distribution, often the standard normal distribution.

Combine Plots efficiently using `ggarrange()`

The following code showcases two plots side-by-side.

library(ggplot2)
library(ggpubr)
PlotHist <- gghistogram(tb, 
            x = "mpg", 
            binwidth = 4,
            add = "mean", 
            rug = TRUE, 
            color = "black" ,
            fill = "lightpink",
            title = "Histogram (binwidth = 4) "
)
PlotBox <- ggboxplot(tb, 
            y = "mpg", 
            rug = TRUE, 
            color = "black" ,
            fill = "lightpink",
            add = "jitter",
            title = "Boxplot of Mileage, using ggpubr"
)
# Combine the plots using ggarrange()
combined_plot <- ggarrange(PlotHist, PlotBox, ncol = 2)
# Display the combined plot
print(combined_plot)

Discussion:

We create a histogram and a boxplot using the same code discussed above.
ggarrange(PlotHist, PlotBox, ncol = 2) : This code helps us combine multiple plots into one. Here, PlotHist (the histogram) and PlotBox (the boxplot) are arranged side by side, as indicated by ncol = 2.
In essence, this code facilitates a side-by-side comparison of the distribution of the mpg variable from the tb dataset using two different types of visualizations: a histogram and a boxplot.

Summary of Chapter 13 – Continuous Data (2 of 2)

In this chapter, we explore how to visualize univariate continuous data using the ggplot2 package in R. We use the mtcars data set, converting it to a tibble called tb for easier manipulation.

The visualization methods we cover include histograms, density plots (Probability Density Function and Cumulative Density Function), box plots, bee swarm plots, violin plots, and Q-Q plots. These are created using functions like geom_histogram(), geom_density(), geom_boxplot(), geom_beeswarm(), geom_violin(), stat_qq(), and stat_qq_line().

For the histogram, we can adjust bin width, color, and number of bins, or define custom bin ranges. The density plots provide a visual representation of the distribution of a variable, and we can color the area under the curve. To create the CDF plot, we first arrange our data and calculate the cumulative distribution, which is plotted as a line graph. For the violin plot, we show how to add a box plot within the violin for additional information. Finally, we explore Q-Q plots, which compare the quantiles of our data to a theoretical distribution, useful for assessing if the data follows a certain theoretical distribution.

References

[1]

Wickham, H. (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org

Henderson, D. R. (1974). Motor Trend Car Road Tests. Motor Trend, 1974. Data retrieved from R mtcars dataset.

Eklund, A. (2020). ggbeeswarm: Categorical Scatter (Violin Point) Plots. R package version 0.6.0. https://CRAN.R-project.org/package=ggbeeswarm

[2]

Kassambara A (2023). ggpubr: ‘ggplot2’ Based Publication Ready Plots. R package version 0.6.0, https://rpkgs.datanovia.com/ggpubr/.

Continuous Data (2 of 2)

Exploring Univariate Continuous Data using ggplot2 and ggpubr

Bee Swarm plot using ggbeeswarm

Histogram using ggplot2

Histogram using ggpubr

Probability Density Function (PDF) plot using ggplot2

PDF using ggpubr

Cumulative Distribution Function (CDF) Plot using ggplot2

Boxplots using ggplot2

Boxplot using ggpubr

Violin plot using ggplot2

Violin plot using ggpubr

Quantile-Quantile (Q-Q) Plots using ggplot2

Combine Plots efficiently using ggarrange()