Data Visualization - Part Two
Miao Yu
2024-01-24
Histogram
To summarize a single numeric variable, the most commonly used chart is a histogram. As below is an example
A good histogram shows the distribution shape of the data set.
Create a histogram
Now let’s learn how to summarize a numeric variable by creating a
histogram. Let’s pick the annual_income since its meaning
is easy to understand.
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate))
By default, there are 30 bins and their ranges are automatically determined. In many cases, this won’t give us a satisfactory graph. We need to customize it.
Changing the bin number - bins=20
In the previous graph, around 10% there are two “missing” bars which look unnatural. We can resolve this by reducing the number of bins (groups).
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), bins = 20) 
Changing the bin number - bins=10
We can make the bin number even smaller to be 10. Among the three histograms, Which one do you think is the best? Why?
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), bins = 10) 
Change the bin width
In some situations, we hope to specify the bin width instead of bin number. We may do the following:
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5) 
Adjust the position of bins
We can specify the center or boundary of
one bin to make adjustments to the position of bins.
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) 
Adjust the position of bins
We can specify the center or boundary of
one bin to make adjustments to the position of bins.
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 1, center = 10) 
Adjust the plotting range of x
It may look a little unnatural if we don’t plot x starting from zero.
We may fix it by using the function xlim.
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 1, center = 10) +
xlim(0, 40)
Density plot
For continuous random variables, it is common practice to have a density plot which plots a smoothed version of the histogram.
The density here is same as “probability density” in statistics. The density plot can be understood as a probability density function fit to the histogram. As below is an example.
ggplot(loans, aes(x = loan_amount)) +
geom_density()
Here geom_density() function creates a density plot:
The total area under the density plot is one.
By default, the density curve is fit to the histogram with the default bin number (30 bins, see the graph below).
To adjust the “smoothness” of the plot, change the variable
adjust.
Plot histogram and density together
Usually, it can be a good idea to plot histogram and density in one plot:
ggplot(loans, aes(x = loan_amount)) +
geom_histogram(aes(y = after_stat(density)),
boundary = 0, colour = "black", fill = "white") +
geom_density(linewidth = 1.2)
Note that to make the histogram also plotted with y-axis being
density, we need to add y = after_stat(density) in the
aes function.
Adjust density smoothness
Larger adjust value gives more smooth density curves.
For example, we can set it to be 30/8 to fit the curve to a
histogram with 8 bins (which is smoother).
ggplot(loans, aes(x = loan_amount)) +
geom_histogram(aes(y = after_stat(density)), binwidth = 5000,
boundary = 0, colour = "black", fill = "white") +
geom_density(adjust = 30/8, linewidth = 1.2) #30/8 = 30bins/8bins
Create a relative frequency histogram (optional)
The after_stat function is used in the example above
because the y-axis is mapped to data that are not a variable in the
original data frame. For histograms, the default y-axis is mapped to
counts, which is computed by another function stat_bin().
The function after_stat(count) or
after_stat(density) indicates that count or
density are only available after the original data are
transformed.
With this understanding, we can create a relative frequency histogram (although rarely used) where the y-axis is the proportion of samples in each bin rather than the counts:
ggplot(loans) +
geom_histogram(mapping = aes(x = loan_amount, y = after_stat(count/sum(count))),
binwidth = 5000, boundary = 0, colour = "black", fill = "white")
Aesthetic Grouping
In many cases, it is very useful to add another level of aesthetic
mapping to a figure. For example, in the mpg data set, if
we plot hwy vs displ, we would see a plot like
this:
Example: How would we explain the red dots which
seem to deviate the overall trend (larger displ leading to
lower hwy)?
The same plot with color groups in vehicle class
How to explain those data points which has good fuel economy with large engine displacement? The following plot answers the question:
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy, color = class))
We see that most of these cars are 2seaters, e.g., sports cars. Those cars are lighter with a powerful engine, thus having better mpg in highway than other non-sports cars (SUV, pickups).
Here, we put a color argument inside the
aes function, this creates a new aesthetic group (in color)
by the categorical variable class.
Example - group by color and size (for ordinal variable)
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy, color = cyl, size = cyl))
Question: What can we learn from this graph?
Aesthetic grouping for histogram
Sometimes we hope to compare histograms between groups. One way to do
this is to use fill in the aes function. For
example, if we want to investigate the effect of
homeownership to loan_amount, we can do the
following:
ggplot(loans, aes(loan_amount, fill = homeownership)) +
geom_histogram(binwidth = 5000, alpha = 0.5) 
The argument alpha is between 0 and 1 that controls the
transparency of each histogram. The smaller alpha is, the
more transparent. It is very useful when we plot multiple charts that
overlap with each other.
Aesthetic grouping for density curve
When the absolute counts between groups are quite different, comparing histograms is not a good idea. Instead, we would like to compare density curves between groups to see their differences.
ggplot(loans, aes(x = loan_amount, fill = homeownership)) +
geom_density(adjust = 2, alpha = 0.5) # Transparency is necessary
So this graph shows the relatively insignificant differences between groups - people with mortgage tend to borrow more money than those renting houses (maybe they care less about having more debts since they are indebted anyway).
Ridge plots for density curves
When there are too many categories, a density ridge plot can be useful.
library(ggridges) # The package "ggridges" must be installed
ggplot(loans, aes(x = loan_amount, y = grade,
fill = grade, color = grade)) +
geom_density_ridges(alpha = 0.5)
This enhanced graph becomes available after installing the package
ggridges. You should be able to understand the code now
without my explanation after studying many examples!
Question: What can we learn from this graph?
Customize the appearance of data-related components
As we see in previous examples, we can customize the color, shape, fill color and other aesthetic components of data-related components (symbols, lines, bars, fills etc.). Note that this is different from aesthetic grouping since we would control the appearance of the whole plot.
These components are customized by arguments inside the
geom_ functions (but outside the aes()
function). For example,
ggplot(data = mpg, mapping = aes(x = cty, y = hwy)) +
geom_point(color = "blue", fill = "green", shape = 21, size = 3) +
geom_smooth(color = "purple", linetype = "dashed", linewidth = 1.5)
All aesthetic features apply to all data components for that
geom_ function.
For more details, please refer to https://ggplot2.tidyverse.org/articles/ggplot2-specs.html
Titles and labels
For a graph to be accessible to a wider audience, it must have proper
axis labels and title. In ggplot, the function
labs() is used to specify these details.
ggplot(data = loans) +
geom_histogram(
mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) +
labs(
title = "Interest rate from lending club data",
x = "Interest Rate (%)",
y = "Count"
)
Example
Let’s look at an example to understand this. For example, we want to center the title in the previous graph. We can do this:
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) +
labs(title = "Interest rate from lending club data", x = "Interest Rate (%)", y = "Count") +
theme(plot.title = element_text(hjust = 0.5))
Another example
Let’s see another example. Now we want to enlarge the font size of title to be 20 pts. The following code would work:
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) +
labs(title = "Interest rate from lending club data", x = "Interest Rate (%)", y = "Count") +
theme(plot.title = element_text(hjust = 0.5, size = 20))
Solution
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) +
labs(title = "Interest rate from lending club data", x = "Interest Rate (%)", y = "Count") +
theme(plot.title = element_text(hjust = 0.5, size = 20), axis.title = element_text(size = 15), axis.text = element_text(size = 15))
Example
An exemplary graph is shown below after adjusting the margin and font colors.
ggplot(data = loans) +
geom_histogram(mapping = aes(x = interest_rate), binwidth = 5, boundary = 10) +
labs(title = "Interest rate from lending club data", x = "Interest Rate (%)", y = "Count") +
theme(plot.title = element_text(hjust = 0.5, size = rel(1.5), colour = "red"), axis.title = element_text(colour = "blue", size = rel(1.2), margin = margin(b = 3)), axis.text = element_text(size = rel(1.2)), plot.margin = margin(1,1,1,1, unit = "cm"))
Setting scales (xlim and ylim)
To set the limits of x and y axis, which is usually needed for graph
polishing, we need to use xlim or ylim
functions:
ggplot(mpg, aes(cty, hwy)) + geom_point() + geom_smooth() +
xlim(0, 40) + ylim(0, 50) +
theme(axis.title.x = element_text(size = rel(1.0), margin = margin(10,0,0,0)), axis.title.y = element_text(size = rel(1.0), margin = margin(0,10,0,0)), axis.text = element_text(size = rel(1.0)), plot.margin = margin(1,1,1,1,"cm"))
Principles of graph polishing
- (Most important) The graph needs to look good to fit the actual needs in its final form.
- With the same graph, when the output format is different, the optimized setting are also different.
- Always try different settings and check your figure in its final form for optimization.
On the next page, I am going to show you a graph that is relatively polished in detail (You need really large font sizes for presentation).
