Take a look at your data

Let’s investigate these variable types as stored in R. Do they make sense to you?22 Are these “ordinal” or “nominal” categorical variables? What about the variable interest_rate?

class(loans_full_schema$homeownership)
#> [1] "factor"
class(loans_full_schema$application_type)
#> [1] "factor"
class(loans_full_schema$interest_rate)
#> [1] "numeric"

Create a dataframe called loans that cleans up the full dataset loans_full_schema to a) make the homeownership variable lower case (all caps is intense…), and b) reorder the “levels” of each variable into a sensible order.33 Note: reordering levels with fct_relevel() is helpful if your variable has a natural ordering to it, as all visuals will follow the order of the factor levels.

loans <- 
  loans_full_schema %>%
  mutate(
    homeownership    = tolower(homeownership), 
    homeownership    = fct_relevel(homeownership, "rent", "mortgage", "own"), 
    application_type = fct_relevel(application_type, "joint", "individual")
    ) 
levels(loans$homeownership)
#> [1] "rent"     "mortgage" "own"

Bar plots

A bar plot is a common way to display a single categorical variable. The left panel below shows a bar plot for the homeownership variable. In the right panel, the counts are converted into proportions, showing the proportion of observations that are in each level.

Question: When might you prefer the left version of the bar plot? When might you prefer the right?

# Bar plot showing count of loans in each homeownership category
p_count <- ggplot(loans, aes(x = homeownership)) +
  geom_bar(fill = "darkgreen") + 
  labs(x = "Homeownership", y = "Count")

# Bar plot showing proportion of loans in each homeownership category
p_proportion <- loans %>%
  count(homeownership) %>%
  mutate(proportion = n / sum(n)) %>%
  ggplot(aes(x = homeownership, y = proportion)) +
  geom_col(fill = "darkgreen") + 
  labs(x = "Homeownership", y = "Proportion")
p_count + p_proportion

Two bar plots: the left panel shows the counts and the right panel shows the proportions of values of the homeownership variable.

Contingency tables

We often care about how two categorical variables interact with one another. For example, are homeowners more likely to apply for a loan with a partner than are renters? A contingency table summarizes the distribution of our data across the two categories jointly.

Each value in the table represents the number of times a particular combination of variable outcomes occurred.

For example, the value 3496 corresponds to the number of loans in the dataset where the borrower rents their home and the application type was by an individual. Row and column totals are also included. The row totals provide the total counts across each row and the column totals down each column.

loans %>%
  count(application_type, homeownership) %>% # counts observations for each application_type X homeownership combination, creating a column called "n"
  pivot_wider(names_from = homeownership, values_from = n) %>% # names_from: What is the output column that you want called? values_from: What column should the cell values come from?
  adorn_totals(where = c("row", "col")) %>% # add "Totals" for both rows and coluns
  kbl(linesep = "", booktabs = TRUE) %>% # kable makes tables look fancy 
  kable_styling(bootstrap_options = c("striped", "condensed"), 
                latex_options = c("striped", "hold_position"), full_width = FALSE) %>%
  column_spec(1:5, width = "6em") # select columns, specify preferred formatting

Bar plots with two variables

We can display the distributions of two categorical variables on a bar plot at the same time. These plots are generally useful for visualizing the relationship between two categorical variables.

For example, here we create three bar plots that visualize the relationship between homeownership and application_type variables.

• First, we make a stacked bar plot, which simply stacks the count of observations in each homeownership type, coloring by application_type. We can see that most of the loan applicants live in mortgaged homes, but it’s hard to say if a joint versus individual applicant is more or less likely to rent, own, or have a mortgage.

p_stacked <- ggplot(loans, aes(x = homeownership, fill = application_type)) +
  geom_bar() +
  scale_fill_manual(values = c("skyblue","seagreen")) +
  labs(x = "Homeownership", y = "Count", fill = "Application type") +
  theme(
  axis.text.x = element_text(size = 20),
  axis.text.y = element_text(size = 20),
  axis.title = element_text(size=20,face="bold"))
p_stacked

p_dodged <- ggplot(loans, aes(x = homeownership, fill = application_type)) +
  geom_bar(position = "dodge") +
  scale_fill_manual(values = c("skyblue", "seagreen")) +
  labs(x = "Homeownership", y = "Count", fill = "Application type") +
  theme(
  axis.text.x = element_text(size = 20),
  axis.text.y = element_text(size = 20),
  axis.title = element_text(size=20,face="bold"))
p_dodged

p_standardized <- ggplot(loans, aes(x = homeownership, fill = application_type)) +
  geom_bar(position = "fill") +
  scale_fill_manual(values = c("skyblue", "seagreen")) +
  labs(x = "Homeownership", y = "Proportion", fill = "Application type")+
  theme(
  axis.text.x = element_text(size = 20),
  axis.text.y = element_text(size = 20),
  axis.title = element_text(size=20,face="bold"))
p_standardized

Histograms

As we discussed in class, we can make a histogram from our sample to learn about what the probability density function of our population is likely to look like. For example, you might want to know if your variable follows a normal distribution or not.

A histogram plots the count (or proportion) of your data that fall into a set of user-specified bins.44 Note: Even if you’re working with continuous data, any histogram function in R will bin up your continuous data into discrete bins, and then plot the proportion of your data in that bin.

We’ll use ggplot and the geom_histogram function to make a histogram of the interest rate associated with all the loans in our loan database.

ggplot(loans, aes(x = interest_rate)) +
  geom_histogram() +
  labs(x = "Interest rate", y = "Count") 

The above plot showed us counts in each bin, where the bins were left unspecified.55 R will remind you to change bin values if you leave them unspecified, since the default is rarely appropriate for your data. The command breaks = seq(5, 27.5, 2.5) creates a vector called breaks that goes from 5 to 25 in intervals of 2.5. Generate this vector and use it within geom_histogram() to create new bin widths in your histogram.

This new histogram describes our data more clearly. What do you see? Use terms from class (e.g., symmetric, skew, tails, etc.) to describe the distribution of the interest rate in this sample of loans. Is the interest rate approximately normally distributed?

ggplot(loans, aes(x = interest_rate)) +
  geom_histogram(breaks = seq(5, 27.5, 2.5)) +
  labs(x = "Interest rate", y = "Count") 

Note: If you want to make a histogram showing proportions instead of counts, you can use aes(y=..density..) inside geom_histogram().

Box plots: A nice way to look at quantiles

Box plots are a standard way for us to visualize quantiles of a variable. Recall, quantiles tell us how much of our data sit below a certain value (e.g., the first tercile or first 3-quantile tells us the value at which 1/3 of the data sit below.).

In their most standard form, box plots show a box where the outer edges of the box indicate the 1st and 3rd quartiles of the data (i.e., 25th and 75th percentiles).66 Recall: The range from the 25th to 75th percentile is called the “inter-quartile range” or IQR. A vertical line is shown through the box indicating the 2nd quartile (i.e., 50th percentile or median). Lines outside the box are called “whiskers” and indicate the median minus (or plus) 1.5 times the IQR. While this is the most standard boxplot, you can customize these cutoffs to any quantiles you’d like.

Here, we repeat the histogram above, showing the distribution of the interest_rate variable in the data. We then make a boxplot using the standard quantiles. Note that outliers beyond the median + 1.5\(\times\)IQR are shown as individual points.

p_hist <- ggplot(loans, aes(x = interest_rate)) +
  geom_histogram(breaks = seq(5, 30, 2.5)) +
  labs(x = "Interest rate", y = "Count") 

p_boxplot <- ggplot(loans, aes(x = interest_rate)) + 
  geom_boxplot(lower=25, middle=50, upper=75, outlier.size = 2.5) + # these arguments control your quantiles and tell you how large to plot the outliers!
  labs(x = "Interest rate") 

p_hist
p_boxplot

What do you notice in the boxplot? Do you prefer communicating skew, tails, and symmetry with the histogram or the boxplot? Why?