2.1 Vectors

To create a vector in R we use the c() (combine) function and then separate the elements of the vector with a comma.

In this course, we will generally use the following vector types:

# Vector types
a <- c(1, 2, 5.3, -2,4)         # numeric vector
b <- c("one","two","three")     # character vector
c <- c(TRUE,TRUE,TRUE,FALSE)    # logical vector

2.2 Factors

Factors are used for nominal or ordinal variables. Converting character variables into factors is useful for data visualization - graphs and tables will present the different category labels in the specified order.

# Create factor variables
tb.ceosal2 <- tb.ceosal2 %>% mutate(
    college = factor( x = college
                    , levels = c(0,1)
                    , labels = c("No College Degree", "College Degree"))
  , grad = factor(    x = grad
                    , levels = c(0,1)
                    , labels = c("No Grad. Degree", "Grad. Degree")))

3.1 Glimpse

As an alternative to head() or View(), we can take a glimpse() of our data set. This will tell us the number of columns (variables) and rows (observations) in the data, and present a list of all variables, their type, and the first few values in each variable.

# Take a glimpse of the data
glimpse(tb.ceosal2)

Rows: 177
Columns: 15
$ salary   <int> 1161, 600, 379, 651, 497, 1067, 945, 1261, 503, 1094, 601, 35…
$ age      <int> 49, 43, 51, 55, 44, 64, 59, 63, 47, 64, 54, 66, 72, 51, 63, 4…
$ college  <fct> College Degree, College Degree, College Degree, College Degre…
$ grad     <fct> Grad. Degree, Grad. Degree, Grad. Degree, No Grad. Degree, Gr…
$ comten   <int> 9, 10, 9, 22, 8, 7, 35, 32, 4, 39, 26, 39, 37, 25, 21, 7, 38,…
$ ceoten   <int> 2, 10, 3, 22, 6, 7, 10, 8, 4, 5, 7, 8, 37, 1, 11, 7, 4, 12, 2…
$ sales    <dbl> 6200, 283, 169, 1100, 351, 19000, 536, 4800, 610, 2900, 1200,…
$ profits  <int> 966, 48, 40, -54, 28, 614, 24, 191, 7, 230, 34, 8, 35, 234, 9…
$ mktval   <dbl> 23200, 1100, 1100, 1000, 387, 3900, 623, 2100, 454, 3900, 533…
$ lsalary  <dbl> 7.057037, 6.396930, 5.937536, 6.478509, 6.208590, 6.972606, 6…
$ lsales   <dbl> 8.732305, 5.645447, 5.129899, 7.003066, 5.860786, 9.852194, 6…
$ lmktval  <dbl> 10.051908, 7.003066, 7.003066, 6.907755, 5.958425, 8.268732, …
$ comtensq <int> 81, 100, 81, 484, 64, 49, 1225, 1024, 16, 1521, 676, 1521, 13…
$ ceotensq <int> 4, 100, 9, 484, 36, 49, 100, 64, 16, 25, 49, 64, 1369, 1, 121…
$ profmarg <dbl> 15.580646, 16.961130, 23.668638, -4.909091, 7.977208, 3.23157…

Note that most variables in the data are either integers or doubles, which means that they are numeric¹. The variables college and grad have already been converted to factors.

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3.2 Skim

The package skimr provides some useful functions for exploring our data sets. An overview of the full data set along with summary statistics and histograms can be obtained using the skim() function.

# Data set overview
skim(tb.ceosal2)

Variable type: factor

Variable type: numeric

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3.3 Stargazer

A quick and easy way to produce a summary statistics table is to use the stargazer function. Note that stargazer will only summarize the numeric variables in the data. Any qualitative variables need to be inspected separately using a different method.

Note: stargazer will not work with tibbles so we must convert the data into a data.frame inside the stargazer function for it to run.

# Quick summary statistics table
stargazer(data.frame(tb.ceosal2), type = "text")

=================================================
Statistic  N    Mean    St. Dev.    Min     Max  
-------------------------------------------------
salary    177  865.864   587.589    100    5,299 
age       177  56.429     8.422      33      86  
comten    177  22.503    12.295      2       58  
ceoten    177   7.955     7.151      0       37  
sales     177 3,529.463 6,088.654    29    51,300
profits   177  207.831   404.454    -463   2,700 
mktval    177 3,600.316 6,442.276   387    45,400
lsalary   177   6.583     0.606    4.605   8.575 
lsales    177   7.231     1.432    3.367   10.845
lmktval   177   7.399     1.133    5.958   10.723
comtensq  177  656.684   577.123     4     3,364 
ceotensq  177  114.124   212.566     0     1,369 
profmarg  177   6.420    17.861   -203.077 47.458
-------------------------------------------------

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4.1 Histograms

We will be focusing on the relationship between CEO salaries and firm profits. We will thus start by plotting the distributions of these two variables.

# Histogram of CEO salary
ggplot(data = tb.ceosal2, aes(x = salary)) + geom_histogram()

# Alternatively:
tb.ceosal2 %>% ggplot(aes(x = salary)) + geom_histogram()

# Histogram of firm profits
ggplot(data = tb.ceosal2, aes(x = profits)) + geom_histogram()

4.2 Boxplots

Box and whisker plots are an alternative (or complementary) way to visualize the distribution of numeric variables. The “box” gives us the first and third quartiles and the line in the middle of the box give us the median value. Outliers are highlighted as dots separated from the box and the whiskers.

# Boxplot of CEO salary (horizontal)
ggplot(data = tb.ceosal2, aes(x = salary)) + geom_boxplot() + scale_y_discrete( ) 

# Boxplot of firm profits (vertical)
ggplot(data = tb.ceosal2, aes(y = profits)) + geom_boxplot() + scale_x_discrete( ) 

4.3 Barplots

Categorical data can be visualized using barplots. Note that the plot will be ordered according to the pre-specified factor ordering.

# Barplot of grad
ggplot(data = tb.ceosal2, aes(x = grad)) + geom_bar()

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5.1 Scatter plots

A scatterplot allows us to visualize the relationship between two numeric variables. Scatterplots can be easily created with ggplot2 by using geom_point(). As before, all plot elements can be customized.

To add a regression line to the scatterplot, we use the layer stat_smooth(method = lm) (the option method = lm indicates we want a linear regression line — the most common). The gray region is the confidence interval for the regression line.

# Create scatterplot and store it as a new object
plot.scatter <-  ggplot(data = tb.ceosal2
                     , aes(x = profits, y = salary)) +
                geom_point(size = 1) +
                theme_few() +
                labs(  x = "1990 profits, millions"
                     , y = "1990 CEO compensation, $1000s"
                     , title = "Relationship between CEO salaries and firm profits") +
                theme(title = element_text(size = 8))

# Print scatterplot
plot.scatter

# Add regression line to scatterplot
plot.scatter +
  # add regression line
  stat_smooth(method = lm, colour="black") 

The scatterplot suggests a positive (when one variable increases, the other increases as well) but weak linear relationship between the two variables (the points do not fall neatly on the straight line). In the scatterplot we can also more clearly detect outlier points.

We can use color, point shape, or point size to add additional layers of information to scatterplots.

# Create scatterplot 
ggplot(data = tb.ceosal2
     , aes(x = profits, y = salary, color = grad)) +
  geom_point(size = 1) +
  # use custom theme and color scheme
  theme_classic() + scale_color_fivethirtyeight() +
  theme(title = element_text(size = 12)) +
  labs(  x     = "1990 profits, millions"
       , y     = "1990 CEO compensation, $1000s"
       , title = "Relationship between CEO salaries and firm profits"
       , color = "")

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5.2 Categorical Data

We can use color in barplots to analyze relationships between two categorical variables.

# Barplot of grad - Counts
ggplot(data = tb.ceosal2
     , aes(x = college, fill = grad)) + 
  geom_bar() +
  # add custom theme and color scheme
  theme_fivethirtyeight() + scale_fill_tableau()

# Barplot of grad - Percent
ggplot(data = tb.ceosal2
     , aes(x = college, fill = grad)) + 
  geom_bar(position="fill") +
  # add custom theme and color scheme
  theme_fivethirtyeight() + scale_fill_tableau()

We can use side-by-side boxplots with or without color to analyze relationships between categorical and numerical variables.

# Boxplot of college and salary
ggplot(data = tb.ceosal2
     , aes(x = grad, y = salary, fill = grad)) + 
  geom_boxplot() +
  # add custom theme and color scheme
  theme_fivethirtyeight() + scale_fill_tableau() 

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5.3 Correlation Tables and Plots

Correlation tables provide us the correlation coefficient for each pair of numeric variables in the data.

# Create correlation matrix 
cor_matrix <- tb.ceosal2 %>% 
  select(salary, age, comten, ceoten, sales, profits, mktval) %>% 
  correlate(diagonal = 1)

# Format table for a professional presentation
cor_matrix %>%
  rearrange() %>%            # rearrange by correlations
  shave() %>%                # Shave off the upper triangle for a clean result
  fashion(decimals = 3)      # Clean presentation

Correlations can also be presented visually. This can be done in different ways (e.g. heatmap, barplot, correlation plot), depending on the data and the researcher’s preferences.

A correlation plot can be created easily using the function rplot().

# Correlation plot
cor_matrix %>% rplot()

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5.4 GGpairs

The function ggpairs() of the package GGally is a good shortcut for visualizing the relationship between several variables all at once. However, you should be careful when using this function: select only a few variables (otherwise the output becomes unreadable) and, if your dataset contains too many observations, make sure to select only a sample of those observations for plotting.

# Visualize distributions, scatterplots, and correlations
ggpairs(tb.ceosal2 %>% select(salary, grad, sales, profits))

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