Relationships between Variables

May 19, 2025

Relationships Between Numerical Variables

Scatterplots

  • We use scatterplots to illustrate the relationship between two numerical variables

  • We can use color, shapes, and sizing to add dimensions

    – That is, to include other variables

Example: GDP per capita and Democracy

  • Same electoral democracy measure

  • What is GDP per capita?

Pull in the VDEM Data

library(tidyverse)
library(vdemdata)
myVdem <- vdem %>% 
   filter(year == 2018)  %>%  
 mutate(region = e_regionpol_6C) %>%   ## make a better region variable
  mutate(region = case_match(region, 
                        1 ~ "Eastern Europe", 
                        2 ~ "Latin America",  
                        3 ~ "Middle East",   
                        4 ~ "Africa", 
                        5 ~ "The West", 
                        6 ~ "Asia")) %>%
  select(country_name, v2x_polyarchy, e_gdppc, region,  e_wb_pop) %>% 
  mutate(lg_gdppc = log(e_gdppc))
#names(vdem2019)
#glimpse(myVdem)

Visualize with a Scatter Plot

How would you interpret this plot?

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point(color = "steelblue4") + # use geom_point() for scatter plots
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute", 
    color = "Region",
    ) + 
  scale_color_viridis_d(option = "inferno", end = .8) +
  theme_bw()

Trend line

The trend line visually illustrates the relationship

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point(color = "steelblue4") + # use geom_point() for scatter plots
  geom_smooth(method = "lm", linewidth = 1) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute", 
    color = "Region",
    ) + 
  scale_color_viridis_d(option = "inferno", end = .8) +
  theme_bw()

Trend line

How should we interpret the outliers?

Add a dimension: World Region

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point(aes(color = region)) + 
    geom_smooth(method = "lm", linewidth = 1) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute", 
    color = "Region",
    ) + 
  scale_color_viridis_d() +
  theme_bw()

Add another dimension, Population

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point(aes(color = region, size = e_wb_pop)) + 
    geom_smooth(method = "lm", linewidth = 1) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute and World Bank", 
    color = "Region",
    size = "Population"
    ) + 
  scale_color_viridis_d() +
  theme_bw()

Does relationship vary by region?

Does GPD per capita have a different relationship to democracy in different regions?

Relationship by Region

Relationship might be different, but this is a bit hard to read

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy, color = region)) + 
  geom_point() + 
    geom_smooth(method = "lm", linewidth = 1, se=FALSE) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute", 
    color = "Region",
    ) + 
  scale_color_viridis_d() +
  theme_bw()

Facet Wrapping

How should we interpret this plot?

Code 
ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point() + 
    geom_smooth(method = "lm", linewidth = 1, se=FALSE) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute") +
    facet_wrap(~region) +
  scale_color_viridis_d() +
  theme_bw()

Examine Specific Countries by Labelling Points

Code 
myVdem %>% 
  filter(region == "Africa") %>% 
  ggplot(. , aes(x = e_gdppc, y = v2x_polyarchy)) + 
    geom_point(color = "steelblue4") + 
    geom_smooth(method = "lm", linewidth = 1, se=FALSE) + 
    geom_text(aes(label = country_name), size = 2, vjust = 2) +
scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy in Africa, 2018", 
    caption = "Source: V-Dem Institute"    ) + 
  scale_color_viridis_d() +
  theme_bw()

Examine Specific Countries by Labelling Points

Code 
myVdem %>% 
  filter(region == "Asia") %>% 
  ggplot(. , aes(x = e_gdppc, y = v2x_polyarchy)) + 
    geom_point(color = "steelblue4") + 
    geom_smooth(method = "lm", linewidth = 1, se=FALSE) + 
    geom_text(aes(label = country_name), size = 2, vjust = 2) +
scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy in Asia, 2018", 
    caption = "Source: V-Dem Institute"  ) + 
  scale_color_viridis_d() +
  theme_bw()

Make it Interactive with plotly

Code 
library(plotly)
modernization_plot <- ggplot( myVdem, aes(x = e_gdppc, y = v2x_polyarchy)) + 
  geom_point(aes(color = region)) + 
  aes(label = country_name) +
  geom_smooth(method = "lm", linewidth = 1) + 
  scale_x_log10(labels = scales::label_number(prefix = "$", suffix = "k")) +
  labs(
    x= "GDP per Capita", 
    y = "Polyarchy Score",
    title = "Wealth and democracy, 2018", 
    caption = "Source: V-Dem Institute", 
    color = "Region",
    ) + 
  scale_color_viridis_d() +
  theme_bw()
ggplotly(modernization_plot, tooltip = "country_name")

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