In this case study, we will attempt to answer two questions using the gapminder dataset: 1. Is the world divided into western rich nations and the developing world in Africa, Asia, and Latin America? 2. Has income inequality across countries worsened during the last 50 years?

library(dslabs)
library(ggplot2)
library(dplyr)
library(tinytex)
data(gapminder)
head(gapminder)

We use scatter plots to analyze the preconceived notion that the world is divided into two groups: the western world (Western Europe and North America), characterized by long life spans and small families, versus the developing world (Africa, Asia, and Latin America) characterized by short life spans and large families.

filter(gapminder, year == 1962) %>%
  ggplot(aes(fertility, life_expectancy)) +
  geom_point()

Most points fall into two distinct categories:

Life expectancy around 70 years and 3 or fewer children per family. Life expectancy lower than 65 years and more than 5 children per family. Are these the countries we expect?

filter(gapminder, year == 1962) %>%
  ggplot( aes(fertility, life_expectancy, color = continent)) +
  geom_point()

It is clear that in 1962, “the West versus developing world” view was grounded in some reality. Is this still the case 50 years later? Side by side plots help us make comparisons:

filter(gapminder, year%in%c(1962, 2012)) %>%
  ggplot(aes(fertility, life_expectancy, col = continent)) +
  geom_point() +
  facet_grid(continent~year)

filter(gapminder, year%in%c(1962, 2012)) %>%
  ggplot(aes(fertility, life_expectancy, col = continent)) +
  geom_point() +
  facet_grid(. ~ year)

This plot clearly shows that the majority of countries have moved from the developing world cluster to the western world one. In 2012, the western versus developing world view no longer makes sense. This is particularly clear when comparing Europe to Asia, the latter of which includes several countries that have made great improvements.

Comparing Asia and Europe across years:

years <- c(1962, 1980, 1990, 2000, 2012)
continents <- c("Europe", "Asia")
gapminder %>% 
  filter(year %in% years & continent %in% continents) %>%
  ggplot( aes(fertility, life_expectancy, col = continent)) +
  geom_point() +
  facet_wrap(~year)

This plot clearly shows how most Asian countries have improved at a much faster rate than European ones.

filter(gapminder, year%in%c(1962, 2012)) %>%
  ggplot(aes(fertility, life_expectancy, col = continent)) +
  geom_point() +
  facet_wrap(. ~ year, scales = "free")

In the plot above, we have to pay special attention to the range to notice that the plot on the right has a larger life expectancy. We will talk about this shortly.

The visualizations here effectively illustrate that data no longer supports the western versus developing world view. Once we see these plots, new questions emerge: -Which countries are improving more and which ones less? -Was the improvement constant during the last 50 years or was it more accelerated during certain periods? Timeseries plots help us answer this questions. Time series plots have time in the x-axis and an outcome or measurement of interest on the y-axis. For example, here is a trend plot of United States fertility rates:

gapminder %>% 
  filter(country == "United States") %>% 
  ggplot(aes(year, fertility)) +
  geom_point()
## Warning: Removed 1 rows containing missing values (geom_point).

We see that the trend is not linear at all. Instead there is sharp drop during the 1960s and 1970s to below 2. Then the trend comes back to 2 and stabilizes during the 1990s. When the points are regularly and densely spaced, as they are here, we create curves by joining the points with lines, to convey that these data are from a single series, here a country.

gapminder %>% 
  filter(country == "United States") %>% 
  ggplot(aes(year, fertility)) +
  geom_line()
## Warning: Removed 1 rows containing missing values (geom_path).

Time-series plots:

countries <- c("South Korea","Germany")

gapminder %>% filter(country %in% countries & !is.na(fertility)) %>% 
  ggplot(aes(year,fertility, col = country)) +
  geom_line()

The plot clearly shows how South Korea’s fertility rate dropped drastically during the 1960s and 1970s, and by 1990 had a similar rate to that of Germany.

labels <- data.frame(country = countries, x = c(1975,1965), y = c(60,72))

gapminder %>% 
  filter(country %in% countries) %>% 
  ggplot(aes(year, life_expectancy, col = country)) +
  geom_line() +
  geom_text(data = labels, aes(x, y, label = country), size = 5) +
  theme(legend.position = "none")

The plot clearly shows how an improvement in life expectancy followed the drops in fertility rates. In 1960, Germans lived 15 years longer than South Koreans, although by 2010 the gap is completely closed. It exemplifies the improvement that many non-western countries have achieved in the last 40 years.

Question two: Have poor countries have become poorer and rich countries become richer? The gapminder data table includes a column with the countries’ gross domestic product (GDP). GDP measures the market value of goods and services produced by a country in a year. The GDP per person is often used as a rough summary of a country’s wealth. Here we divide this quantity by 365 to obtain the more interpretable measure dollars per day. Using current US dollars as a unit, a person surviving on an income of less than $2 a day is defined to be living in absolute poverty and add this variable to the data table:

gapminder <- gapminder %>%  mutate(dollars_per_day = gdp/population/365)
past_year <- 1970
gapminder %>% 
  filter(year == past_year & !is.na(gdp)) %>%
  ggplot(aes(dollars_per_day)) + 
  geom_histogram(binwidth = 1, color = "black")

gapminder %>% 
  filter(year == past_year & !is.na(gdp)) %>%
  ggplot(aes(log2(dollars_per_day))) + 
  geom_histogram(binwidth = 1, color = "black")

In a way this provides a close-up of the mid to lower income countries. The histogram does not show us if the two groups of countries are west versus the developing world.

gapminder %>% 
  filter(year == past_year & !is.na(gdp)) %>%
  mutate(region = reorder(region, dollars_per_day, FUN = median)) %>%
  ggplot(aes(dollars_per_day, region)) +
  geom_point() +
  scale_x_continuous(trans = "log2")

We can already see that there is indeed a “west versus the rest” dichotomy: we see two clear groups, with the rich group composed of North America, Northern and Western Europe, New Zealand and Australia. We define groups based on this observation:

gapminder <- gapminder %>% 
  mutate(group = case_when(
    region %in% c("Western Europe", "Northern Europe","Southern Europe", 
                    "Northern America", 
                  "Australia and New Zealand") ~ "West",
    region %in% c("Eastern Asia", "South-Eastern Asia") ~ "East Asia",
    region %in% c("Caribbean", "Central America", 
                  "South America") ~ "Latin America",
    continent == "Africa" & 
      region != "Northern Africa" ~ "Sub-Saharan",
    TRUE ~ "Others"))
gapminder <- gapminder %>% 
  mutate(group = factor(group, levels = c("Others", "Latin America", 
                                          "East Asia", "Sub-Saharan",
                                          "West")))
p <- gapminder %>% 
  filter(year == past_year & !is.na(gdp)) %>%
  ggplot(aes(group, dollars_per_day)) +
  geom_boxplot() +
  scale_y_continuous(trans = "log2") +
  xlab("") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) 
p

p + geom_point(alpha = 0.5)

Data exploration clearly shows that in 1970 there was a “west versus the rest” dichotomy. But does this dichotomy persist?

past_year <- 1970
present_year <- 2010
years <- c(past_year, present_year)
gapminder %>% 
  filter(year %in% years & !is.na(gdp)) %>%
  mutate(west = ifelse(group == "West", "West", "Developing")) %>%
  ggplot(aes(dollars_per_day)) +
  geom_histogram(binwidth = 1, color = "black") +
  scale_x_continuous(trans = "log2") + 
  facet_grid(year ~ west)

There are more countries represented in the 2010 histograms than in 1970: the total counts are larger. One reason for this is that several countries were founded after 1970. For example, the Soviet Union divided into several countries during the 1990s. Another reason is that data was available for more countries in 2010.

Here are the plots using only countries with data available for both years.

country_list_1 <- gapminder %>% 
  filter(year == past_year & !is.na(dollars_per_day)) %>% 
  pull(country)

country_list_2 <- gapminder %>% 
  filter(year == present_year & !is.na(dollars_per_day)) %>% 
  pull(country)
      
country_list <- intersect(country_list_1, country_list_2)
past_year <- 1970
present_year <- 2010
years <- c(past_year, present_year)
gapminder %>% 
  filter(country %in% country_list, year %in% years & !is.na(gdp)) %>%
  mutate(west = ifelse(group == "West", "West", "Developing")) %>%
  ggplot(aes(dollars_per_day)) +
  geom_histogram(binwidth = 1, color = "black") +
  scale_x_continuous(trans = "log2") + 
  facet_grid(year ~ west)

The rich countries have become a bit richer, but percentage-wise, the poor countries appear to have improved more. In particular, we see that the proportion of developing countries earning more than $16 a day increased substantially.

Which specific regions improved the most? Boxplots enablee us to compare the two years:

gapminder %>% 
  filter(year %in% years & country %in% country_list) %>%
  mutate(year = factor(year)) %>%
  ggplot(aes(group, dollars_per_day, fill = year)) +
  geom_boxplot() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  scale_y_continuous(trans = "log2") +
  xlab("")

The previous data exploration suggested that the income gap between rich and poor countries has narrowed considerably during the last 40 years. A series of histograms and boxplots help us see this clearly. We can conveeey this info with one plot:

Note that the density plots for income distribution in 1970 and 2010 deliver the message that the gap is closing:

gapminder %>% 
  filter(year %in% years & country %in% country_list) %>%
  ggplot(aes(dollars_per_day)) +
  geom_density(fill = "grey") + 
  scale_x_continuous(trans = "log2") + 
  facet_grid(. ~ year)

aes(x = dollars_per_day, y = ..count..)
## Aesthetic mapping: 
## * `x` -> `dollars_per_day`
## * `y` -> `..count..`
p <- gapminder %>% 
  filter(year %in% years & country %in% country_list) %>%
  mutate(group = ifelse(group == "West", "West", "Developing")) %>%
  ggplot(aes(dollars_per_day, y = ..count.., fill = group)) +
  scale_x_continuous(trans = "log2", limit = c(0.125, 300))

p + geom_density(alpha = 0.2) + 
  facet_grid(year ~ .)

p + geom_density(alpha = 0.2, bw = 0.75) + facet_grid(year ~ .)

This plot now shows what is happening very clearly. The developing world distribution is changing. A third mode appears consisting of the countries that most narrowed the gap.

To visualize if any of the groups defined above are driving this we can quickly make a ridge plot:

gapminder %>% 
    filter(year %in% years & country %in% country_list) %>%
  group_by(year) %>%
  mutate(weight = population/sum(population)*2) %>%
  ungroup() %>%
  ggplot(aes(dollars_per_day, fill = group)) +
  scale_x_continuous(trans = "log2", limit = c(0.125, 300)) + 
  geom_density(alpha = 0.2, bw = 0.75, position = "stack") + 
  facet_grid(year ~ .)

Here we can clearly see how the distributions for East Asia, Latin America, and others shift markedly to the right. While Sub-Saharan Africa remains stagnant.

I order the levels of the group so that the West’s density is plotted first, then Sub-Saharan Africa. Having the two extremes plotted first allows us to see the remaining bimodality better