life_expectancy PCA
Lily C
Introduction
This activity aims to explore and analyze the relationship between a country’s development level and its health outcomes using Principal Component Analysis (PCA). The focus is on understanding how various health indicators (such as mortality rates, life expectancy, and disease prevalence) vary across countries with different stages of development.
About the dataset
The Global Health Observatory (GHO) data repository under World Health Organization (WHO) keeps track of the health status as well as many other related factors for all countries. The dataset related to life expectancy, health factors for 193 countries has been collected from the same WHO data repository website and its corresponding economic data was collected from United Nation website.
You can read more about the dataset in here: https://www.kaggle.com/datasets/kumarajarshi/life-expectancy-who?resource=download
library(tidyverse)
setwd("~/data 110")
life_data<- read_csv("life_expectancy_who.csv")
# Fix the columns' names
names(life_data) <- tolower(names(life_data)) # Convert all column names to lowercase
# Replace spaces and slashes with underscores to improve readability
names(life_data) <- gsub(" ", "_", names(life_data))
names(life_data) <- gsub("/", "_", names(life_data)) Data Preparation:
The first step is to clean and filter the dataset to retain relevant variables. The code is set up, but you need to add other indicators that you believe can be relevant to this analysis. We focus on numerical health and development indicators and remove any missing values.
# Clean & filter: keep only numeric columns + identifiers
life_clean <- life_data |>
select(country, status, life_expectancy, adult_mortality, infant_deaths,
hiv_aids, hepatitis_b, measles, polio, gdp) |>
drop_na()Principal Component Analysis (PCA) Setup:
Use PCA to reduce the dimensionality of the dataset while retaining as much variance as possible.
Ensure that the dataset is scaled before performing PCA.
Perform PCA on the numerical columns and extract the principal components (PC1 and PC2). What do the first two principal components explain about the data?
# Perform PCA on numeric variables
life_expectancy_pca <- life_clean |>
select(where(is.numeric)) |>
scale() |>
prcomp()
life_expectancy_pca## Standard deviations (1, .., p=8):
## [1] 1.6555745 1.2661279 1.0718721 0.9491823 0.7173510 0.6698868 0.6430729
## [8] 0.4788035
##
## Rotation (n x k) = (8 x 8):
## PC1 PC2 PC3 PC4 PC5
## life_expectancy 0.5344423 -0.16477535 0.1049686 -0.04053914 -0.06961659
## adult_mortality -0.4659712 0.27481309 -0.1568497 -0.12520327 0.16246779
## infant_deaths -0.2103954 -0.59185580 -0.2699163 -0.07038576 0.03096162
## hiv_aids -0.3881862 0.30550119 -0.2022601 -0.44179067 -0.21896461
## hepatitis_b 0.2807830 0.28873227 -0.5798968 0.16168086 0.65808735
## measles -0.1415068 -0.58205466 -0.4039493 -0.09010430 0.06713094
## polio 0.3341892 0.17366594 -0.5809920 -0.05903679 -0.64794562
## gdp 0.3028892 -0.03726634 0.1166566 -0.86301955 0.24986912
## PC6 PC7 PC8
## life_expectancy 0.11802175 0.04441094 0.8085856748
## adult_mortality -0.26756498 -0.59496125 0.4637944019
## infant_deaths -0.61813266 0.35976802 0.1230929665
## hiv_aids 0.33550122 0.55582922 0.2245877253
## hepatitis_b 0.01508458 0.20510244 -0.0001685303
## measles 0.60225229 -0.31769442 -0.0418361861
## polio -0.19689155 -0.20475021 -0.1288341767
## gdp -0.13464452 -0.14404938 -0.2171264484# View PCA resultVisualize PCA Results:
Create a scatter plot of the first two principal components (PC1 and PC2) to visualize how countries cluster based on their health and development indicators.
Add color coding or labels based on the development status (e.g., developed vs. developing countries) to better understand how these groups are positioned in the PCA space.
Add the arrows of PC1 and PC2, make sure they are labeled.
library(ggplot2)
library(broom)
arrow_style <- arrow(
angle = 20, length = grid::unit(8, "pt"),
ends = "first", type = "closed"
)
life_expectancy_pca |>
augment(life_clean) |>
ggplot(aes(.fittedPC1, .fittedPC2, color = status)) +
geom_point(alpha = 0.5) 
Create the Rotation Arrows:
life_expectancy_pca |>
augment(life_clean) |>
ggplot(aes(.fittedPC1, .fittedPC2, color = status)) +
geom_point(alpha = 0.5) +
geom_segment(aes(x = -10, y = 0, xend = 5, yend = 0),
arrow = arrow(type = "closed", length = unit(0.1, "inches")),
color = "black") +
geom_segment(aes(x = 0, y = -14, xend = 0, yend = 4),
arrow = arrow(type = "closed", length = unit(0.1, "inches")),
color = "black") +
geom_text(aes(x = 5, y = 0, label = "PC1"),
vjust = -0.5, color = "black") +
geom_text(aes(x = 0, y = 4, label = "PC2"),
hjust = -0.5, color = "black") 
arrow_style <- arrow(
angle = 20, length = grid::unit(8, "pt"),
ends = "first", type = "closed"
)
life_expectancy_pca |>
# extract rotation matrix
tidy(matrix = "rotation") |>
pivot_wider(
names_from = "PC", values_from = "value",
names_prefix = "PC"
) |>
ggplot(aes(PC1, PC2)) +
geom_segment(
xend = 0, yend = 0,
arrow = arrow_style
) +
geom_text(aes(label = column), hjust = 1) +
xlim(-1.0, 0.5) + ylim(-0.7, 0.5) +
coord_fixed()+
theme_minimal()## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_segment()`).## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_text()`).
Summarize the findings of the PCA.
What does PC1 show?
The difference between developed and developing. Is the country developed or not.
What does PC2 show?
The different factors: hiv_aids, adult_mortality, infant_deaths, measles, hepatisis, polio, and gdp. It seems that for developing countries, infanct deaths are correlated with measles, and adult mortality and hiv/aids are correlated. For developed countries, they have a higher gdp but also higher polio and hepatitis rates?
What does the analysis reveal about the relationship between development level and health outcomes in different countries?
Plot the variance explained by each PC- bargraph
life_expectancy_pca |>
# extract eigenvalues
tidy(matrix = "eigenvalues") |>
ggplot(aes(PC, percent)) +
geom_col(fill= "lightblue") +
scale_x_continuous(
# create one axis tick per PC
breaks = 1:8
) +
scale_y_continuous(
name = "variance explained",
breaks = seq(0, 1, by = 0.1),
# format y axis ticks as percent values
label = scales::label_percent(accuracy = 1)
)+
xlab("Principal Component (PC)") +
theme_minimal()
How much variation is explained by PC1 and PC2?
About 54.3 percent of the variance is explained by PC1 and PC2?
life_expectancy_pca |>
tidy(matrix = "eigenvalues")## # A tibble: 8 × 4
## PC std.dev percent cumulative
## <dbl> <dbl> <dbl> <dbl>
## 1 1 1.66 0.343 0.343
## 2 2 1.27 0.200 0.543
## 3 3 1.07 0.144 0.687
## 4 4 0.949 0.113 0.799
## 5 5 0.717 0.0643 0.864
## 6 6 0.670 0.0561 0.920
## 7 7 0.643 0.0517 0.971
## 8 8 0.479 0.0287 1