Chapter 5 Principal Component Analysis (PCA)
Main information about PCA:
- Step 1: No country selection process has been decided at this stage. Taking all countries in the imputed file - 194 economies.
- Step 2: Countries identified as with “at least 1 data point available” - 129 economies.
- Step 3: Countries identified as with “at least 2 data points available” - 107 economies.
Taking 2022 as the reference year.
The difference from the previous edition is that we have a full panel data set. All pillars are available for the same number of countries.
5.1 Pillar 1 - Economy
Pillar 1, Economy, includes 6 indicators. Three principal components were retained, together explaining 92.6 per cent of the total variance of the six original variables selected to measure the economy.
TO CHECK: In this case, the first component (interpreted as Economic Development) accounts for 48.7 per cent of total variance. The second component (Employment) accounts for 17.2 per cent of total variance, while the third component (Trade) accounts for a further 26.6 per cent.
## [1] "IGI_1-1" "IGI_1-2" "IGI_1-3" "IGI_1-4" "IGI_1-5"
## [6] "IGI_1-6"## # A tibble: 6 × 2
## Code Indicator
## <chr> <chr>
## 1 IGI_1-1 GDP per capita, PPP (constant 2017 internation…
## 2 IGI_1-2 Adjusted net national income per capita (const…
## 3 IGI_1-3 Labour productivity - GDP per person employed …
## 4 IGI_1-4 Employment to population ratio, 15+, total (%)…
## 5 IGI_1-5 Electricity consumption/population (kWh per ca…
## 6 IGI_1-6 Exports of goods and services (% of GDP)## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.9274 1.0261 0.8766 0.61866
## Proportion of Variance 0.6191 0.1755 0.1281 0.06379
## Cumulative Proportion 0.6191 0.7946 0.9227 0.98650
## PC5 PC6
## Standard deviation 0.27189 0.08419
## Proportion of Variance 0.01232 0.00118
## Cumulative Proportion 0.99882 1.00000## [1] 3.714927619 1.052899125 0.768421213 0.382739047
## [5] 0.073924399 0.007088597
##
## Loadings:
## [,1] [,2] [,3]
## IGI_1-1 0.847 0.502
## IGI_1-2 0.899 0.314
## IGI_1-3 0.828 -0.142 0.494
## IGI_1-4 0.992
## IGI_1-5 0.871 0.169
## IGI_1-6 0.203 0.938
##
## [,1] [,2] [,3]
## SS loadings 3.016 1.038 1.482
## Proportion Var 0.503 0.173 0.247
## Cumulative Var 0.503 0.676 0.923
5.2 Pillar 2 - Living conditions
Pillar 2, Living Conditions, includes 7 indicators. Three principal components were retained, together explaining 91.4 per cent of the total variance of the 7 original variables selected to measure the economy.
TO CHECK: The first component (Social & Health conditions) accounts for 45.7 per cent of total variance, while the second (Logistics & Finance) and third (Environmental Conditions) account for 29.2 and 16.4 per cent of total variance, respectively.
## [1] "IGI_2-1" "IGI_2-2" "IGI_2-3" "IGI_2-4" "IGI_2-5"
## [6] "IGI_2-6" "IGI_2-7"## # A tibble: 7 × 2
## Code Indicator
## <chr> <chr>
## 1 IGI_2-1 Logistics performance index: Overall (1=low to…
## 2 IGI_2-2 Fixed broadband subscriptions per 100 inhabita…
## 3 IGI_2-3 Under-five mortality rate, by sex (deaths per …
## 4 IGI_2-4 Proportion of population using safely managed …
## 5 IGI_2-5 School enrollment, secondary (% gross)
## 6 IGI_2-6 Universal health coverage (UHC) service covera…
## 7 IGI_2-7 Proportion of adults (15 years and older) with…## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 2.355 0.70607 0.53876 0.48257
## Proportion of Variance 0.792 0.07122 0.04147 0.03327
## Cumulative Proportion 0.792 0.86323 0.90470 0.93797
## PC5 PC6 PC7
## Standard deviation 0.41421 0.40139 0.31865
## Proportion of Variance 0.02451 0.02302 0.01451
## Cumulative Proportion 0.96248 0.98549 1.00000## [1] 5.5441085 0.4985323 0.2902589 0.2328752 0.1715719
## [6] 0.1611129 0.1015403
##
## Loadings:
## [,1] [,2] [,3]
## IGI_2-1 0.318 -0.873 -0.304
## IGI_2-2 0.590 -0.637 -0.345
## IGI_2-3 0.882 -0.211 -0.289
## IGI_2-4 0.763 -0.444 -0.287
## IGI_2-5 0.788 -0.349 -0.283
## IGI_2-6 0.767 -0.488 -0.296
## IGI_2-7 0.399 -0.386 -0.831
##
## [,1] [,2] [,3]
## SS loadings 3.179 1.918 1.236
## Proportion Var 0.454 0.274 0.177
## Cumulative Var 0.454 0.728 0.905
5.3 Pillar 3 - Equality
Pillar 3, Equality, includes 10 indicators. Six principal components were retained. Together, these six principal components explained 86.9 per cent of the total variance of the seven original variables selected to measure inequality.
TO CHECK: The first component (Equal Labour Participation) accounts for 24.1 per cent of total variance. The second component (Income Equality) accounts for 21.2 per cent, whereas the third (School Enrolment) and fourth (Equal Political Participation) components account for 11.2 and 10.5 per cent, respectively.
The fifth and six one for 10 and 9.9 per cent, respectively.
## # A tibble: 10 × 2
## Code Indicator
## <chr> <chr>
## 1 IGI_3-1 "Gini index"
## 2 IGI_3-2 "Poverty headcount ratio at $3.65 a day (201…
## 3 IGI_3-3 "School enrolment, secondary (gross), gender…
## 4 IGI_3-4 "Ratio of female to male employment-to-popul…
## 5 IGI_3-5 "Ratio of youth to adult employment-to-popul…
## 6 IGI_3-6 "Gender parity in the number of seats held b…
## 7 IGI_3-7 "Ratio of female to male labour force partic…
## 8 IGI_3-8 "Ratio of female age of first marriage to ma…
## 9 IGI_3-9 "Ratio of the share of wage and salaried wor…
## 10 IGI_3-10 "Employment in services, female (% of female…## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.5786 1.5174 1.0696 0.98217
## Proportion of Variance 0.2492 0.2302 0.1144 0.09647
## Cumulative Proportion 0.2492 0.4794 0.5939 0.69033
## PC5 PC6 PC7 PC8
## Standard deviation 0.95956 0.86754 0.81571 0.68809
## Proportion of Variance 0.09208 0.07526 0.06654 0.04735
## Cumulative Proportion 0.78240 0.85767 0.92420 0.97155
## PC9 PC10
## Standard deviation 0.52779 0.07704
## Proportion of Variance 0.02786 0.00059
## Cumulative Proportion 0.99941 1.00000## [1] 2.492131895 2.302357500 1.144135543 0.964663256
## [5] 0.920750451 0.752617838 0.665375479 0.473473044
## [9] 0.278559465 0.005935528
##
## Loadings:
## [,1] [,2] [,3] [,4] [,5] [,6]
## IGI_3-1 -0.208 0.917
## IGI_3-2 0.212 -0.858 0.189
## IGI_3-3 -0.119 -0.984
## IGI_3-4 -0.974 0.153
## IGI_3-5 -0.147 0.833 0.229
## IGI_3-6 -0.140 -0.225 0.737 -0.298
## IGI_3-7 -0.978 0.132
## IGI_3-8 -0.335 -0.733 0.207
## IGI_3-9 -0.831 -0.156
## IGI_3-10 0.114 -0.984
##
## [,1] [,2] [,3] [,4] [,5] [,6]
## SS loadings 2.129 2.075 1.008 0.998 1.329 1.038
## Proportion Var 0.213 0.208 0.101 0.100 0.133 0.104
## Cumulative Var 0.213 0.420 0.521 0.621 0.754 0.858
5.4 Pillar 4 - Environment
Pillar 4, Environment, includes 4 indicators. Three principal components were retained. Together, these three principal components explained 84.4 per cent of the total variance of the seven original variables selected to measure inequality.
The first component accounts for 31.6 per cent of total variance. The second component accounts for 27.5 per cent, whereas the third component accounts for 25.4 per cent.
## [1] "IGI_4-1" "IGI_4-2" "IGI_4-3" "IGI_4-4"## # A tibble: 4 × 2
## Code Indicator
## <chr> <chr>
## 1 IGI_4-1 Carbon dioxide emissions per unit of GDP PPP (…
## 2 IGI_4-2 Energy intensity level of primary energy (mega…
## 3 IGI_4-3 Water Use Efficiency (United States dollars pe…
## 4 IGI_4-4 Terrestrial biodiversity area as % total prote…## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.2608 0.9565 0.9184 0.8075
## Proportion of Variance 0.3974 0.2287 0.2109 0.1630
## Cumulative Proportion 0.3974 0.6261 0.8370 1.0000## [1] 1.5895836 0.9148873 0.8434482 0.6520808
##
## Loadings:
## [,1] [,2] [,3]
## IGI_4-1 -0.602 0.598 -0.142
## IGI_4-2 -0.883 0.220
## IGI_4-3 -0.136 0.118 0.951
## IGI_4-4 0.895 0.188
##
## [,1] [,2] [,3]
## SS loadings 1.163 1.176 1.009
## Proportion Var 0.291 0.294 0.252
## Cumulative Var 0.291 0.585 0.837