1.2.1 GDP vs Average Life Expectancy

Let’s compare and maybe we can find a connection between GDP and Average Life Expectancy.

ggplot(hpi, aes(x=GDP, y=Avg.Life.Expectancy)) + 
  geom_point(aes(size=Population, color=Region)) +
  coord_trans(x = 'log10') +
  geom_smooth(method = 'loess') + 
  ggtitle('Life Expectancy and GDP per Capita in USD') +
  theme_classic() +
  theme(legend.justification = "left", legend.title = element_text(face = "bold")) +
  ylim(40, 90) +
  labs(x = "GDP in USD (with log transformation)",
       y = "Average Life Expectancy (year)")

After log transformation, the relationship between GDP per capita and life expectancy is more clear and looks relatively strong. These two variables are concordant. The Pearson correlation between this two variable is reasonably high, at approximate 0.62.

cor.test(hpi$GDP, hpi$Avg.Life.Expectancy)

## 
##  Pearson's product-moment correlation
## 
## data:  hpi$GDP and hpi$Avg.Life.Expectancy
## t = 9.3042, df = 138, p-value = 2.766e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5072215 0.7133067
## sample estimates:
##       cor 
## 0.6208781

1.2.2 Average Life Expectany vs HPI

Let’s compare and maybe we can find a connection between Average Life Expectancy and Happy Planet Index Score.

ggplot(hpi, aes(x=Avg.Life.Expectancy, y=HPI)) + 
  geom_point(aes(size=Population, color=Region)) + 
  geom_smooth(method = 'loess') + 
  ggtitle('Average Life Expectancy and Happy Planet Index Score') +
  theme_classic() +
  theme(legend.justification = "left", legend.title = element_text(face = "bold")) +
  ylim(0, 50) +
  labs(x = "Average Life Expectancy (year)",
       y = "Happy Planet Index Score")

Many countries in Europe and Americas end up with middle-to-low HPI index probably because of their big carbon footprints, despite long life expectancy.

cor.test(hpi$Avg.Life.Expectancy, hpi$HPI)

## 
##  Pearson's product-moment correlation
## 
## data:  hpi$Avg.Life.Expectancy and hpi$HPI
## t = 7.5519, df = 138, p-value = 5.314e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4118020 0.6484859
## sample estimates:
##       cor 
## 0.5407609

1.2.3 GDP vs HPI

Let’s compare and maybe we can find a connection between GDP and Happy Planet Index Score.

ggplot(hpi, aes(x=GDP, y=HPI)) + 
  geom_point(aes(size=Population, color=Region)) + 
  coord_trans(x = 'log10') +
  geom_smooth(method = 'loess') + 
  ggtitle('GDP in USD (with log transformation) and Happy Planet Index Score') +
  theme_classic() +
  theme(legend.justification = "left", legend.title = element_text(face = "bold")) +
  ylim(0, 50) +
  labs(x = "GDP",
       y = "Happy Planet Index Score")

Apparently, money (GDP) can’t buy happiness. The correlation between GDP and Happy Planet Index score is indeed very low, at about 0.11.

cor.test(hpi$GDP, hpi$HPI)

## 
##  Pearson's product-moment correlation
## 
## data:  hpi$GDP and hpi$HPI
## t = 1.3507, df = 138, p-value = 0.179
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.05267424  0.27492060
## sample estimates:
##       cor 
## 0.1142272

2.1.1 A simple correlation heatmap

From this heatmap, we can see the correlation of the variables with each other.

qplot(x=Var1, y=Var2, data=melt(cor(hpi_scale, use="p")), fill=value, geom="tile") +
  scale_fill_gradient2(limits=c(-1, 1)) +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) + 
             labs(title="Heatmap of Correlation Matrix", 
                  x=NULL, y=NULL)

2.1.2 Principal Component Analysis (PCA)

PCA is a procedure for identifying a smaller number of uncorrelated variables, called principal components, from a large set of data. The goal of principal components analysis is to explain the maximum amount of variance with the minimum number of principal components.

hpi.pca <- PCA(hpi_scale, graph=FALSE)
print(hpi.pca)

## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 140 individuals, described by 10 variables
## *The results are available in the following objects:
## 
##    name               description                          
## 1  "$eig"             "eigenvalues"                        
## 2  "$var"             "results for the variables"          
## 3  "$var$coord"       "coord. for the variables"           
## 4  "$var$cor"         "correlations variables - dimensions"
## 5  "$var$cos2"        "cos2 for the variables"             
## 6  "$var$contrib"     "contributions of the variables"     
## 7  "$ind"             "results for the individuals"        
## 8  "$ind$coord"       "coord. for the individuals"         
## 9  "$ind$cos2"        "cos2 for the individuals"           
## 10 "$ind$contrib"     "contributions of the individuals"   
## 11 "$call"            "summary statistics"                 
## 12 "$call$centre"     "mean of the variables"              
## 13 "$call$ecart.type" "standard error of the variables"    
## 14 "$call$row.w"      "weights for the individuals"        
## 15 "$call$col.w"      "weights for the variables"

eigenvalues <- hpi.pca$eig
head(eigenvalues)

##        eigenvalue percentage of variance cumulative percentage of variance
## comp 1 6.66741533             66.6741533                          66.67415
## comp 2 1.31161290             13.1161290                          79.79028
## comp 3 0.97036077              9.7036077                          89.49389
## comp 4 0.70128270              7.0128270                          96.50672
## comp 5 0.24150648              2.4150648                          98.92178
## comp 6 0.05229306              0.5229306                          99.44471

2.1.3 Interpretation

The proportion of variation retained by the principal components was extracted above. eigenvalues is the amount of variation retained by each principal component (PC). The first PC corresponds to the maximum amount of variation in the data set. In this case, the first two principal components are worthy of consideration because A commonly used criterion for the number of factors to rotate is the eigenvalues-greater-than-one rule proposed by Kaiser (1960).

fviz_screeplot(hpi.pca, addlabels = TRUE, ylim = c(0, 70)) +
  theme_classic()

The scree plot shows us which components explain most of the variability in the data. In this case, almost 80% of the variances contained in the data are retained by the first two principal components.

head(hpi.pca$var$contrib)

##                         Dim.1       Dim.2       Dim.3      Dim.4
## Avg.Life.Expectancy 12.275001  2.29815687 0.002516184 18.4965447
## Avg.Wellbeing       12.318469  0.07472989 0.198445432 22.1593907
## Happy.Life.Years    14.793710  0.01288175 0.027105103  0.7180341
## Footprint.gha        9.021277 24.71161977 2.982449522  0.4891428
## Inequality          13.363651  0.30494623 0.010038818  9.7957329
## Inequality.LE       12.677892  0.95800977 0.001525891 19.5589843
##                          Dim.5
## Avg.Life.Expectancy 0.31797242
## Avg.Wellbeing       6.37614629
## Happy.Life.Years    0.03254368
## Footprint.gha       7.62967135
## Inequality          2.97699333
## Inequality.LE       0.07545215

Variables that are correlated with PC1 and PC2 are the most important in explaining the variability in the data set.

The contribution of variables was extracted above: The larger the value of the contribution, the more the variable contributes to the component.

fviz_pca_var(hpi.pca, col.var="contrib",
             gradient.cols = c("red", "yellow", "blue"),
             repel = TRUE 
             )

This highlights the most important variables in explaining the variations retained by the principal components.

2.2.1 The visualization of Pam Clustering Analysis

I use fviz_cluster() which provides ggplot2-based elegant visualization of partitioning methods including kmeans, pam, HCPC (from FactoMineR), etc. Observations are represented by points in the plot, using principal components if ncol(data) > 2. An ellipse is drawn around each cluster.

fviz_cluster(pam, stand = FALSE, geom = "point",
             ellipse.type = "norm", ggtheme = theme_classic())

Hmmm.. It’s easy to understand, but which country belong to which cluster? Well, I think we’ll get the idea better if we use world map to visualize our cluster.

2.4.1 Cluster 1

C1 <- hpi[hpi$Cluster == 1, ]
C1 <- C1[, c("Country", "Region", "Avg.Life.Expectancy", "Avg.Wellbeing", "Footprint.gha", "Inequality", "HPI", "GDP", "Population")]

C1$Country

##  [1] "Afghanistan"       "Benin"             "Bolivia"          
##  [4] "Botswana"          "Burkina Faso"      "Burundi"          
##  [7] "Cambodia"          "Cameroon"          "Chad"             
## [10] "Comoros"           "Cote d'Ivoire"     "Djibouti"         
## [13] "Ethiopia"          "Gabon"             "Ghana"            
## [16] "Guinea"            "Haiti"             "India"            
## [19] "Kenya"             "Lesotho"           "Liberia"          
## [22] "Malawi"            "Mauritania"        "Mozambique"       
## [25] "Myanmar"           "Namibia"           "Niger"            
## [28] "Nigeria"           "Pakistan"          "Republic of Congo"
## [31] "Rwanda"            "Senegal"           "Sierra Leone"     
## [34] "South Africa"      "Swaziland"         "Syria"            
## [37] "Tanzania"          "Togo"              "Turkmenistan"     
## [40] "Uganda"            "Yemen"             "Zambia"           
## [43] "Zimbabwe"

summary(C1[, c(2:9)])

##                           Region   Avg.Life.Expectancy Avg.Wellbeing  
##  Americas                    : 2   Min.   :48.91       Min.   :2.867  
##  Asia Pacific                : 4   1st Qu.:56.71       1st Qu.:3.900  
##  Europe                      : 0   Median :60.31       Median :4.400  
##  Middle East and North Africa: 3   Mean   :59.88       Mean   :4.340  
##  Post-communist              : 1   3rd Qu.:63.44       3rd Qu.:4.850  
##  Sub Saharan Africa          :33   Max.   :70.39       Max.   :6.000  
##  Footprint.gha     Inequality          HPI             GDP         
##  Min.   :0.610   Min.   :0.2630   Min.   :12.78   Min.   :  244.2  
##  1st Qu.:1.030   1st Qu.:0.3529   1st Qu.:16.52   1st Qu.:  670.2  
##  Median :1.240   Median :0.3873   Median :19.63   Median : 1158.8  
##  Mean   :1.559   Mean   :0.3867   Mean   :20.11   Mean   : 1917.2  
##  3rd Qu.:1.610   3rd Qu.:0.4268   3rd Qu.:22.93   3rd Qu.: 1664.2  
##  Max.   :5.470   Max.   :0.5073   Max.   :31.50   Max.   :10642.4  
##    Population       
##  Min.   :7.337e+05  
##  1st Qu.:5.608e+06  
##  Median :1.457e+07  
##  Mean   :5.414e+07  
##  3rd Qu.:2.564e+07  
##  Max.   :1.264e+09

Cluster 1 are mostly from Sub Saharan Africa, the countries experiencing conflicts such as Afghanistan, Syria, and Myanmar.

With low income (average GDP is USD 1917), low wellbeing score (average 4.34) and low life expectancy (60 years old), the average HPI of the countries in this cluster is 20.11, the lowest from the three.

2.4.2 Cluster 2

C2 <- hpi[hpi$Cluster == 2, ]
C2 <- C2[, c("Country", "Region", "Avg.Life.Expectancy", "Avg.Wellbeing", "Footprint.gha", "Inequality", "HPI", "GDP", "Population")]

C2$Country

##  [1] "Albania"                "Algeria"               
##  [3] "Argentina"              "Armenia"               
##  [5] "Bangladesh"             "Belarus"               
##  [7] "Belize"                 "Bhutan"                
##  [9] "Bosnia and Herzegovina" "Brazil"                
## [11] "Bulgaria"               "China"                 
## [13] "Colombia"               "Croatia"               
## [15] "Dominican Republic"     "Ecuador"               
## [17] "Egypt"                  "El Salvador"           
## [19] "Estonia"                "Georgia"               
## [21] "Greece"                 "Guatemala"             
## [23] "Honduras"               "Hungary"               
## [25] "Indonesia"              "Iran"                  
## [27] "Iraq"                   "Jamaica"               
## [29] "Kazakhstan"             "Kyrgyzstan"            
## [31] "Latvia"                 "Lebanon"               
## [33] "Lithuania"              "Macedonia"             
## [35] "Malaysia"               "Malta"                 
## [37] "Mauritius"              "Mongolia"              
## [39] "Montenegro"             "Morocco"               
## [41] "Nepal"                  "Nicaragua"             
## [43] "Palestine"              "Panama"                
## [45] "Paraguay"               "Peru"                  
## [47] "Philippines"            "Poland"                
## [49] "Portugal"               "Romania"               
## [51] "Russia"                 "Serbia"                
## [53] "Slovakia"               "Sri Lanka"             
## [55] "Suriname"               "Tajikistan"            
## [57] "Thailand"               "Trinidad and Tobago"   
## [59] "Tunisia"                "Turkey"                
## [61] "Ukraine"                "Uruguay"               
## [63] "Uzbekistan"             "Vanuatu"               
## [65] "Venezuela"              "Vietnam"

summary(C2[, c(2:9)])

##                           Region   Avg.Life.Expectancy Avg.Wellbeing  
##  Americas                    :18   Min.   :67.95       Min.   :4.200  
##  Asia Pacific                :12   1st Qu.:70.85       1st Qu.:4.800  
##  Europe                      : 3   Median :74.03       Median :5.400  
##  Middle East and North Africa: 9   Mean   :73.48       Mean   :5.404  
##  Post-communist              :23   3rd Qu.:75.36       3rd Qu.:5.900  
##  Sub Saharan Africa          : 1   Max.   :80.50       Max.   :7.100  
##  Footprint.gha     Inequality          HPI             GDP         
##  Min.   :0.720   Min.   :0.1018   Min.   :14.27   Min.   :  685.5  
##  1st Qu.:1.890   1st Qu.:0.1652   1st Qu.:25.17   1st Qu.: 3599.3  
##  Median :2.750   Median :0.1904   Median :29.01   Median : 5942.5  
##  Mean   :3.022   Mean   :0.1983   Mean   :29.29   Mean   : 7698.1  
##  3rd Qu.:3.825   3rd Qu.:0.2292   3rd Qu.:34.44   3rd Qu.:11798.9  
##  Max.   :7.920   Max.   :0.3111   Max.   :40.70   Max.   :22242.7  
##    Population       
##  Min.   :2.475e+05  
##  1st Qu.:3.484e+06  
##  Median :9.692e+06  
##  Mean   :4.958e+07  
##  3rd Qu.:3.293e+07  
##  Max.   :1.351e+09

Cluster 2 are dominated with post-communist and developing countries in Asia Pacific and Americas.

The average HPI of the countries in this cluster is 29.29, increases significantly compared to cluster 1’s average HPI.

2.4.3 Cluster 3

C3 <- hpi[hpi$Cluster == 3, ]
C3 <- C3[, c("Country", "Region", "Avg.Life.Expectancy", "Avg.Wellbeing", "Footprint.gha", "Inequality", "HPI", "GDP", "Population")]

C3$Country

##  [1] "Australia"                "Austria"                 
##  [3] "Belgium"                  "Canada"                  
##  [5] "Chile"                    "Costa Rica"              
##  [7] "Cyprus"                   "Czech Republic"          
##  [9] "Denmark"                  "Finland"                 
## [11] "France"                   "Germany"                 
## [13] "Hong Kong"                "Iceland"                 
## [15] "Ireland"                  "Israel"                  
## [17] "Italy"                    "Japan"                   
## [19] "Luxembourg"               "Mexico"                  
## [21] "Netherlands"              "New Zealand"             
## [23] "Norway"                   "Oman"                    
## [25] "Slovenia"                 "South Korea"             
## [27] "Spain"                    "Sweden"                  
## [29] "Switzerland"              "United Kingdom"          
## [31] "United States of America"

summary(C3[, c(2:9)])

##                           Region   Avg.Life.Expectancy Avg.Wellbeing  
##  Americas                    : 5   Min.   :76.30       Min.   :5.500  
##  Asia Pacific                : 5   1st Qu.:80.17       1st Qu.:6.450  
##  Europe                      :17   Median :81.11       Median :7.000  
##  Middle East and North Africa: 2   Mean   :80.80       Mean   :6.897  
##  Post-communist              : 2   3rd Qu.:81.89       3rd Qu.:7.400  
##  Sub Saharan Africa          : 0   Max.   :83.57       Max.   :7.800  
##  Footprint.gha      Inequality           HPI             GDP        
##  Min.   : 2.840   Min.   :0.04322   Min.   :13.15   Min.   :  9703  
##  1st Qu.: 5.000   1st Qu.:0.07118   1st Qu.:24.71   1st Qu.: 28758  
##  Median : 5.600   Median :0.08537   Median :30.02   Median : 44011  
##  Mean   : 6.114   Mean   :0.09316   Mean   :29.03   Mean   : 43775  
##  3rd Qu.: 6.838   3rd Qu.:0.10641   3rd Qu.:31.79   3rd Qu.: 50466  
##  Max.   :15.820   Max.   :0.18770   Max.   :44.71   Max.   :105447  
##    Population       
##  Min.   :   320716  
##  1st Qu.:  4836360  
##  Median :  9519374  
##  Mean   : 36172836  
##  3rd Qu.: 48388748  
##  Max.   :314112078

Cluster 3, the happiest of them all. The average HPI of the countries in this cluster is 29.03, almost the same with cluster 2, but there’s a big difference in average life expectancy (73.48 vs 80.80), average wellbeing (5.404 vs 6.897), inequality (19.83% vs 9.31%), and carbon footprint (3.022 gha vs 6.114 gha). The countries in cluster 3 produce more carbon footprint than countries in cluster 2 (more than twice per capita) and that what makes the HPI score is practically the same with countries in cluster 2.