Table of Contents

  1. Introduction
  2. Descriptive Analysis
  3. Principal Components Analysis
  4. Correlation between components
  5. Conclusion

Introduction

Please refer to the Introduction of “World Happiness Report - A Cluster Analysis [1/2]” as this is the second part of this work.

Descriptive Analysis

Please refer to the Descriptive Analysis of “World Happiness Report - A Cluster Analysis [1/2]” as this is the second part of this work.

Outliers

Please refer to the outliers detection in the “World Happiness Report - A Cluster Analysis [1/2]” as this is the second part of this work.

Principal Components Analysis

  • Standardize the data (z-score)
  • Correlation matrix (using the Pearson test), where the correlation matrix and the identity matrix are compared
  • Bartlett test, checks if there is any difference among the variances (H0 states that the variances are the same)
chisq p-value degrees of freedom
313.0526 6.729122e-46 36

Since the p-value is very low (<0.05), there is no proof to say that the correlation matrix is the same as the identity matrix. The null hypothesis is not accepted. This means that the variables are correlated so we can go on with the analysis.

Eigenvalues

Using the Principal components analysis function, the eigenvalues are calculated:

components eigenvalue percentage of variance cumulative percentage of variance
comp 1 4.6181826 51.313140 51.31314
comp 2 1.7267115 19.185684 70.49882
comp 3 1.0142289 11.269211 81.76803
comp 4 0.5323246 5.914717 87.68275
comp 5 0.4069073 4.521193 92.20394
comp 6 0.2331299 2.590332 94.79428
comp 7 0.1853060 2.058956 96.85323
comp 8 0.1547838 1.719821 98.57305
comp 9 0.1284253 1.426948 100.00000

The first three components have an eigenvalue > 1 and together have the 81% of total cumulative variance. Using three components for the analysis is then the recommendation.

In this screeplot is shown how the graph starts to fall straight after the third component. Therefore, three components will be used for the analysis.

Loadings (cargas factoriales)

Variables Comp.1 Comp.2 Comp.3
Life ladder 0.432 N/A N/A
log GDP per capita 0.371 0.370 N/A
Social support 0.333 0.280 0.431
Healthy life expectancy 0.303 0.335 -0.379
Freedom to make life choices 0.257 -0.486 N/A
Perception of corruption -0.392 0.199 0.294
Positive affect 0.155 -0.559 0.295
Negative affect -0.345 N/A -0.538
Confidence in national goverment 0.331 -0.274 -0.445

Given the correlation between the variable and the components, these groups are defined:

First component Second component Third component
Quality of life Economy and Corruption Social support and Corruption

Correlation between components

COS2 how well a variable is represented in a component.

  • The closer the variables arrow with each other, the more correlated are the variables.
  • The closer the variables arrow to the circumference, the more are significant to the components (x or y depending on the axis).

Components 1 (Quality of Life) and 2 (Economy-Corruption)

On Component 1: On Component 2
Biggest influence: log GDP per capita, Life ladder log GDP per capita, Positive affect

  • Best Quality of life & Economy (perceived as corrupted): the Netherlands
  • Best Quality of life & Economy: Scandivinian countries and Switerzland
  • Worst Quality of life & Economy: Bolivia, El Salvador

Components 1 (Quality of Life) and 3 (Social Support-Corruption)

On Component 1: On Component 3
log GDP per capita, Life ladder, Negative affect, Perception of corruption Negative affect, Social support, Confidence in the government

  • Best Social support & Quality of life: Iceland, Finland
  • Best Quality of life: Scandinivian countries, Switerzland
  • Best Social support: Latvia, Panama
  • Worst Social support & Quality of life: Bolivia, Ecuador

Components 2 (Economy-Corruption) and 3 (Social Support-Corruption)

On Component 2: On Component 3
Positive affect, Freedom to make life choices Negative affect, Social support, Confidence in the government

  • Best Social Support & Economy (albeit perceived as corrupted): Lithuania, Latvia
  • Worst Social Support & Economy: El Salvador, Ecuador

Conclusion

The analysis confirms that Nordic countries and Switerzland are the countries that score best and the Latin American countries El Salvador, Ecuador and Bolivia appear to be the worst ranked.