The Analysis of Human Development Index (HDI) for Categorizing the Member States of the United Nations (UN)

The Human Development index (HDI), which is to evaluate the development of a UN country from the perspective of well-being of human-beings, in addition to the economic advancement, is basically an index composed of three measures, namely life expectancy, education, and per capita income. It has widely accepted and practiced by many people such as academicians, politicians, and donor organizations. However, the current version of the index formulation published in 2016 needs research to better understand and to gap-fill the knowledge base that can enhance the index formulation to facilitate the direction of attention such as release of funds.

Therefore, in this paper, based on principal component analysis and K-means clustering algorithm, the data that reflected the measures of life expectancy index (LEI), education index (EI), and income index (II) were analyzed to categorize and to rank the member states of the UN using R statistical software package, an open source extensible programming language for statistical computing and graphics.

The outcome of the study showed that the proportion of total eigen value (i.e., proportion of total variance) explained by PCA-1 (i.e., first principal component) accounted for more than 85% of the total variation. Moreover, the proportion of total eigen value explained by PCA-1 increased with time (i.e., yearly) though the amount of increase with time was not significant. However, the proportions of total eigen value explained by PCA-2 and PCA-3 decreased with time. Therefore, the loss of information in choosing PCA-1 to represent the chosen explanatory variables (i.e., LEI, EI, and II) might diminish with time if the trend of increasing pattern of proportion of total eigen value explained by PCA-1 with time continued in the future as well. On the other hand, the correlation between EI and PCA-1 increased with time although the magnitude of increase was not that significant. This same trend was observed in II as well. However, in contrast to these observations, the correlation between PCA-1 and LEI decreased with time.

These findings imply that the contributions of EI and II to PCA-1 increase with time, but the contribution of LEI to PCA-1 decreases with time. On top of these, as per Hopkins statistic, the clusterability of the information conveyed by PCA-1 alone is far better than the clusterability of the information conveyed by PCA scores (i.e., PCA-1, PCA-2, and PCA-3) and the explanatory variables. In short, choosing PCA-1 to represent the chosen explanatory variables is becoming more concrete.

Article by Sivarajah Mylevaganam, from Texas A&M University, College Station, USA.

Full access: http://mrw.so/3j2wos

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