摘要
To categorize the nations to reflect the development status, to date, there are many conceptual frameworks. The Human Development index (HDI) that is published by the United Nations Development Programme is widely accepted and practiced by many people such as academicians, politicians, and donor organizations. However, though the development of HDI has gone through many revisions since its formulation in 1990, even 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 reflect the measures of life expectancy index (LEI), education index (EI), and income index (II) are 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 shows that the proportion of total eigen value (i.e., proportion of total variance) explained by PCA-1 (i.e., first principal component) accounts for more than 85% of the total variation. Moreover, the proportion of total eigen value explained by PCA-1 increases with time (i.e., yearly) though the amount of increase with time is not significant. However, the proportions of total eigen value explained by PCA-2 and PCA-3 decrease with time. Therefore, the loss of information in choosing PCA-1 to represent the chosen explanatory variables (i.e., LEI, EI, and II) may diminish with time if the trend of increasing pattern of proportion of total eigen value explained by PCA-1 with time continues in the future as well. On the other hand, the correlation between EI and PCA-1 increases with time although the magnitude of increase is not that significant. This same trend is observed in II as well. However, in contrast to these observations, the correlation between PCA-1 and LEI decreases 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. Therefore, choosing PCA-1 to represent the chosen explanatory variables is becoming more concrete.
To categorize the nations to reflect the development status, to date, there are many conceptual frameworks. The Human Development index (HDI) that is published by the United Nations Development Programme is widely accepted and practiced by many people such as academicians, politicians, and donor organizations. However, though the development of HDI has gone through many revisions since its formulation in 1990, even 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 reflect the measures of life expectancy index (LEI), education index (EI), and income index (II) are 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 shows that the proportion of total eigen value (i.e., proportion of total variance) explained by PCA-1 (i.e., first principal component) accounts for more than 85% of the total variation. Moreover, the proportion of total eigen value explained by PCA-1 increases with time (i.e., yearly) though the amount of increase with time is not significant. However, the proportions of total eigen value explained by PCA-2 and PCA-3 decrease with time. Therefore, the loss of information in choosing PCA-1 to represent the chosen explanatory variables (i.e., LEI, EI, and II) may diminish with time if the trend of increasing pattern of proportion of total eigen value explained by PCA-1 with time continues in the future as well. On the other hand, the correlation between EI and PCA-1 increases with time although the magnitude of increase is not that significant. This same trend is observed in II as well. However, in contrast to these observations, the correlation between PCA-1 and LEI decreases 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. Therefore, choosing PCA-1 to represent the chosen explanatory variables is becoming more concrete.
