Modeling Human Development Index Using Finite Mixtures of Distributions

Abstract

The Human Development Index (HDI) measures the development of a country which was designed by the United Nations Development Programme (UNDP). Since the values of HDI for different countries show differences according to the development of a country, the distribution of HDI may have one more mode, thick tail or skewness. Therefore, we can use mixtures of distributions to model the HDI data set to handle modality, heavy-tailedness and/or skewness. In this study, we propose to model the data set from the HDI report 2015 for 188 countries with finite mixtures of distributions. We give the basic scheme of the maximum likelihood (ML) estimation using Expectation-Maximization (EM) algorithm for the finite mixture model. To obtain the best model for HDI data set, we first find the appropriate cluster number using model-based clustering. Then, we use the finite mixture models obtained from some symmetric and/or heavy-tailed and skew and/or heavytailed distributions to find the best model for HDI data set.

Compact Urban Form and Human Development: Retest Based on Heterogeneous Effects

“…It is possible that the insignificance of the coefficients is due to poor model setting. According to Doğru (2017) [ 24 ], HDI does not necessarily obey a normal distribution. The results of fixed effects can be biased when the dependent variable does not obey a normal distribution.…”

“…Each latent class has its own regression model that can be fitted. As a result, FMMs are widely used to model and analyze heterogeneous data sets with skewness [ 23 , 24 ].…”