Marta Nai Ruscone

The 2030 Agenda for Sustainable Development has the seventeen Sustainable Development Goals (SDGs) at its heart and describes the path to ensure well-being, reduce inequality, encourage economic growth, and preserve the environment. Goals and targets are interconnected by construction. A standard approach to quantify synergies and trade-offs relies on the computation of positive and negative correlation coefficients between the indicators. In this work, we propose a method based on copulas to analyze SDGs interactions, offering a practical and innovative solution. Copulas allow studying more specific types of dependence beyond the linear association described by the correlation coefficients. We illustrate the practical application of this approach by analyzing the interactions between the goals' targets related to health and well-being (Goal 3) and those related to biodiversity (Goals 6,13,14,15).

Existing methods can perform likelihood-based clustering on a multivariate data matrix of ordinal data, using finite mixtures to cluster the rows (observations) of the matrix. These models can incorporate the main effects of individual rows and columns, as well as cluster effects, to model the matrix of responses. However, many real-world applications also include available covariates, which provide insights into the main characteristics of the clusters and determine clustering structures based on both the individuals’ similar patterns of responses and the effects of the covariates on the individuals' responses. In our research we have extended the mixture-based models to include covariates and test what effect this has on the resulting clustering structures. We focus on clustering the rows of the data matrix, using the proportional odds cumulative logit model for ordinal data. We fit the models using the Expectation-Maximization algorithm and assess performance using a simulation study. We also illustrate an application of the models to the well-known arthritis clinical trial data set.

The HDI (Human Development Index) is a widely used index based on the average of measures of health, education, and income. It assesses the progress of countries worldwide. The publicly available data set associated with the HDI can be seen as a table with 3 dimensions (three-way table): countries, indexes regarding progress, and years (from 2010 to 2018). Thus, modeling the serial dependence structure of this type of intricate three-way tables is a challenge. D-vine copulas are a special class of multivariate copulas that are particularly suited for modeling serial dependence. This work aims to assess the evolution of the dependence relationship between the indexes of the HDI data set over time through D-vine copulas, which has not been fully used before in the area, as far as we are concerned. We tested our approach to European and African countries and compare their results.