Alberto Arcagni

PARSEC: An R Package for Poset-Based Evaluation of Multidimensional Poverty

The paper introduces PARSEC, a new software package implementing basic partial order tools for multidimensional poverty evaluation with ordinal variables. The package has been developed in the R environment and is freely available from the authors. Its main goal is to provide socio-economic scholars with an integrated set of elementary functions for multidimensional poverty evaluation, based on ordinal information. The package is organized in four main parts. The first two comprise functions for data management and basic partial order analysis; the third and the fourth are devoted to evaluation and implement both the poset-based approach and a more classical counting procedure. The paper briefly sketches the two evaluation methodologies, illustrates the structure and the main functionalities of PARSEC, and provides some examples of its use.

Higher order assortativity in complex networks

Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metric and describes the tendency of high degree nodes to be directly connected to high degree nodes and low degree nodes to low degree nodes. It can be interpreted as a first order measure of the connection between nodes, i.e. the first autocorrelation of the degree–degree vector. Even though assortativity has been used so extensively, to the author’s knowledge, no attempt has been made to extend it theoretically. Indeed, Newman assortativity is about “being adjacent”, but even though two nodes may not by connected through an edge, they could have possibly a strong level of connectivity through a large number of walks and paths between them. This is the scope of our paper. We introduce, for undirected and unweighted networks, higher order assortativity by extending the Newman index based on a suitable choice of the matrix driving the connections. Higher order assortativity be defined for paths, shortest paths and random walks of a given length. The Newman assortativity is a particular case of each of these measures when the matrix is the adjacency matrix, or, in other words, the autocorrelation is of order 1. Our higher order assortativity indices help discriminating networks having the same Newman index and may reveal new topological network features. An application to airline network (Italy and US) and to Enron email network, as well as examples and simulations, are discussed.

Measuring Structural Dissimilarity Between Finite Partial Orders

In this paper, we address the problem of measuring structural dissimilarity between two partial orders with n elements. We propose a structural dissimilarity measure, based on the distance between isomorphism classes of partial orders, and propose an interpretation in terms of graph theory. We give examples of structural dissimilarity computations, using a simulated annealing algorithm for numerical optimization.

PARSEC: An R Package for Partial Orders in Socio-Economics

Partially ordered sets are getting more important in socio-economical applications. In particular, their application in poverty evaluation (Fattore et al., New perspectives in statistical modeling and data analysis. Springer, Berlin, 2011) shows the advantages of their use in multivariate statistics on ordinal variables. A combinatory approach is necessary to apply this methodology, therefore the development of computational tools about partial orders is required. R is a widespread environment for statistical computing and graphics. The recent publication of the parsec (PARtial orders in Socio-EConomics) package on CRAN (the Comprehensive R Archive Network) is an achievement for the diffusion of computational tools devoted to the applications of partial orders in socio-economics. The package also implements functions related to composite indicators (Fattore et al., Quality of life in Italy. Springer, Berlin, 2012) in order to provide results of different approaches that can be compared. The aim of this work is to explain the functionalities of parsec, through examples and descriptions of its main functions.

Non-aggregative Assessment of Subjective Well-Being

In this paper, we introduce a new methodology for socio-economic evaluation with ordinal data, which allows to compute synthetic indicators without variable aggregation, overcoming some of the major problems when classical evaluation procedures are employed in an ordinal setting. In the paper, we describe the methodology step by step, discussing its conceptual and analytical structure. For exemplification purposes, we apply the methodology to real data pertaining to subjective well-being in Italy, for year 2010.