Giancarlo Ragozini

On the use of Multiple Correspondence Analysis to visually explore affiliation networks

Abstract In this paper we discuss the use of Multiple Correspondence Analysis to analyze and graphically represent two-mode networks, and we propose to apply it in a Greenacres doubling perspective. We discuss how Multiple Correspondence Analysis: (i) properly takes into account the nature of relational data and the intrinsic asymmetry of actors/events in two-mode networks; (ii) allows a proper graphical appraisal of the underlying relational structure of actors or events; (iii) makes it possible to add actor and event attributes to the analysis in order to improve results interpretation; and (iv) gives different results with respect to the usual Simple Correspondence Analysis.

Interval Archetypes: A New Tool for Interval Data Analysis

Archetypal analysis aims at synthesizing single-valued data sets through a few (not necessarily observed) points that are called archetypes, under the constraint that all points can be represented as a convex combination of the archetypes themselves and that the archetypes are a convex combination of the data. In this paper, we extend this methodology to the case of interval-valued data, which represent a special case of set-valued data, where the sets are compact and identified by ordered pairs of values. In addition, we propose to use interval archetypes as a tool in an analysis strategy to explore and mine complex data sets.

Future-oriented or present-focused? The role of social support and identity styles on ‘futuring’ in Italian late adolescents and emerging adults

Late adolescence and emerging adulthood are periods in the life cycle when individuals are involved in anticipating and planning for the future (futuring). However, in the last five or six years, as the effects of the recession have made themselves felt in Southern Europe, the situation that young people face has deteriorated dramatically. As a consequence, contemporary young people’s relationship with the future is strongly marked by these social difficulties, and family support becomes essential to their survival. The present study was interested in how futuring could be influenced by identity styles and perceptions of social support. Participants were 1201 Italian late adolescents and emerging adults attending the last year of high school and first years of university. We used three self-report measures: Functions of Identity Scale, Identity Style Inventory, and Social Support Scale. Findings indicate that futuring was influenced by the normative style and the diffuse-avoidant style and by the interactions between both normative identity style and diffuse/avoidant identity styles with peer support. Gender and age differences are discussed.

Multiple factor analysis for time-varying two-mode networks

Most social networks present complex structures. They can be both multi-modal and multi-relational. In addition, each relationship can be observed across time occasions. Relational data observed in such conditions can be organized into multidimensional arrays and statistical methods from the theory of multiway data analysis may be exploited to reveal the underlying data structure. In this paper, we adopt an exploratory data analysis point of view, and we present a procedure based on multiple factor analysis and multiple correspondence analysis to deal with time-varying two-mode networks. This procedure allows us to create static displays in order to explore network evolutions and to visually analyze the degree of similarity of actor/event network profiles over time while preserving the different statuses of the two modes.

Exploring Data Through Archetypes

In this paper we propose a mixed analytical and graphical exploratory strategy based on data archetypes for the exploratory analysis of multivariate data. Our approach is of considerable help in exploring the periphery of the data scatter, exploiting an outward-inward perspective, to highlight small peripheral groups as well as anomalies, outliers and irregularities in the data cloud shape. The strategy is carried out in a comprehensive quantitative programming environment provided by the joint use of the software system R and of the visualization system GGobi. It provides a visualization system involving both static and dynamic graphics based on the so-called multiple views paradigm. The views are organized in a spreadplot and heavily exploit dynamics and interactive statistical graphics.

Archetypal Analysis for Data Driven Benchmarking

In this work, adopting an exploratory and graphical approach, we suggest to consider archetypal analysis as a basis for a data driven benchmarking procedure. The procedure is aimed at defining some reference performers, at understanding their features, and at comparing observed performances with them. Being archetypes some extreme points, we propose to consider them as reference performers. Then, we offer a set of graphical tools in order to describe these archetypal benchmarks, and to evaluate the observed performances with respect to them.

Exploring the Periphery of Data Scatters: Are There Outliers?

Outliers are observations that are particularly discordant with respect to others, lying hence on the periphery of the data region. In the literature, many tools have been proposed with the aim of detecting multiple outliers. Most of the recent and attractive methods are based on some measure of the distance of each data point from a center. However, they are really effective only if the shape of the data scatter is symmetrical with respect to such a center. Otherwise, asymmetry will make these measures misleading. For this reason, we propose a method that allows direct exploration of the periphery of the data scatter, without considering any center. The methodology we propose is based on a two-step procedure that exploits the sample convex hull and radial projections. It explores gaps in the data scatter and proximities to its boundary, highlighting how the data structure is sparse at its periphery. A complementary graphical display is finally offered as a useful tool to visualize boundary features.

Archetypal Networks

In this paper we propose a method to analyze and synthesize a set of N networks that refer to a common scenario and that are comparable among each other. Examples of this type of data are: a set of collaboration networks, each defined for a different scientific field; or a set of ego networks, where egos belong to a same category; a set of governance networks, etc. For these kind of sets of networks it can be of interest to find a small number of representative networks that can serve as a condensed view of the data set. In a statistical perspective this goal amount to find a small number of networks that are able to typify the network structures starting from the observed ones. In addition, these networks should have a clear and interpretable profile in terms of their most relevant features and their specificity in contrast to the others. Given the set of N networks, we propose to find these representative networks by using the archetypal analysis, yielding what we call Archetypal Networks. The Archetypal Networks can serve to understand the data structure, as benchmarks for the other networks, and are useful also to compare networks among each other. We exemplify the proposed procedure by analyzing a set of 36 governance networks of public structures devoted to provide youth services and referring to 36 different territorial districts in Campania region in Italy. Our results highlight the presence of different network structures that can be interpreted in terms of the governance forms established in literature.

Minimum volume peeling

Among the measures of a distributions location, the mode is probably the least often used, although it has some appealing properties. Estimators for the mode of univariate distributions are widely available. However, few contributions can be found for the multivariate case. A consistent direct multivariate mode estimation procedure, called minimum volume peeling, can be outlined as follows. The approach iteratively selects nested subsamples with a decreasing fraction of sample points, looking for the minimum volume subsample at each step. The mode is then estimated by calculating the mean of all points in the final set. The robustness of the method is investigated by analyzing its finite sample breakdown point and algorithms to determine minimum volume sets are discussed. Simulation results confirm that using minimum volume peeling leads to efficient mode estimates both in uncontaminated as well as contaminated situations.

A Comparison of χ2 Metrics for the Assessment of Relational Similarities in Affiliation Networks

Factorial techniques are widely used in Social Network Analysis to analyze and visualize networks. When the purpose is to represent the relational similarities, simple correspondence analysis is the most frequent used technique. However, in the case of affiliation networks, its use can be criticized because the involved χ 2 distance does not adequately reflect the actual relational patterns. In this paper we perform a simulation study to compare the metric involved in Correspondence Analysis with respect to the one in Multiple Correspondence Analysis. Analytical results and simulation outcomes show that Multiple Correspondence Analysis allows a proper graphical appraisal of the underlying two-mode relational structure.