Correspondence Analysis with Doubling for Two-Mode Valued Networks

Two-mode networks are data structure in which relations are collected on two different sets of actors (dyadic), or one set of actors and one set of events (affiliation). In some cases, the level/strength of ties can be discrete, continuous or coded by a set of ordered categories. Many analytical tools used to analyze one-mode network must have been adapted in order to deal with such networks. Usually, when relationships are valued, the data are dichotomized (often by adopting an arbitrary level of dichotomization) resulting in information loss. When the interest consists in visualizing and graphically analyzing the relational structures, it is possible to use weighted bipartite graphs, spring embedding and correspondence analysis (CA). In this work we will discuss how CA with doubling coding can be useful to analyze and graphically represent valued two-mode networks. Doubling has been originally designed to handle bipolar variables –ordinal variables or ratings– like those resulting from the detection of level/strength of ties with rating scale. In particular we will discuss how the proposed approach: i) takes into account the nature of relational data and the asymmetry of the two sets of entities in two-mode networks; ii) permits to directly analyze valued relational data, avoiding loss of information; iii) deals with the nature of the ratings and their bipolar character; v) improves visualization readability and results interpretation. In a nutshell, the proposed method allows to suitably represent the underlying weighted relational distance among actors and events. Moreover, the positions of actors and events in their respective factorial spaces have a nice relational interpretation, depending on the level/strength of the observed ties. We present the proposed approach by analyzing a subset of the relational data on the 1980 monetary donations from corporations to non-profit organizations in the Minneapolis-St.Paul area.