Multiple Correspondence Analysis for Relational Data

Correspondence analysis (CA) has been frequently used in social network analysis (SNA), to analyze and graphically represent two-mode networks (Wasserman et al., 1989; Roberts, 2000). According to Wasserman et al. (1989), CA is a data analytic technique used to study contingency tables which is applicable in a variety of ways to relational data. Its use is principally due to the similarity between the affiliation matrix F associated to a two-mode network and the usual contingency table. However, as CA is not designed to treat relational data its use in social network analysis has been criticized by some authors (Borgatti and Everett, 1997). Furthermore, in our opinion, CA is not appropriate and correct approach in dealing with binary affiliation matrices even if it could lead to meaningful results. Hence, aiming at exploring and visualizing the relational structure of a two-mode network, we propose a more suitable approach based on an appropriate transformation of the raw affiliation matrix. In particular, we propose the use of multiple correspondence analysis (MCA) for two-mode networks. MCA has been used by some authors with different purposes (Wasserman et al., 1989). Here we follow a different approach which consists in CA performed on a special case of indicator matrix Z build up from F and in the use of the concept of “doubling” (Greenacre, 1984). We will show that MCA, thanks to its properties, presents some notable advantages with respect to CA.