Non-Symmetrical Correspondence Analysis to explore dependence structure in Social Networks

In Social Network Analysis (SNA), a common approach to analyze two-mode network (affiliation matrix) consists on prior converting it into two one-mode adiacency matrices and examining separately each mode. Alternative methods, like factor analysis and related approaches, have been proposed to simultaneously explore relationships among actors and events. In particular, in the case of binary data a correspondence analysis can be performed to identify the underlying dimensions of the joint factorial map defined by both actors and events (Faust, 2005). Such an approach assumes actors and events to be interdependent, i.e they are simply associated among them without any direction. However, in many cases the a priori knowledge allows to assume a dependency structure for the data, i.e. the actors depend on the event, or vice versa. In such a case the classical correspondence analysis is misleading. In this contribution, we propose to use Non-Symmetrical Correspondence Analysis (NSCA) to explore the relationship structure in two-mode networks when a dependency structure between two node set can be hypothesized. The NSCA has been introduced to deal with the analytical and graphical analysis of contingency table when rows depend on columns (Lauro, D’Ambra, 1984). In the framework of SNA, the use of NSCA can be a fruitful approach to explore the association pattern in the network dependence structure. Our proposal will be applied within a research in the labour market context in Naples. The analyzed affiliation matrix has professional profiles related to undeclared works of officially unemployed people as nodes, and the professional profiles of their three most important friends as events. The aim is to analyze how the undeclared labour market position of interviewed people yields a sort of social and occupational segregation in the friendship networks.