Factorial methods to visually explore three-way two-mode networks

Three-way two mode networks are characterized by a set of n actors and a set of m events in which actors are involved, observed at r different levels (e.g., space or time occasions). They are represented by a three-dimensional relational matrix A=(aijk), where i=1, \u2026 , n; j=1,\u2026,m and k=1,\u2026,r. Usually a simultaneous analysis of ways and modes of such a matrix is not explicitly considered. Traditional approaches drop out a mode (e.g., conversion approach of two-mode networks) or a way (e.g., using of trajectories). In this work we propose to analyze the two-mode network as it is. We show how the usual representation through the correspondence analysis does not reproduce correctly relational patterns. At the same time we propose to use Multiple Correspondence Analysis (MCA) to visually explore two-mode network. The adopted metric and the method assumptions better reproduce the structural equivalence pattern present in the two mode network. Finally, we propose the use of Multiple Factorial Analysis, that is useful to generalize MCA to three way matrix, to analyze three way two-mode networks. This method allows to visualize simultaneously the two-mode network observed in different times or spaces