On null models for contagion effects in multidimensional networks

Abstract

Multidimensional networks are networks where edges are differentiated with different nominal classes, called layers. Inference of contagion effects has issues both in simple networks with only one layer and in multidimensional networks. However the inherent complexity of multidimensional networks makes almost impossible, at least with traditional approached based on regression models, a reliable inference of the “contagiousness” of a feature within a network. In the first part of the manuscript are provided introductory notions to run regression models and simulation models of multidimensional networks. The approach only requires knowledge of tabular data and mixed models of regression and not of tensor algebra, so the approach should be more congenial to social scientists. In the second part, it is introduced the concept of neutral model as a peculiar case of null model for statistical inference. Finally, given the aforementioned concerns, it is discussed why methods based on union of independent layers (chimera networks) are generally better than procedural model for parameterisation of neutral models of multidimensional networks. An example of chimera as a join of two blockmodels is provided.