The paper stems from the idea to draw a statistical soft-modeling framework to network data. Network data arise in very different and multidisciplinary fields (Sociology, Economics, Informatics, Communications, and so on), in order to study relational ties among units. The different fields highlighted in recent years the necessity to collect together relational and attribute data, as well as meta-data describing the actors in the network. Usual relational datasets are characterized by i) very different amount of units (from very few units to huge networks), ii) biased sampling (for instance snow-ball samplings are biased because they give people with more social connections a higher chance of selection, iii) heterogeneous kind of information attached to both nodes and ties. These facets highlights the difficulties, and sometime the impossibility, for classical statistical tools and models to be satisfactory applied. From a different point of view, many theoretical behavioral models, often assumed in social network analysis, are far from being directly observable. It still remains the possibility of measuring them as latent factors depending from multidimensional constructs. In these frameworks, we propose a component-based approach to network data through Partial Least Squares algorithms.
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