  When people are asked to recall their social networks, theoretical and
empirical work tells us that they rely on shortcuts, or heuristics. Cognitive
Social Structures (CSS) are multilayer social networks where each layer
corresponds to an individual's perception of the network. With multiple
perceptions of the same network, CSSs contain rich information about how these
heuristics manifest, motivating the question, Can we identify people who share
the same heuristics? In this work, we propose a method for identifying
cognitive structure across multiple network perceptions, analogous to how
community detection aims to identify social structure in a network. To
simultaneously model the joint latent social and cognitive structure, we study
CSSs as three-dimensional tensors, employing low-rank nonnegative Tucker
decompositions (NNTuck) to approximate the CSS--a procedure closely related to
estimating a multilayer stochastic block model (SBM) from such data. We propose
the resulting latent cognitive space as an operationalization of the
sociological theory of social cognition by identifying individuals who share
relational schema. In addition to modeling cognitively independent, dependent,
and redundant networks, we propose a specific model instance and related
statistical test for testing when there is social-cognitive agreement in a
network: when the social and cognitive structures are equivalent. We use our
approach to analyze four different CSSs and give insights into the latent
cognitive structures of those networks.
