Latent Variable Modeling of Social Networks with Directional Relations: An Exploration of Profile Similarity of Latent Factors

Abstract

Statistical analysis of networks has gained increasing popularity in social and psychological sciences. This study introduces a latent variable model for self-reported directional relations within social networks, specifically focusing on predicting relationships based on actor attributes and latent traits. In a directional relation, the initiator is termed the “sender,” and the recipient is the “receiver.” Traditional symmetric similarity measures, such as Mahalanobis distance, often fall short of capturing the nuanced impact of sender and receiver latent traits in these scenarios. To overcome this limitation, we propose four distinct measures of trait similarity ( p sender , p receiver , m sender , and m receiver ), aiming to discern subtle distinctions between the impact of senders and receivers characteristics on the perceived social relations. We demonstrate the applicability and relevance of these measures in real-world network scenarios by applying our proposed framework to analyze a college friendship network. Among competing models, our findings affirm a potential non-linear trend between personality similarity and perceived friendship. Notably, the quadratic model with m receiver ( Q 8 ) outperformed others, exhibiting both significant linear and quadratic terms. Our results underscore the significance of the projected components of the receiver’s personality along with the sender’s orientation, with larger and smaller components both indicating a higher probability of perceived friendship.