Modeling Dyadic Relationships within Social Networks: Latent Interdependence Models and Latent Non-Independence Models

Abstract

Relational data in social networks reflect information regarding relationship constructs and the characteristics of networks. Traditional approaches in social network analysis (e.g., the p* models and the latent space models) are focused on understanding the roles of network’s characteristics in bringing about the data. The objective of this dissertation is to develop two psychometric models aimed at mapping observed dyadic relational data in social networks onto latent relational construct scores. The latent interdependence models (LAIDM) are based on a basic fact that dyadic data come from a mutual-rating process and are inter-dependent. Therefore, they can be explained by both rating-receiver’s and rating-sender’s latent traits. The latent non-independence models (LANIM) refine the explanatory mechanism by stressing that dyadic responses not only depend on dyad members’ latent traits, but also on the interaction between the latent traits of both sides. The interaction between dyad members’ latent traits is termed as latent non-independence, operationally defined as the similarity/dissimilarity between trait scores, and quantified by the Euclidean distance. To estimate both models, Bayesian estimation procedures using Markov chain Monte Carlo (MCMC) method were introduced. The efficacy of model parameterizations and model estimations were examined in a simulation study. The results of parameter recovery support the parameterization of both models and the effectiveness of Bayesian estimation procedures. The accuracy of model estimation was significantly improved when the network size grows. In addition, the results of cross-estimation suggest both models were robust to the violation of model parameterization.