Modeling Psychometric Relational Data in Social Networks: Latent Interdependence Models

Abstract

In the current paper, we propose a latent interdependence approach to modeling psychometric data in social networks. The idea of latent interdependence is adopted from social relations models (SRMs), which formulate a mutual-rating process by both dyad members' characteristics. Under the framework of the latent interdependence approach, we introduce two psychometric models: The first model includes the main effects of both rating-sender and rating-receiver, and the second model includes a latent distance effect to assess the influence from the dissimilarity between the latent characteristics of both sides. The latent distance effect is quantified by the Euclidean distance between both sides' trait scores. Both models use Bayesian estimation via Markov chain Monte Carlo. How accurately model parameters were estimated was evaluated in a simulation study. Parameter recovery results showed that all parameters were accurately recovered under most of the conditions investigated. As expected, the accuracy of model estimation was significantly improved as network size grew. Also, through analyzing empirical data, we showed how to use the estimates of model parameters to predict the latent weight of connections among group members and rebuild either a univariate or multivariate network at a latent trait level. Finally, we discuss issues regarding model comparison and offer suggestions for future studies.

Keywords: Bayesian estimation; latent inter-dependence models; psychometric models; relationship measurement; social networks.