Social Network Mediation Analysis: A Latent Space Approach
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SOCIAL NETWORK MEDIATION ANALYSIS: A LATENT SPACE APPROACH
Haiyan Liu UNIVERSITY OF CALIFORNIA, MERCED
Ick Hoon Jin YONSEI UNIVERSITY
Zhiyong Zhang UNIVERSITY OF NOTRE DAME
Ying Yuan THE UNIVERSITY OF TEXAS MD, ANDERSON CANCER CENTER
A social network comprises both actors and the social connections among them. Such connections reflect the dependence among social actors, which is essential for individuals’ mental health and social development. In this article, we propose a mediation model with a social network as a mediator to investigate the potential mediation role of a social network. In the model, the dependence among actors is accounted for by a few mutually orthogonal latent dimensions which form a social space. The individuals’ positions in such a latent social space are directly involved in the mediation process between an independent and dependent variable. After showing that all the latent dimensions are equivalent in terms of their relationship to the social network and the meaning of each dimension is arbitrary, we propose to measure the whole mediation effect of a network. Although individuals’ positions in the latent space are not unique, we rigorously articulate that the proposed network mediation effect is still well defined. We use a Bayesian estimation method to estimate the model and evaluate its performance through an extensive simulation study under representative conditions. The usefulness of the network mediation model is demonstrated through an application to a college friendship network. Key words: friendship network, mediation analysis, social network analysis, latent space modeling, Bayesian estimation, smoking behavior.
1. Introduction Network analysis is an interdisciplinary research domain of mathematics, statistics, and computer sciences (Epskamp et al., 2017; Schmittmann et al., 2013; Wasserman & Faust, 1994). It has been adopted in diverse fields to address different research interests (Grunspan et al., 2014). Researchers have been working on social networks from different perspectives (Carrington et al., 2005). Graph theory is often used by mathematicians to examine the network structure (Newman et al., 2002). Different modeling frameworks and algorithms are developed by computer scientists and statisticians to detect and understand network communities (Yang et al., 2013; Zhao et al., 2012). Probability and statistical models with social networks as dependent variables are built on This study was partially supported by the Institute for Scholarship in the Liberal Arts, College of Arts and Letters, University of Notre Dame, by Humanities and Social Sciences Research Project in 2020 (2020-22-0389), Yonsei University and by Basic Science Research Program through the National Research Foundation of Korea (NRF 2020R1A2C1A01009881). Correspondence should be made to Haiyan Liu, Psychological Sciences, University of California, Merced, 5200 N. Lake Road, Merced, CA 95343, USA. Email: [email protected]
© 2020 The Psychometric Society
PSYCHOMETRIKA
understanding actors’ dependence
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