[Paper Review] Social Network Mediation Analysis: a Latent Space Approach

Haiyan Liu, Ick Hoon Jin+2 more|arXiv (Cornell University)|Oct 8, 2018

Mental Health Research TopicsPsychology76 references3 citations

TL;DR

This paper proposes a novel Bayesian mediation model that treats a social network as a mediator using a latent space to capture actor dependencies. By modeling network positions in orthogonal latent dimensions, the approach enables valid estimation of the total indirect effect despite non-unique latent positions, with simulation and empirical validation showing accurate parameter recovery and evidence that gender influences smoking behavior both directly and indirectly through friendship networks.

ABSTRACT

Social networks contain data on both actor attributes and social connections among them. Such connections reflect the dependence among social actors, which is important for individual's mental health and social development. To investigate the potential mediation role of a social network, we propose a mediation model with a social network as a mediator. In the model, dependence among actors is accounted by a few mutually orthogonal latent dimensions. The scores on these dimensions are directly involved in the intervention process between an independent variable and a dependent variable. Because all the latent dimensions are equivalent in terms of their relationship to social networks, it is hardly to name them. The intervening effect through an individual dimension is thus of little practical interest. Therefore, we would rather focus on the mediation effect of a network. Although the scores are not unique, we rigorously articulate that the proposed network mediation effect is still well-defined. To estimate the model, we adopt a Bayesian estimation method. This modeling framework and the Bayesian estimation method is evaluated through a simulation study under representative conditions. Its usefulness is demonstrated through an empirical application to a college friendship network.

Motivation & Objective

• To develop a mediation model where a social network acts as a mediator between an independent variable (e.g., gender) and a dependent variable (e.g., smoking behavior), accounting for actor dependencies.
• To address the challenge of dependence among social actors by embedding individuals in a low-dimensional latent social space with orthogonal dimensions.
• To define and estimate the total mediation effect of the entire social network, even when individual latent positions are non-unique.
• To evaluate the performance of the proposed model through extensive simulations and a real-world college friendship network dataset.
• To provide a methodological framework for network mediation that extends beyond binary networks and can be adapted to valued, directed, or nonlinear relations.

Proposed method

• Uses a latent space model (LSM) to represent social network ties as arising from unobserved, orthogonal dimensions of social proximity.
• Models the network as a function of actor positions in the latent space, with edge probabilities determined by inter-individual distances in this space.
• Applies a Bayesian hierarchical framework to estimate the model parameters, including the indirect effect via the network mediator.
• Employs Markov Chain Monte Carlo (MCMC) sampling to obtain posterior distributions of the indirect effect, accounting for uncertainty and dependence between path coefficients.
• Defines the total network mediation effect as the product of the path from X to the latent network (a) and from the latent network to Y (b), integrating over all latent dimensions.
• Uses equal-tail 95% credible intervals for inference and evaluates coverage rates and bias in simulation studies under varying sample sizes and dimensionality.

Experimental results

Research questions

• RQ1 To what extent does a student’s gender influence their smoking behavior through the structure of their friendship network?
• RQ2 How can the mediation effect of an entire social network be defined and estimated when individual positions in the latent space are not unique?
• RQ3 What is the performance of the Bayesian estimation method in recovering the true network mediation effect under various sample sizes and latent dimension counts?
• RQ4 Can the proposed model detect indirect effects in real-world social networks while accounting for dependence among actors?
• RQ5 How does the inclusion of multiple latent dimensions affect estimation accuracy and coverage rates in network mediation analysis?

Key findings

• The Bayesian estimation method produced accurate parameter estimates when sample sizes were above 100, with coverage rates of 95% credible intervals mostly within the acceptable range of [92.5%, 97.5%].
• For small sample sizes (e.g., 50 or 100), bias in parameter estimates increased with the number of latent dimensions, with more instances exceeding 10% bias.
• The total network mediation effect was well-defined and estimable despite non-unique latent positions, as the model's structure ensures identifiability of the indirect effect.
• In the empirical analysis of a college friendship network, gender had a significant direct effect on smoking behavior, and part of the effect was mediated through the friendship network.
• The results suggest that female students smoked less than male students, and this difference was partially explained by differences in their network positions and social ties.
• The model demonstrated feasibility in capturing network-mediated effects, though future work is needed to interpret individual latent dimensions and extend to longitudinal and nonlinear settings.