Conditionally Dyadic Independent Models for Longitudinal Analysis of the Effect of Health Traits on Relationships in a Social Network

• Activity Number: 211
• Type: Invited
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): A. James O'Malley*+ and Sudeshna Paul
• Companies: Harvard Medical School and Harvard Medical School
• Keywords: Dyadic independence ; Lagged predictors ; Latent variables ; Longitudinal model ; Social network and health ; Transitivity

Abstract

We develop a new longitudinal model for transitions in the relationship status of pairs of individuals (dyads) in a social network. We first specify a model for the relationship status of two individuals ("dyads"), which in the case of binary-valued relationships follows a four-component multinomial distribution. To account for complexities due to the dependence of observations between dyads we assume dyads are conditionally independent given latent variables (random effects) of the actors in a dyad and lagged covariates judiciously chosen to account for important inter-dyad dependencies (e.g., transitivity - "a friend of a friend is a friend"). Model parameters are estimated using Bayesian analysis implemented via Markov chain Monte Carlo (MCMC). The model is applied to the friendship networks from an excerpt of the Teenage Health and Lifestyle Study. Results of the analysis indicate a strong dependence across time, high reciprocation of ties between individuals, and extensive triadic clustering. Examination of model fit revealed that our model successfully captured the most important features of the data.