Longitudinal Latent Space Network Model With Vector Autoregressive (VAR) Evolution

• In Event: Methods and Models for Your Social Network Data

Abstract

In many real world applications of longitudinal social network analysis, it is often of interest to identify and understand important changes in the network over time. For example, in instructional advice seeking network of teachers (Spillane et al., 2012), education researchers are interested in how advice seeking behavior of the teachers changes with time, given the interventions in the network at different time points. In this talk, I will focus on the longitudinal extension of the static latent space network model of Hoff et al. (2002, with assumption that the nodes in the networks have underlying positions in a low dimensional Euclidean space and that the probabilities of ties are inversely related to the inter-nodal latent distances. It is further assumed that the network dynamics in time are direct functions of the temporal dependence in the latent nodal positions which show stationary vector autoregressive (VAR) evolution of order 1. I will also present an MCMC algorithm to draw samples from the posterior distribution of the parameters, and explain some of the challenges with un-identifiability associated in this approach. Finally, I use the proposed model to analyze advice seeking networks among teachers observed at different time points. This analysis gives us insights into the important structural changes in the network and the implications of those changes.

Author

• Samrachana Adhikari, Harvard University