UCLA

The structure of many complex social networks is determined by nodal and dyadic covariates that are endogenous to the tie variables. While exponential-family random graph models (ERGMs) have been very successful in modeling social networks with exogenous covariates, they are often misspecified for networks where some covariates are stochastic. Exponential-family random network models (ERNMs) are an extension of ERGM that retain the desirable properties of ERGM, but allow the joint modeling of tie variables and covariates. We compare ERGM to ERNM to show how conclusions of ERGM modeling are improved by consideration of the ERNM framework. In particular, ERNM simultaneously represents the effects of social influence and social selection processes while commonly used models do not. We also look into the latent class models for group clustering problems in social network. The random nodal attributes can be observed or latent in ERNM. When the attributes is treated as latent, we can investigate the probability of cluster group. Stochastic Block Models are a well-known statistical models for group classification, however, they rely on the relational data and omit the nodal characteristics. We compare these two models and provide a case study to illustrate the main points.