Covariate-defined latent space random effects model

• Latent space random effects model with a covariate-defined social space is proposed.
• The latent social space is defined as a two-dimensional linear regression.
• The model allows for prediction of missing links in an incompletely observed network.
• Provides a framework for describing why people connect in the network via covariates.

Latent factor models are a useful and intuitive class of models; one limitation is their inability to predict links in a dynamic network. We propose a latent space random effects model with a covariate-defined social space, where the social space is a linear combination of the covariates as estimated by an MCMC algorithm. The model allows for the prediction of links in a network; it also provides an interpretable framework to explain why people connect. We fit the model using the Adolescent Health Network dataset and three simulated networks to illustrate its effectiveness in recognizing patterns in the data.