Additive and Multiplicative Effects Network Models

Abstract

Network datasets typically exhibit certain types of statistical patterns, such as within-dyad correlation, degree heterogeneity, and triadic patterns such as transitivity and clustering. The first two of these can be well represented with a social relations model, a type of additive effects model originally developed for continuous dyadic data. Higher-order patterns can be represented with multiplicative effects models, which are related to matrix decompositions that are commonly used for matrix-variate data analysis. Additionally, these multiplicative effects models generalize other popular latent feature network models, such as the stochastic blockmodel and the latent space model. In this article, we review a general regression framework for the analysis of network data that combines these two types of effects, and accommodates a variety of network data types, including continuous, binary and ordinal network relations.