  Network datasets typically exhibit certain types of statistical dependencies,
such as within-dyad correlation, row and column heterogeneity, and third-order
dependence patterns such as transitivity and clustering. The first two of these
can be well-represented statistically with a social relations model, a type of
additive random effects model originally developed for continuous dyadic data.
Third-order patterns can be represented with multiplicative random effects
models, which are related to matrix decompositions commonly used for
matrix-variate data analysis. Additionally, these multiplicative random effects
models generalize other popular latent variable 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 random effects and accommodates a variety of network data
types, including continuous, binary and ordinal network relations.
