Additive and multiplicative effects network models

TL;DR

This paper reviews a comprehensive regression framework for network data that combines additive and multiplicative effects to model complex dependencies like transitivity, clustering, and heterogeneity across various data types.

Contribution

It introduces a unified model integrating additive and multiplicative effects, generalizing existing latent variable models for diverse network data types.

Findings

Models complex dependencies such as transitivity and clustering.

Generalizes stochastic blockmodel and latent space models.

Applicable to continuous, binary, and ordinal network data.

Abstract

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.