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Additive and multiplicative effects network models (AMEN models) providea statistical modeling framework for dyadic network and relational data,built upon familiar data analysis tools such as linear regression,random effects models and matrix decompositions. Theamen packageprovides Bayesian model fitting algorithms for AMEN models, andaccommodates a variety of types of network relations, includingcontinuous, binary and ordinal dyadic variables.

The basic AMEN model is of the formy_i, j ∼ β^⊤x_i, j + u_i^⊤v_j + a_i + b_j + ϵ_i, jwhere

• y_i, j is the observed dyadic variable being modeledandx_i, j is an observed vector of regressors;

• a_i + b_j + ϵ_i, j is anadditive random effects term that describes sender and receivervariance (such as outdegree and indegree heterogeneity) and dyadiccorrelation;

• u_i^⊤v_j is a multiplicativerandom effects term that describes third-order dependence patterns(such as transitivity and clustering) and can be estimated andanalyzed to uncover low-dimensional structure in the network.

# Current version on GitHubdevtools::install_github("pdhoff/amen")# CRAN-approved version on CRANinstall.packages("amen")

A tutorial article and many data analysis examples are available via thetutorial.Please cite this as

Hoff, P.D. (2015) “Dyadic data analysis withamen”. arXiv:1506.08237.

A review article that provides some mathematical details and derivationsis available onarXiv. Please citethis

Hoff, P.D. (2018) “Additive and multiplicative effects network models”.arXiv:1807.08038.

The first version of the AMEN model appeared in

Hoff, P.D. (2005) “Bilinear mixed-effects models for dyadic data”. JASA100(469) 286-295.

That version restricted the multiplicative sender and receiver effectsto be equal (u_i = v_i). The AMEN model inits current form does not have this restriction. The current AMEN modelfirst appeared in

Hoff, P.D., Fosdick, B.K., Volfovsky, A. and Stovel, K. (2013)“Likelihoods for fixed rank nomination networks”. Network Science,1(3):253–277.

• Modeling a binary outcome

• DIY Modeling of a binary outcome

• DIY Poisson regression