## amen

#### Additive and
multiplicative effects network models

Package website

#### About

Additive and multiplicative effects network models (AMEN models)
provide a 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. The
`amen`

package provides Bayesian model fitting algorithms for
AMEN models, and accommodates a variety of types of network relations,
including continuous, binary and ordinal dyadic variables.

The basic AMEN model is of the form
*y*_{i, j} ∼ *β*^{⊤}*x*_{i, j} + *u*_{i}^{⊤}*v*_{j} + *a*_{i} + *b*_{j} + *ϵ*_{i, j}
where

*y*_{i, j} is the observed
dyadic variable being modeled and
*x*_{i, j} is an observed vector of
regressors;

*a*_{i} + *b*_{j} + *ϵ*_{i, j}
is an additive random effects term that describes sender and receiver
variance (such as outdegree and indegree heterogeneity) and dyadic
correlation;

*u*_{i}^{⊤}*v*_{j}
is a multiplicative random effects term that describes third-order
dependence patterns (such as transitivity and clustering) and can be
estimated and analyzed to uncover low-dimensional structure in the
network.

#### Installation

```
# Current version on GitHub
devtools::install_github("pdhoff/amen")
# CRAN-approved version on CRAN
install.packages("amen")
```

#### Documentation and citation

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

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

A review article that provides some mathematical details and
derivations is available on arXiv. Please cite this

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”.
JASA 100(469) 286-295.

That version restricted the multiplicative sender and receiver
effects to be equal
(*u*_{i} = *v*_{i}). The
AMEN model in its current form does not have this restriction. The
current AMEN model first 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.

#### Some examples