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lame hex

Longitudinal Additive and Multiplicative Effects Models for Networks

The lame package builds on and extends Peter Hoff’s amen package, which implements Additive and Multiplicative Effects (AME) models for cross-sectional network analysis. While amen provides the foundational Bayesian framework for modeling network data with latent factor and nodal random effects, lame extends this in several directions: (1) longitudinal network analysis via lame() with dynamic additive and multiplicative effects modeled as AR(1) processes, (2) support for bipartite (rectangular) network structures, (3) C++ acceleration of core MCMC sampling routines via Rcpp and RcppArmadillo, and (4) a full suite of S3 methods (coef(), vcov(), confint(), predict(), fitted(), residuals(), simulate()) for standard R model interoperability.

The package includes two main functions: ame() for cross-sectional network analysis and lame() for longitudinal network analysis with dynamic effects that capture temporal heterogeneity through autoregressive processes. Both functions support unipartite (square) and bipartite (rectangular) network structures.

Installation

Install from GitHub (requires C++ build tools: Xcode CLI on macOS, Rtools on Windows, or build-essential on Linux):

# install.packages("devtools")
devtools::install_github("netify-dev/lame", dependencies = TRUE)

Quick Start 

library(lame)

# Load example data (creates Y, Xdyad, Xrow, Xcol in your workspace)
data("vignette_data")

# Y      — list of 4 binary network matrices (35 × 35, years 1993–2000)
# Xdyad  — list of dyadic covariate arrays (distance, shared IGOs)
# Xrow   — list of sender covariate matrices (GDP, population)
# Xcol   — list of receiver covariate matrices (GDP, population)

# Fit a basic longitudinal AME model
fit <- lame(
  Y = Y,                    # List of T network matrices
  Xdyad = Xdyad,           # Dyadic covariates
  Xrow = Xrow,             # Sender covariates
  Xcol = Xcol,             # Receiver covariates
  family = "binary",       # Network type
  R = 2,                   # Latent dimensions
  burn = 100,              # Burn-in iterations
  nscan = 500              # Post-burn samples
)

# Summary and diagnostics
summary(fit)

Dynamic Effects

The key innovation in lame is time-varying network effects:

# Fit model with dynamic effects (builds on fit and data from Quick Start above)
fit_dynamic <- lame(
  Y = Y,
  Xdyad = Xdyad,
  Xrow = Xrow,
  Xcol = Xcol,
  family = "binary",
  dynamic_ab = TRUE,       # Time-varying sender/receiver effects
  dynamic_uv = TRUE,       # Time-varying latent positions
  R = 2,
  burn = 100,
  nscan = 500,
  prior = list(
    rho_uv_mean = 0.9,    # High persistence for latent factors
    rho_ab_mean = 0.8     # Moderate persistence for additive effects
  )
)

Visualization 

# Additive effects (sender/receiver)
ab_plot(fit, effect = "sender")                    # Static effects
ab_plot(fit_dynamic, plot_type = "trajectory")     # Dynamic over time

# Multiplicative effects (latent factors)
uv_plot(fit)                                       # Static latent positions
uv_plot(fit_dynamic, plot_type = "trajectory")     # Dynamic trajectories

# Diagnostics
trace_plot(fit)                                     # MCMC convergence
gof_plot(fit)                                       # Goodness-of-fit

Key Features

Network Analysis

  • Cross-sectional: ame() fits AME models for a single network snapshot
  • Longitudinal: lame() fits AME models for networks observed over multiple time periods
  • Bipartite: full support for two-mode (rectangular) networks in both ame() and lame()
  • 8 families: normal, binary, ordinal, poisson, tobit, censored binary, fixed rank nomination, row-ranked likelihood

Dynamic Modeling

  • Time-varying latent positions (dynamic_uv): captures evolving community structure via AR(1) processes
  • Time-varying heterogeneity (dynamic_ab): models changing sender/receiver activity over time
  • Flexible priors: customizable temporal persistence and innovation variance

Inference and Diagnostics

Documentation

Vignette Topic
vignette("lame-overview") Getting started
vignette("cross_sec_ame") Cross-sectional AME models
vignette("lame") Longitudinal models
vignette("bipartite") Bipartite networks
vignette("dynamic_effects") Dynamic effects

Citation

If you use lame in your research, please cite:

@Manual{lame2026,
  title = {lame: Longitudinal Additive and Multiplicative Effects Models for Networks},
  author = {Cassy Dorff and Shahryar Minhas and Tosin Salau},
  year = {2026},
  note = {R package version 1.0.0},
  url = {https://github.com/netify-dev/lame},
}

The dynamic effects implementation draws on:

  • Sewell, D. K., & Chen, Y. (2015). Latent space models for dynamic networks. Journal of the American Statistical Association, 110(512), 1646-1657. doi:10.1080/01621459.2014.988214
  • Durante, D., & Dunson, D. B. (2014). Nonparametric Bayes dynamic modeling of relational data. Biometrika, 101(4), 883-898. doi:10.1093/biomet/asu040

Contributors

  • Cassy Dorff (Vanderbilt University)
  • Shahryar Minhas (Michigan State University)
  • Tosin Salau (Michigan State University)

License

MIT License - see LICENSE file for details.

Support