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Introduction to LAME

Source: vignettes/lame.Rmd
lame.Rmd

Overview

The LAME (Longitudinal Analysis of Multilevel nEtworks) package implements Additive and Multiplicative Effects (AME) models for longitudinal network data. It extends the AME framework to handle temporal dependencies through dynamic latent factors and additive effects.

Key Features

  • Longitudinal Network Analysis: Model network evolution over time
  • Dynamic Effects: Time-varying additive and multiplicative effects with AR(1) processes
  • Bipartite Networks: Full support for two-mode networks with rectangular adjacency matrices
  • Efficient Implementation: C++ backend for computational efficiency

Basic Usage

Fitting a Simple Model 

# Load example data (list of networks over time)
data(example_networks)  # This would be your data

# Fit a basic LAME model
fit <- lame(
  Y = example_networks,
  R = 2,                # 2 latent dimensions
  family = "binary",    # Binary networks
  nscan = 5000,        # Number of MCMC iterations
  burn = 500,          # Burn-in period
  odens = 25           # Output density
)

# View results
summary(fit)
plot(fit)

Dynamic Effects

Model time-varying sender/receiver effects and latent positions:

# Fit model with dynamic effects
fit_dynamic <- lame(
  Y = example_networks,
  R = 2,
  dynamic_ab = TRUE,   # Dynamic additive effects
  dynamic_uv = TRUE,   # Dynamic multiplicative effects
  family = "binary",
  nscan = 10000,
  burn = 1000,
  odens = 25
)

# Visualize temporal evolution
ab_plot(fit_dynamic, plot_type = "trajectory")
uv_plot(fit_dynamic, time_point = "all")

Including Covariates 

# Fit model with covariates
fit_cov <- lame(
  Y = example_networks,
  Xdyad = dyadic_covariates,    # Dyadic covariates
  Xrow = sender_covariates,      # Sender covariates
  Xcol = receiver_covariates,    # Receiver covariates
  R = 2,
  family = "binary",
  nscan = 10000
)

Model Families

LAME supports various network data types:

  • "normal": Continuous valued networks
  • "binary": Binary networks
  • "ordinal": Ordinal networks
  • "poisson": Count networks
  • "tobit": Censored continuous networks
  • "frn": Fixed rank nomination networks
  • "cbin": Censored binary networks
  • "rrl": Row-ranked likelihood networks

Bipartite Networks

For two-mode networks with different row and column node sets:

# Fit bipartite model
fit_bip <- lame(
  Y = bipartite_networks,
  mode = "bipartite",
  R_row = 3,           # 3 dimensions for row nodes
  R_col = 2,           # 2 dimensions for column nodes
  family = "binary",
  nscan = 10000
)

# Access the interaction matrix
fit_bip$G  # Rectangular matrix mapping row to column latent spaces

Model Assessment

Goodness-of-Fit 

# Plot GOF statistics
gof_plot(fit)

# Access GOF statistics directly
gof_stats <- fit$GOF

MCMC Diagnostics 

# Trace plots for convergence assessment
trace_plot(fit)

# Effective sample sizes
fit$ESS

Advanced Options

Priors

Customize prior distributions:

fit_custom <- lame(
  Y = example_networks,
  prior = list(
    Sab0 = diag(2),     # Prior scale for variance
    eta0 = 10,          # Prior degrees of freedom
    rho_ab_mean = 0.8,  # AR(1) mean for dynamic effects
    rho_ab_sd = 0.1     # AR(1) standard deviation
  ),
  nscan = 10000
)

Symmetric Networks

For undirected networks:

fit_sym <- lame(
  Y = undirected_networks,
  symmetric = TRUE,
  R = 2,
  family = "normal",
  nscan = 10000
)