REM.jl

Relational Event Models for Julia

A Julia package for statistical analysis of time-stamped relational events in networks.

Overview

Relational Event Models (REM) are statistical models for analyzing sequences of time-stamped relational events. An event is a directed interaction from a sender to a receiver at a specific point in time. REMs uncover factors explaining why certain actors interact at higher rates than others.

REM.jl is a port of eventnet, providing efficient tools for modeling sequences of directed interactions between actors.

What is a Relational Event?

A relational event is a time-stamped directed interaction:

Actor A → Actor B at time t

Examples include:

• Emails sent between colleagues
• Messages in a chat application
• Trade transactions between countries
• Collaboration events between scientists

Key Concepts

Applications

REMs are widely used in:

• Social network analysis: Understanding communication patterns
• Organizational studies: Modeling collaboration and coordination
• International relations: Analyzing diplomatic interactions
• Animal behavior: Studying social hierarchies and mating patterns
• Online platforms: Modeling user interactions and content sharing

Features

• Rich statistic library: 25+ statistics covering dyadic, degree, triadic, four-cycle, and attribute effects
• Efficient computation: Incremental network state updates for fast statistic calculation
• Temporal decay: Support for exponential decay of network effects
• Case-control sampling: Efficient estimation for large networks via stratified conditional logistic regression
• Flexible timestamps: Works with numeric, DateTime, and Date timestamps
• Easy data loading: Load events from DataFrames or CSV files

Installation

using Pkg
Pkg.add(url="https://github.com/simoneSantoni/REM.jl")

Or for development:

using Pkg
Pkg.develop(path="/path/to/REM.jl")

Quick Start

using REM

# Create events
events = [
    Event(1, 2, 1.0),  # Actor 1 → Actor 2 at time 1.0
    Event(2, 1, 2.0),  # Actor 2 → Actor 1 at time 2.0 (reciprocation)
    Event(1, 3, 3.0),  # Actor 1 → Actor 3 at time 3.0
    Event(1, 2, 4.0),  # Actor 1 → Actor 2 at time 4.0 (repetition)
]
seq = EventSequence(events)

# Define model statistics
stats = [
    Repetition(),        # Tendency to repeat past interactions
    Reciprocity(),       # Tendency to reciprocate
    SenderActivity(),    # Sender's past activity level
    ReceiverPopularity() # Receiver's past popularity
]

# Fit model with case-control sampling
result = fit_rem(seq, stats; n_controls=100, seed=42)

# View results
println(result)

Choosing Statistics

Documentation

• Getting Started
• • Installation
  • Basic Workflow
  • Step 1: Create an Event Sequence
  • Step 2: Define Statistics
  • Step 3: Fit the Model
  • Step 4: Interpret Results
  • Complete Example
  • Working with Temporal Decay
  • Comparing Models
  • Best Practices
  • Next Steps
• Events and Data
• • Events
  • Event Sequences
  • Loading Data
  • Node Attributes
  • Actor Sets
  • Risk Sets
  • Working with Different Time Scales
  • Data Validation
  • Utility Functions
• Statistics
• • Statistics Interface
  • Statistic Categories
  • Dyad Statistics
  • Degree Statistics
  • Triangle Statistics
  • Four-Cycle Statistics
  • Node Attribute Statistics
  • Using Statistics in Practice
  • Statistic Sets
  • Choosing Statistics
• Model Estimation
• • Overview
  • Why Case-Control Sampling?
  • Configuring the Sampler
  • Generating Observations
  • Fitting Models
  • Understanding Results
  • Interpreting Coefficients
  • Computing Statistics Without Sampling
  • Model Comparison
  • Convergence Issues
  • Advanced Topics
  • Best Practices
• Temporal Decay
• • Why Use Decay?
  • The Exponential Decay Model
  • Setting the Decay Rate
  • Using Decay in Models
  • Decay with Different Time Types
  • How Decay Affects Statistics
  • Choosing the Right Halflife
  • Recency Statistic vs Global Decay
  • No Decay (Default)
  • Example: Email Network
  • Computational Notes
• Types API Reference
• • Events
  • Actor Data
  • Network State
  • State Query Functions
  • Time Utilities
• Statistics API Reference
• • Base Types and Interface
  • Dyad Statistics
  • Degree Statistics
  • Triangle Statistics
  • Four-Cycle Statistics
  • Node Attribute Statistics
• Estimation API Reference
• • Data Loading
  • Observation Generation
  • Model Fitting
  • Utility Functions

Theoretical Background

The Relational Event Model

REMs model the rate at which events occur as a function of the network's history. For a potential event from sender $s$ to receiver $r$ at time $t$, the hazard rate is:

\[\lambda_{sr}(t) = \exp\left(\sum_k \beta_k x_k(s, r, t)\right)\]

Where:

• \[x_k(s, r, t)\]

  are statistics computed from the network history

• \[\beta_k\]

  are coefficients to be estimated

Case-Control Sampling

For large networks, computing statistics for all possible dyads is expensive. REM.jl uses case-control sampling:

1. For each observed event (case), sample non-events (controls) from the risk set
2. Compute statistics for both cases and controls
3. Estimate via stratified conditional logistic regression

This approach is statistically consistent and dramatically reduces computation time.

References

1. Butts, C.T. (2008). A relational event framework for social action. Sociological Methodology, 38(1), 155-200.

2. Lerner, J., Lomi, A. (2020). Reliability of relational event model estimates under sampling: How to fit a relational event model to 360 million dyadic events. Network Science, 8(1), 97-135.

3. Lerner, J., Bussmann, M., Snijders, T.A.B., Brandes, U. (2013). Modeling frequency and type of interaction in event networks. Corvinus Journal of Sociology and Social Policy, 4(1), 3-32.

4. Brandes, U., Lerner, J., Snijders, T.A.B. (2009). Networks evolving step by step: Statistical analysis of dyadic event data. 2009 International Conference on Advances in Social Network Analysis and Mining, 200-205.

5. Perry, P.O., Wolfe, P.J. (2013). Point process modelling for directed interaction networks. Journal of the Royal Statistical Society: Series B, 75(5), 821-849.