Relational Event Model (REM) Estimation

Estimates a Relational Event Model (REM) for network data, focusing on the incidence of discrete events between pairs of actors. See dem for the full Durational Event Model, which extends the REM to handle interactions with non-negligible duration.

Usage

rem(
  events,
  training_start = 0,
  exogenous_end = NULL,
  formula = NULL,
  n_nodes = NULL,
  directed = FALSE,
  coef = NULL,
  semiparametric = FALSE,
  control = control.redeem()
)

Arguments

events

A matrix of events with columns time, from, to, and optionally type (1 for start, 3 for exogenous changes).

training_start

Numeric; the time point at which to start the estimation. Defaults to 0.

exogenous_end

Numeric; optional end time for exogenous baseline changes. Defaults to NULL.

formula

A one-sided formula specifying the sufficient statistics to include in the intensity function. The right-hand side must be composed of terms from redeem_terms. For example: ~ inertia() + reciprocity() + degree. An intercept (~ 1) is the minimal specification. Defaults to NULL.

n_nodes

Integer; the total number of actors in the network. If NULL (default), it is automatically identified based on the actors in the events set.

directed

Logical; whether the interaction events are directed. Defaults to FALSE.

coef

Numeric vector; initial coefficients for the model. If provided, this must be a concatenated vector of:

Core coefficients: values for sufficient statistics in the formula.
Degree coefficients (if degree is in the formula): a vector of length n_nodes (undirected) or 2 * n_nodes (directed, sender effects first then receiver effects).
Baseline coefficients (if temporal changepoints are present): a vector of length equal to the number of baseline intervals (equal to number of changepoints if an intercept/degree is present, or changepoints + 1 if neither is present).

Defaults to NULL, in which case default starting values are automatically computed.

semiparametric

Logical; whether to use a semiparametric baseline. Defaults to FALSE. See the 'Semiparametric Baseline' section for details.

control

A list of control parameters from control.redeem. Defaults to control.redeem().

Value

An object of class rem_object containing model estimates and log-likelihoods. See rem_object for details on the components of the returned object and S3 methods.

Details

The REM can be viewed as the incidence sub-model of the full dem, corresponding to the formation process $\lambda^{0\rightarrow 1}$. It uses a counting process approach to estimate the influence of various covariates on the timing and occurrence of events, assuming that events are instantaneous points in time.

Model Formulation

The Relational Event Model characterizes the instantaneous rate at which actor pair $(i,j)$ initiates an event. Under the log-linear specification, the event intensity at time $t$ is: $$\lambda_{i,j}(t \mid \mathscr{H}_t,\, \theta) = \exp\!\bigl(s_{i,j}(\mathscr{H}_t)^\top \alpha + \beta_i + \beta_j + f(t, \gamma)\bigr)$$ where:

$s_{i,j}(\mathscr{H}_t)$ is a vector of sufficient statistics computed from the event history $\mathscr{H}_t$; see redeem_terms for available terms.
$\alpha$ is the vector of covariate effects.
$\beta_i$ and $\beta_j$ are optional actor-specific baselines (sender and receiver sociality), included via the bare symbol degree in the formula.
$f(t, \gamma)$ is an optional piecewise-constant temporal baseline, included via baseline(changepoints) in the formula.

Semiparametric Baseline

When semiparametric = TRUE, the temporal baseline rate of event occurrence is left completely unspecified, and the model parameters are estimated via the Cox partial likelihood using the survival package. In this path:

Each observed event time is treated as a failure time, and all non-occurring dyads at that time constitute the risk set.
The exact waiting times between events are conditioned away, meaning that inference is based solely on the sequence of events and the relative dyadic intensities.
This approach is equivalent to the ordered (or conditional) REM likelihood introduced by Butts (2008). It is highly robust to temporal fluctuations and baseline misspecification since no piecewise baseline or changepoints need to be specified.
Limitations: This path does not support the specialized scalable estimation of sender/receiver popularity effects (degree) or piecewise-constant temporal baselines.

References

Fritz, C., Rastelli, R., Fop, M., & Caimo, A. (2026). Scalable Durational Event Models: Application to Physical and Digital Interactions. arXiv:2504.00049.

Butts, C. T. (2008). A Relational Event Framework for Social Action. Sociological Methodology, 38(1), 155-200.

Examples

if (FALSE) { # \dontrun{
# Simulate some relational event data
n <- 20
events <- matrix(c(
  1.2, 1, 5,
  3.1, 2, 8,
  4.5, 1, 3
), ncol = 3, byrow = TRUE)
colnames(events) <- c("time", "from", "to")

# Estimate a simple REM
fit <- rem(
  events = events,
  n_nodes = n,
  formula = ~1,
  control = control.redeem(it_max = 50)
)
summary(fit)
} # }