Goodness of fit for a fitted relational event model

Cumulative martingale-residual tests for a model fitted with rem(method = "gam"), following Boschi & Wit (2025). The test works on the fit itself, so it covers linear and smooth (nl, tv, tvnl) terms and the penalised estimates rem() returns. The null distribution comes from a multiplier bootstrap that subtracts the drift due to estimating the coefficients, rather than from the asymptotic Brownian bridge used by gof_univariate() and its siblings, which refit a linear model from the event log.

Usage

gof_rem(
  fit,
  term,
  test = c("time", "functional_form", "functional_form_score"),
  data = NULL,
  time = NULL,
  n_sim = 2000,
  max_grid = 500,
  seed = NULL
)

Arguments

fit: A rem object fitted with method = "gam".
term: Name of the covariate to test, as written in the rem() formula (e.g. "x" for x, nl(x) or tv(x)).
test: Which process to test; see Tests.
data: The wide data the model was fitted on. Needed for linear terms (to read <term>_ev / <term>_nv) and for test = "time" (to read the event times); nl() terms carry their event and control values in the fit.
time: Name of the event-time column in data; defaults to the time argument of the rem() call. A column <time>_ev is used when <time> is absent.
n_sim: Number of bootstrap replicates.
max_grid: Maximum number of grid points of the process.
seed: Optional seed for the bootstrap multipliers; the caller's random number state is restored afterwards.

Value

An object of class "rem_gof": a list with p_value, statistic, the bootstrap suprema statistic_sim, the observed process process, the bootstrap processes process_sim (grid points x replicates), the grid (x, and u on the quantile scale), test and term. It has print() and plot() methods; plot(x, n_show = 20, main = NULL, legend = "topright") draws the observed process against n_show bootstrap processes, with the legend at a graphics::legend() position or none (legend = NULL).

Tests

"time": The residual process of term's columns, cumulated over event time. Detects an effect that changes over time when the model holds it constant.
"functional_form": The residual process cumulated over the empirical quantiles of the covariate, pooling event and control values: at each quantile \(u\) the increment is \(I(x_{ev} \le x_{(u)}) - I(x_{nv} \le x_{(u)})\). Detects a wrong shape of the covariate effect, e.g. a linear term fitted to a non-linear effect.
"functional_form_score": As "functional_form", with each indicator weighted by the term's basis evaluated at the event and at the control. Supported for linear and nl() terms.

The statistic is the supremum over the grid of the absolute process ("functional_form") or of its Euclidean norm across the term's columns (the other two tests); the p-value is the share of bootstrap replicates whose supremum is at least as large.

References

Boschi M, Wit EC (2025). Goodness-of-fit tests for relational event models based on cumulative martingale residuals. Statistics and Computing 36, 4. doi:10.1007/s11222-025-10751-2 .

Examples

set.seed(1)
w <- simulate_relational_events(
  n_events = 300, senders = paste0("a", 1:12), receivers = paste0("a", 1:12),
  n_controls = 1, endogenous_stats = "reciprocity_count",
  endogenous_effects = c(reciprocity_count = 0.6), wide = TRUE)
fit <- rem(~ reciprocity_count, data = w, method = "gam", time = "time")
g <- gof_rem(fit, "reciprocity_count", test = "functional_form", data = w,
             n_sim = 500, seed = 1)
g
#> Martingale-residual GoF test of 'reciprocity_count': functional form
#>   sup statistic = 0.1160, p-value = 0.3620 (500 bootstrap replicates, n = 300)
plot(g)