Multivariate GOF test for smooth or random-effect covariates

Implements the multivariate test of Boschi & Wit (2025), Section 3.4. Builds a q-dimensional cumulative residual process from the spline basis of the requested covariate's smooth effect, normalises by the inverse-square-root of the empirical variance-covariance matrix \(\hat J\) (eq. 17), and tests against a q-dimensional standard Brownian bridge via \(T_\psi = \sup_u \lVert\hat W\rVert^2\). The p-value is computed empirically by simulating n_sim Brownian bridge trajectories.

Usage

gof_multivariate(
  event_log,
  model,
  covariate,
  k_basis = 5,
  n_sim = 1000,
  scope = "all",
  mode = "one",
  half_life = NULL,
  seed = NULL
)

Arguments

event_log: Dyadic event log.
model: Named character vector of <stat> = "linear" mapping (for the rest of the model); the test target is covariate with a flexible smooth basis of dimension k_basis - 1.
covariate: Name of the covariate to test under a smooth effect.
k_basis: Spline-basis dimension for covariate (passed as k to mgcv::s(); the resulting design matrix has k_basis - 1 columns under thin-plate identifiability constraints).
n_sim: Number of simulated Brownian bridges for the empirical p-value (default 1000).
scope, mode, half_life, seed: See compare_models().

Value

List with statistic (\(T_\psi\)), p_value, W (n x q matrix), u, and covariate.

References

Boschi M, Wit EC (2025). Goodness of fit in relational event models. Statistics and Computing 36(4).