Repeated-trial functional mixed effects

Use this route when participants contribute repeated trials and the response is continuous/approximately Gaussian, especially when predictors vary by trial or participant/trial covariance is scientifically consequential.

1. Preserve the hierarchy

Keep participant, trial and time identities explicit:

participant -> trial -> time

Do not flatten trial-time rows into independent observations.

2. Fit the smallest scientifically justified mixed model

fit = fit_functional_mixed_effects_regression(
    trajectories,
    design,
    predictors=("condition",),
    participant_column="participant_id",
    dimension="response",
    fixed_basis_size=4,
)

The canonical starting point is the documented participant functional random effect. Random functional slopes, trial functional effects and residual correlation are advanced extensions that should be declared because the scientific design requires them, not added automatically.

3. Diagnose covariance attribution

Inspect random-effect covariance diagnostics and residual dependence. If a serial covariance model is fitted, whitened residuals—not raw residuals—are the relevant check for remaining serial structure.

4. Separate coefficient inference from covariance sensitivity

Use bootstrap_functional_mixed_effects_coefficients() for whole-function coefficient bands. Use full-refit bootstrap or covariance-structure sensitivity only when variance-component uncertainty or defensible competing covariance structures are part of the scientific question.

5. Report estimand and hierarchy

Use functional_mixed_effects_reporting_text(). Report participant/trial mapping, fixed and random bases, residual covariance specification, ML/REML contract, resampling unit, convergence/boundary diagnostics and simultaneous coverage scope.

Do not use this route when

The response is genuinely Bernoulli, grouped binomial or Poisson. The current mixed-effects subsystem is Gaussian; use the generalized marginal GEE workflow for those observation families.