Continuous gaze exploration and FPCA

Use this route when the primary scientific object is a continuous gaze trajectory or derived function and the first question is how trajectories vary, not yet how a predictor changes them.

1. Start from an explicit trajectory representation

Import or construct a TrajectorySet with time units, coordinate semantics, curve IDs and participant/trial metadata. Do not silently interpolate, normalize time, smooth or register curves.

For planar gaze, use fit_mfpca(); for one functional dimension, use fit_fpca().

fit = fit_mfpca(
    trajectories,
    n_components=0.95,
    scaling="dimension_sd",
)

2. Check the representation before interpreting components

Inspect data completeness, time support, scaling choice and whether phase variation is scientifically meaningful. Registration is not a default preprocessing step. Sparse/irregular PACE, compositional AOI trajectories and phase analysis are advanced branches, not replacements for the canonical common-grid workflow.

3. Quantify stability rather than treating components as fixed truths

When component interpretation matters, use held-out reconstruction, bootstrap-matched component stability, eigengap/subspace diagnostics or component uncertainty as appropriate. Near-tied eigenvalues should shift interpretation toward the subspace rather than individual component labels.

4. Interpret the scientific object

Report explained variation, component functions/scores and reconstruction quality. Do not interpret sign conventions as substantive; matched components may be sign-aligned for comparison.

5. Produce an auditable report

Use summarise_fpca() and fpca_reporting_text(), and retain preprocessing and basis provenance.

Do not use this route when

• the primary target is a trial-varying experimental coefficient function;
• repeated-trial covariance is central to inference;
• the response is Bernoulli/count rather than approximately Gaussian;
• recurrence/nonlinear structure is the actual scientific target.

Those questions have separate canonical routes.