Worked example: FPCA stability

Start with repeated synthetic gaze trials:

gaze = simulate_planar_trajectories(
    n_participants=30,
    trials_per_participant=6,
    random_state=27,
)

Run participant-level bootstrap because trials are nested within participants:

stability = bootstrap_fpca_stability(
    gaze,
    n_bootstrap=200,
    n_components=3,
    scaling="dimension_sd",
    resample_unit="participant",
    participant_column="participant_id",
    random_state=27,
)

Summarize and visualize:

table = summarise_fpca_stability(stability)
plot_fpca_stability(stability)

What to inspect

A component can explain substantial variance yet have modest bootstrap similarity. Conversely, a lower-variance component may have a very consistent shape.

Use stability to qualify interpretation, not to create a new significance threshold.

Add reconstruction

curve = fpca_reconstruction_curve(
    stability.reference,
    gaze,
)

plot_reconstruction_curve(curve)

This separates two questions:

1. Are the retained components stable?
2. Do the retained components reconstruct the trajectories adequately?