Worked example: simultaneous fixed-target FPCR wild bootstrap¶

This example first constructs the ordinary heteroscedastic target-wise wild-bootstrap result and then post-calibrates the same bootstrap roots across a declared four-target family.

Simulate independent trajectories and a heteroscedastic outcome¶

import numpy as np

from eyetrajectoriespy import (
    fit_mfpca,
    simulate_planar_trajectories,
    wild_bootstrap_fpca_projection,
)

gaze = simulate_planar_trajectories(
    n_participants=60,
    trials_per_participant=1,
    n_time=41,
    random_state=2028,
)

reference = fit_mfpca(
    gaze,
    n_components=3,
    scaling="dimension_sd",
)

rng = np.random.default_rng(2028)
score1 = reference.scores[:, 0]
score2 = reference.scores[:, 1]
noise_sd = (
    0.25
    + 0.30 * np.abs(score1)
    / max(np.std(score1, ddof=1), 1e-8)
)
outcome = (
    1.0
    + 1.2 * score1
    - 0.5 * score2
    + rng.normal(0.0, noise_sd)
)

Declare the target family in the base analysis¶

targets = gaze.subset([0, 1, 2, 3])

base = wild_bootstrap_fpca_projection(
    gaze,
    outcome,
    targets=targets,
    n_bootstrap=500,
    residual_components=2,
    inference_components=3,
    scaling="dimension_sd",
    multiplier="normal",
    confidence_level=0.95,
    independent_unit_column="participant_id",
    random_state=2028,
)

The four targets above define the family. Adding or removing targets changes the familywise question.

Calibrate one maximum statistic across targets¶

from eyetrajectoriespy import (
    fpca_wild_bootstrap_projection_simultaneous_interval,
)

simultaneous = fpca_wild_bootstrap_projection_simultaneous_interval(base)

No FPCA fit, regression fit, residual calculation, multiplier draw, or bootstrap replicate is rerun here.

Compare marginal and familywise intervals¶

from eyetrajectoriespy import fpca_wild_bootstrap_simultaneous_frame

table = fpca_wild_bootstrap_simultaneous_frame(simultaneous)
print(table)

The table exposes both target-wise and simultaneous limits and their corresponding critical values.

Plot both layers¶

from eyetrajectoriespy import plot_fpca_wild_bootstrap_simultaneous_interval

plot_fpca_wild_bootstrap_simultaneous_interval(
    simultaneous,
    max_targets=4,
    show_targetwise=True,
)

The familywise bars should be at least as wide as the target-wise bars at the same confidence level.

Recalibrate the same roots at a different confidence level¶

high = fpca_wild_bootstrap_projection_simultaneous_interval(
    base,
    confidence_level=0.99,
)

Changing the confidence level recalibrates the stored roots. It does not trigger a new bootstrap.

Reporting text¶

from eyetrajectoriespy import fpca_wild_bootstrap_simultaneous_reporting_text

print(fpca_wild_bootstrap_simultaneous_reporting_text(simultaneous))

Interpretation¶

The simultaneous interval controls the declared family of fixed centered FPCR projections under the base independent-curve wild-bootstrap contract.

It is not a future-outcome prediction interval, does not authorize adding targets after inspection, and does not solve repeated-participant dependence.