test_one_sample_gau: One-sample test for mean structure under antedependence

In antedep: Antedependence Models for Longitudinal Data

One-sample test for mean structure under antedependence

Description

Tests the null hypothesis that the mean vector equals a specified value mu = mu_0 against the alternative mu != mu_0, under an AD(p) covariance structure. This implements Theorem 7.1 of Zimmerman & Núñez-Antón (2009).

Usage

test_one_sample_gau(y, mu0, p = 1L, order = NULL, use_modified = TRUE)

Arguments

y	Numeric matrix with n_subjects rows and n_time columns.
mu0	Hypothesized mean vector under the null (length n_time).
p	Antedependence order of the covariance structure. This is the same order parameter named order in fit_gau.
order	Optional alias for p. Supply only one of p or order.
use_modified	Logical. If TRUE (default), use the modified test statistic (formula 7.7) for better small-sample approximation.

Details

The test exploits the AD structure to gain power over tests that don't assume any covariance structure. The likelihood ratio test statistic (Theorem 7.1) is:

N \sum_{i=1}^{n} [\log RSS_i(\mu_0) - \log RSS_i(\hat{\mu})]

where RSS_i(mu) is the residual sum of squares from the regression of Y_i - mu_i on its p predecessors Y_(i-1) - mu_(i-1), ..., Y_(i-p) - mu_(i-p).

The test has n degrees of freedom (one for each component of mu).

Value

A list with class gau_mean_test containing:

method

Inference method used ("lrt").

test_type

"one-sample"

mu0

Hypothesized mean under null

mu_hat

MLE of mean (sample mean)

statistic

Test statistic value

statistic_modified

Modified test statistic (if use_modified = TRUE)

df

Degrees of freedom (n_time)

p_value

P-value from chi-square distribution

p_value_modified

P-value from modified test

order

Antedependence order used

References

Zimmerman, D.L. and Núñez-Antón, V. (2009). Antedependence Models for Longitudinal Data. Chapman & Hall/CRC. Chapter 7.

See Also

test_two_sample_gau, test_order_gau

Examples

# Simulate data with known mean
mu_true <- c(10, 11, 12, 13, 14, 15)
y <- simulate_gau(n_subjects = 50, n_time = 6, order = 1, mu = mu_true)

# Test if mean is zero
test <- test_one_sample_gau(y, mu0 = rep(0, 6), p = 1)
print(test)

# Test if mean equals true value (should not reject)
test2 <- test_one_sample_gau(y, mu0 = mu_true, p = 1)
print(test2)

antedep documentation built on April 25, 2026, 1:06 a.m.