test_order_gau: Likelihood ratio test for antedependence order (Gaussian AD...

In antedep: Antedependence Models for Longitudinal Data

Likelihood ratio test for antedependence order (Gaussian AD data)

Description

Tests the null hypothesis that the data follow an AD(p) model against the alternative that they follow an AD(p+q) model, using the likelihood ratio test described in Theorem 6.4 and 6.5 of Zimmerman & Núñez-Antón (2009).

Usage

test_order_gau(
  y,
  p = 0L,
  q = 1L,
  mu = NULL,
  use_modified = TRUE,
  order_null = NULL,
  order_alt = NULL
)

Arguments

y	Numeric matrix with n_subjects rows and n_time columns.
p	Order under the null hypothesis (default 0). This is the same antedependence order parameter named order in fit_gau.
q	Order increment under the alternative (default 1, so alternative is AD(p+q)).
mu	Optional mean vector. If NULL, the saturated mean (sample means) is used.
use_modified	Logical. If TRUE (default), use the modified test statistic (formula 6.9) which has better small-sample properties.
order_null	Optional alias for p (null order).
order_alt	Optional absolute order under the alternative. When supplied, q is computed as order_alt - p.

Details

The test is based on the intervenor-adjusted sample partial correlations. Under the null hypothesis AD(p), the partial correlations r_(i,i-k|(i-k+1:i-1)) should be zero for k > p.

The likelihood ratio test statistic (Theorem 6.4) is:

-N \sum_{j=1}^{q} \sum_{i=p+j+1}^{n} \log(1 - r^2_{i,i-p-j\cdot(i-p-j+1:i-1)})

which is asymptotically chi-square with (2n - 2p - q - 1)(q/2) degrees of freedom.

The modified test (formula 6.9) adjusts for small-sample bias using Kenward's (1987) correction.

Value

A list with class gau_order_test containing:

method

Inference method used ("lrt").

p

Order under null hypothesis

q

Order increment

statistic

Test statistic value

statistic_modified

Modified test statistic (if use_modified = TRUE)

df

Degrees of freedom

p_value

P-value from chi-square distribution

p_value_modified

P-value from modified test (if use_modified = TRUE)

n_subjects

Number of subjects

n_time

Number of time points

References

Zimmerman, D.L. and Núñez-Antón, V. (2009). Antedependence Models for Longitudinal Data. Chapman & Hall/CRC. Chapter 6.

Kenward, M.G. (1987). A method for comparing profiles of repeated measurements. Applied Statistics, 36, 296-308.

See Also

test_one_sample_gau, test_homogeneity_gau

Examples

# Simulate AD(1) data
y <- simulate_gau(n_subjects = 50, n_time = 6, order = 1, phi = 0.5)

# Test AD(0) vs AD(1)
test01 <- test_order_gau(y, p = 0, q = 1)
print(test01)

# Test AD(1) vs AD(2)
test12 <- test_order_gau(y, p = 1, q = 1)
print(test12)

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