test_stationarity_gau: Likelihood ratio test for stationarity (Gaussian AD data)

In antedep: Antedependence Models for Longitudinal Data

Likelihood ratio test for stationarity (Gaussian AD data)

Description

Tests whether time-varying Gaussian AD covariance parameters can be constrained to be constant over time.

Usage

test_stationarity_gau(
  y,
  order = 1L,
  blocks = NULL,
  constrain = "both",
  fit_unconstrained = NULL,
  verbose = FALSE,
  max_iter = 2000L,
  rel_tol = 1e-08,
  ...
)

Arguments

y	Numeric matrix with n_subjects rows and n_time columns.
order	Antedependence order (0, 1, or 2).
blocks	Optional vector of block memberships (length n_subjects).
constrain	Constraint to test: for order 0: "sigma" (or "all"); for order 1: "phi", "sigma", or "both"/"all"; for order 2: "phi1", "phi2", "phi", "sigma", or "all"/"both".
fit_unconstrained	Optional pre-computed unconstrained fit from fit_gau.
verbose	Logical; if TRUE, prints fitting progress.
max_iter	Maximum number of optimization iterations for constrained fit.
rel_tol	Relative tolerance for constrained optimization.
...	Additional arguments passed to fit_gau when fit_unconstrained is not provided.

Details

The mean structure is kept unrestricted in both models (time-specific means plus optional block shifts), and the test constrains covariance parameters: innovation standard deviations and/or antedependence coefficients.

The likelihood-ratio statistic is:

\lambda = 2(\ell_{alt} - \ell_{null})

where \ell_{null} and \ell_{alt} are maximized log-likelihoods under the constrained and unconstrained models, respectively.

Degrees of freedom are computed from the number of constraints implied by constrain.

Value

A list with class "test_stationarity_gau" containing:

method

Inference method used ("lrt").

fit_unconstrained

Unconstrained Gaussian AD fit

fit_constrained

Constrained Gaussian AD fit

constraint

Human-readable null constraint description

lrt_stat

Likelihood-ratio statistic

df

Degrees of freedom

p_value

Chi-square p-value

bic_unconstrained

BIC of unconstrained model

bic_constrained

BIC of constrained model

bic_selected

Model selected by BIC

table

Two-row model summary table

References

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

See Also

run_stationarity_tests_gau, test_order_gau, fit_gau

Examples

set.seed(1)
y <- simulate_gau(n_subjects = 80, n_time = 6, order = 1, phi = 0.4, sigma = 1)

# Test jointly constant phi and sigma (order 1)
out <- test_stationarity_gau(y, order = 1, constrain = "both")
out$p_value

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