Likelihood ratio test for stationarity (Gaussian AD data)

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.

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

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.

References

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

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
#> [1] 0.3343081