Likelihood ratio test for antedependence order (INAD data)

Performs a likelihood ratio test comparing INAD models of different orders.

Usage

test_order_inad(
  y,
  order_null = 0,
  order_alt = 1,
  thinning = "binom",
  innovation = "pois",
  blocks = NULL,
  use_chibar = TRUE,
  weights = NULL,
  fit_null = NULL,
  fit_alt = NULL,
  ...
)

Arguments

y: Integer matrix with n_subjects rows and n_time columns.
order_null: Order under null hypothesis (0 or 1).
order_alt: Order under alternative hypothesis (1 or 2). Must be order_null + 1.
thinning: Thinning operator: "binom", "pois", or "nbinom".
innovation: Innovation distribution: "pois", "bell", or "nbinom".
blocks: Optional integer vector for block effects.
use_chibar: Logical; if TRUE, use chi-bar-square for boundary test.
weights: Optional weights for chi-bar-square mixture.
fit_null: Optional pre-computed null fit.
fit_alt: Optional pre-computed alternative fit.
...: Additional arguments passed to fit_inad.

Value

A list with class "test_order_inad" containing:

method: Inference method used ("lrt").
fit_null: Fitted model under H0
fit_alt: Fitted model under H1
statistic: Test statistic value
lrt_stat: Likelihood ratio test statistic
df: Degrees of freedom
p_value: Chi-square p-value
p_value_chibar: Chi-bar-square p-value (if use_chibar = TRUE)
bic_null: BIC under H0
bic_alt: BIC under H1
bic_selected: Which model BIC prefers
table: Two-row model comparison table
settings: Input and derived settings for the test

Details

The test compares nested INAD models of orders order_null and order_alt = order_null + 1 using: $$\lambda = 2(\ell_{alt} - \ell_{null})$$ where $\ell_{null}$ and $\ell_{alt}$ are maximized log-likelihoods under the null and alternative models.

The default p-value uses the chi-square approximation with degrees of freedom matching the number of additional dependence parameters introduced under the higher-order model. When use_chibar = TRUE, a chi-bar-square mixture p-value is also reported for boundary-aware inference.

Missing-data inputs are supported through the same na_action options available in fit_inad. If y has missing values and na_action is not supplied via ..., this function defaults to na_action = "marginalize".

References

Li, C. and Zimmerman, D.L. (2026). Integer-valued antedependence models for longitudinal count data. Biostatistics.

Examples

set.seed(1)
y <- simulate_inad(
  n_subjects = 40,
  n_time = 5,
  order = 1,
  thinning = "binom",
  innovation = "pois",
  alpha = 0.3,
  theta = 2
)
out <- test_order_inad(
  y,
  order_null = 0,
  order_alt = 1,
  thinning = "binom",
  innovation = "pois",
  max_iter = 20
)
out$statistic
#> [1] 18.99281