test_timeinvariance_cat: Likelihood ratio test for time-invariance (categorical data)

In antedep: Antedependence Models for Longitudinal Data

Likelihood ratio test for time-invariance (categorical data)

Description

Tests whether transition probabilities are constant over time in a categorical antedependence model.

Usage

test_timeinvariance_cat(
  y,
  order = 1,
  blocks = NULL,
  homogeneous = TRUE,
  n_categories = NULL,
  test = c("lrt", "score", "mlrt")
)

Arguments

y	Integer matrix with n_subjects rows and n_time columns. Each entry should be a category code from 1 to c.
order	Antedependence order p. Default is 1.
blocks	Optional integer vector of length n_subjects specifying group membership.
homogeneous	Logical. If TRUE (default), parameters are shared across all groups.
n_categories	Number of categories. If NULL, inferred from data.
test	Type of test statistic. One of "lrt" (default), "score", or "mlrt".

Details

The null hypothesis is that all transition probabilities (for k > p) are equal across time:

H_0: \pi_{y_k | y_{k-p}, \ldots, y_{k-1}} \text{ is constant for } k = p+1, \ldots, n

This reduces (n-p) separate transition matrices/arrays to a single one.

The degrees of freedom are:

df = (c-1) \times c^p \times (n - p - 1)

This function currently supports complete data only. If y contains missing values, use model-fitting functions (for example fit_cat) directly with missing-data handling instead of this test wrapper.

Value

A list of class "cat_lrt" containing:

method

Inference method used: one of "lrt", "score", "mlrt", or "wald".

lrt_stat

Likelihood ratio test statistic

df

Degrees of freedom

p_value

P-value from chi-square distribution

fit_null

Fitted time-invariant model (H0)

fit_alt

Fitted time-varying model (H1)

table

Summary data frame

References

Xie, Y. and Zimmerman, D. L. (2013). Antedependence models for nonstationary categorical longitudinal data with ignorable missingness: likelihood-based inference. Statistics in Medicine, 32, 3274-3289.

See Also

fit_cat, test_order_cat

Examples

# Simulate data with time-invariant transitions
set.seed(123)
y <- simulate_cat(200, 6, order = 1, n_categories = 2)

# Test time-invariance
test <- test_timeinvariance_cat(y, order = 1)
print(test)

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