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Likelihood ratio test for stationarity (categorical AD data)

Source: R/lrt_stationarity_cat.R
test_stationarity_cat.Rd

Tests whether a categorical antedependence process satisfies stationarity constraints in the AD parameterization.

Usage

test_stationarity_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".

Value

A list of class "cat_lrt" containing:

method

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

lrt_stat

Likelihood ratio test statistic

df

Degrees of freedom

p_value

P-value from chi-square distribution

fit_null

Fitted stationary model (H0)

fit_alt

Fitted non-stationary model (H1)

table

Summary data frame

Details

The tested constraints are:

  1. The marginal distribution P(Yk) is constant for all k

  2. The transition probabilities P(Yk | Y(k-p), ..., Y(k-1)) are constant for all k > p

For AD order 1, these two constraints correspond to strict stationarity. For AD order greater than 1, this function should be interpreted as testing marginal-constancy plus time-invariant transitions; these constraints are not, in general, sufficient for full strict stationarity.

This is stronger than time-invariance alone, which only requires condition 2.

This function currently supports complete data only.

The null hypothesis is tested against the general (non-stationary) AD(p) model. The degrees of freedom are computed from the fitted parameter counts: $$df = n_{params}(H_1) - n_{params}(H_0)$$ where \(H_1\) is the unconstrained non-stationary model and \(H_0\) is the stationary model.

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

test_timeinvariance_cat, test_order_cat

Examples

if (FALSE) { # \dontrun{
# Simulate stationary AD(1) data
set.seed(123)
y <- simulate_cat(200, 6, order = 1, n_categories = 2)

# Test stationarity
test <- test_stationarity_cat(y, order = 1)
print(test)
} # }