Likelihood ratio test for homogeneity across groups (categorical AD data)

Tests whether multiple groups share the same transition probability parameters in a categorical antedependence model.

Usage

test_homogeneity_cat(
  y = NULL,
  blocks = NULL,
  order = 1,
  n_categories = NULL,
  fit_null = NULL,
  fit_alt = 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. Can be NULL if both fit_null and fit_alt are provided.

blocks

Integer vector of length n_subjects specifying group membership. Required unless pre-fitted models are provided.

order

Antedependence order p. Default is 1.

n_categories

Number of categories. If NULL, inferred from data.

fit_null

Optional pre-fitted homogeneous model (class "cat_fit" with homogeneous = TRUE). If provided, y is not required for fitting under H0.

fit_alt

Optional pre-fitted heterogeneous model (class "cat_fit" with homogeneous = FALSE). If provided, y is not required for fitting under H1.

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", "mlrt", or "wald".

lrt_stat

Likelihood ratio test statistic

df

Degrees of freedom

p_value

P-value from chi-square distribution

fit_null

Fitted homogeneous model (H0)

fit_alt

Fitted heterogeneous model (H1)

n_groups

Number of groups

table

Summary data frame

Details

The null hypothesis is that all G groups share the same transition probability parameters: $$H_0: \pi^{(1)} = \pi^{(2)} = \ldots = \pi^{(G)}$$

The alternative hypothesis allows each group to have its own parameters.

The degrees of freedom are: $$df = (G-1) \times k$$ where G is the number of groups and k is the number of free parameters per population.

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

if (FALSE) { # \dontrun{
# Simulate data with different transition probabilities for two groups
set.seed(123)
marg1 <- list(t1 = c(0.7, 0.3))
marg2 <- list(t1 = c(0.4, 0.6))
trans1 <- list(t2 = matrix(c(0.9, 0.1, 0.2, 0.8), 2, byrow = TRUE),
               t3 = matrix(c(0.9, 0.1, 0.2, 0.8), 2, byrow = TRUE))
trans2 <- list(t2 = matrix(c(0.5, 0.5, 0.5, 0.5), 2, byrow = TRUE),
               t3 = matrix(c(0.5, 0.5, 0.5, 0.5), 2, byrow = TRUE))

y1 <- simulate_cat(100, 3, order = 1, n_categories = 2,
                   marginal = marg1, transition = trans1)
y2 <- simulate_cat(100, 3, order = 1, n_categories = 2,
                   marginal = marg2, transition = trans2)
y <- rbind(y1, y2)
blocks <- c(rep(1, 100), rep(2, 100))

# Test homogeneity
test <- test_homogeneity_cat(y, blocks, order = 1)
print(test)
} # }