Likelihood ratio test for homogeneity across groups (INAD data)

Tests hypotheses about parameter equality across treatment or grouping factors in integer-valued antedependence models. Implements the homogeneity testing framework from Section 3.7 of Li & Zimmerman (2026).

Usage

test_homogeneity_inad(
  y,
  blocks,
  order = 1,
  thinning = "binom",
  innovation = "pois",
  test = c("all", "mean", "dependence"),
  fit_pooled = NULL,
  fit_inadfe = NULL,
  fit_hetero = NULL,
  ...
)

Arguments

y

Integer matrix with n_subjects rows and n_time columns.

blocks

Integer vector of length n_subjects specifying group membership.

order

Antedependence order (0, 1, or 2).

thinning

Thinning operator: "binom", "pois", or "nbinom".

innovation

Innovation distribution: "pois", "bell", or "nbinom".

test

Type of homogeneity test:

"all": Tests M1 (pooled) vs M3 (fully heterogeneous)
"mean": Tests M1 (pooled) vs M2 (shared dependence, different means)
"dependence": Tests M2 (INADFE) vs M3 (fully heterogeneous)

fit_pooled

Optional pre-computed pooled fit (M1).

fit_inadfe

Optional pre-computed INADFE fit (M2).

fit_hetero

Optional pre-computed heterogeneous fit (M3).

...

Additional arguments passed to fit_inad.

Value

A list with class "test_homogeneity_inad" containing:

method: Inference method used ("lrt").
statistic: Test statistic value
lrt_stat: Likelihood ratio test statistic
df: Degrees of freedom
p_value: P-value from chi-square distribution
test: Type of test performed
fit_null: Fitted model under H0
fit_alt: Fitted model under H1
bic_null: BIC under H0
bic_alt: BIC under H1
bic_selected: Which model BIC prefers
table: Summary data frame

Details

The function supports three nested model comparisons as described in the paper:

M1 (Pooled): All parameters are common across groups. This corresponds to fitting fit_inad(y, blocks = NULL).

M2 (INADFE): The thinning parameters \(\alpha\) are shared across groups, but innovation means differ via block effects \(\tau\). This is the standard INADFE model fitted via fit_inad(y, blocks = blocks).

M3 (Fully Heterogeneous): Both \(\alpha\) and \(\theta\) parameters can differ across groups. This is fitted by running separate fit_inad calls for each group.

The three test types correspond to:

"all": H0: M1 vs H1: M3 (complete homogeneity vs complete heterogeneity)
"mean": H0: M1 vs H1: M2 (test for group differences in means only)
"dependence": H0: M2 vs H1: M3 (test for group differences in dependence)

Degrees of freedom are computed as the difference in free parameters between the null and alternative models.

References

Li, C. and Zimmerman, D.L. (2026). Integer-valued antedependence models for longitudinal count data. Biostatistics. Section 3.7.

Examples

if (FALSE) { # \dontrun{
data("bolus_inad")
y <- bolus_inad$y
blocks <- bolus_inad$blocks

# Test for any group differences (M1 vs M3)
test_all <- test_homogeneity_inad(y, blocks, order = 1,
                                  thinning = "nbinom", innovation = "bell",
                                  test = "all")
print(test_all)

# Test only for mean differences (M1 vs M2)
test_mean <- test_homogeneity_inad(y, blocks, order = 1,
                                   thinning = "nbinom", innovation = "bell",
                                   test = "mean")
print(test_mean)

# Test for dependence differences given different means (M2 vs M3)
test_dep <- test_homogeneity_inad(y, blocks, order = 1,
                                  thinning = "nbinom", innovation = "bell",
                                  test = "dependence")
print(test_dep)
} # }