logL_cat: Log-likelihood for categorical AD models (with missing data...

In antedep: Antedependence Models for Longitudinal Data

Log-likelihood for categorical AD models (with missing data support)

Description

Evaluates the log-likelihood of an AD(p) model for categorical longitudinal data at given parameter values.

Usage

logL_cat(
  y,
  order,
  marginal,
  transition = NULL,
  blocks = NULL,
  homogeneous = TRUE,
  n_categories = NULL,
  na_action = c("fail", "complete", "marginalize")
)

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. Must be 0, 1, or 2.
marginal	List of marginal/joint probabilities for initial time points. Structure depends on order (see Details).
transition	List of transition probability arrays for time points k = p+1 to n. Each element should be an array of dimension c^p x c where the last dimension corresponds to the current time point.
blocks	Optional integer vector of length n_subjects specifying group membership. Required if homogeneous = FALSE.
homogeneous	Logical. If TRUE (default), same parameters used for all subjects. If FALSE, marginal and transition should be lists indexed by block.
n_categories	Number of categories. If NULL, inferred from data.
na_action	Handling of missing values in y. One of "fail" (default, error if any missing), "complete" (drop subjects with any missing values), or "marginalize" (integrate over missing categorical outcomes under the AD model).

Details

The log-likelihood for AD(p) decomposes into contributions from initial time points and transition time points.

For order 0 (independence), the log-likelihood is the sum of log marginal probabilities at each time point.

Parameter structure for marginal:

• Order 0: List with elements t1, t2, ..., tn, each a vector of length c

• Order 1: List with element t1 (vector of length c)

• Order 2: List with t1 (vector), t2_given_1to1 (c x c matrix)

Parameter structure for transition:

• Order 0: Not used (NULL or empty list)

• Order 1: List with elements t2, t3, ..., tn, each c x c matrix

• Order 2: List with elements t3, t4, ..., tn, each c x c x c array

Value

Scalar log-likelihood value.

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.

Examples

set.seed(1)
y <- simulate_cat(n_subjects = 40, n_time = 5, order = 1, n_categories = 3)
fit <- fit_cat(y, order = 1, n_categories = 3)
logL_cat(
  y = y,
  order = 1,
  marginal = fit$marginal,
  transition = fit$transition,
  n_categories = 3
)

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