Introduction to antedep

Overview

antedep supports three model families:

AD (Gaussian) for continuous longitudinal outcomes
INAD for count longitudinal outcomes
CAT (categorical AD) for discrete state longitudinal outcomes

Packaged datasets include bolus_inad, cattle_growth, cochlear_implant, labor_force_cat, and race_100km.

data("race_100km")
dim(race_100km$y)
colMeans(race_100km$y)

Production-Readiness Matrix

Model	Data type	Complete-data fit/logLik	Missing-data fit/logLik	Notes
AD	Continuous	Ready	Ready (`fit_gau`, `logL_gau`)	Missing-data fit supports EM / observed-data likelihood modes
INAD	Counts	Ready	Ready (`fit_inad`, `logL_inad`)	Missing-data fit supports `na_action = "marginalize"`
CAT	Categorical states	Ready	Ready (`fit_cat`, `logL_cat`)	Missing-data fit supports orders 0, 1, 2

Visualizing Longitudinal Data

data("bolus_inad")
plot_profile(
  bolus_inad$y,
  blocks = bolus_inad$blocks,
  block_labels = c("Group 1", "Group 2"),
  title = "Bolus Longitudinal Profiles"
)

# More detailed dependence diagnostic
plot_prism(bolus_inad$y)

AD Workflow (Continuous Outcomes)

Complete-data fit and order comparison

y_gau <- simulate_gau(n_subjects = 20, n_time = 4, order = 1, phi = 0.5)
fit_gau1 <- fit_gau(y_gau, order = 1)
fit_gau2 <- fit_gau(y_gau, order = 2)

c(order1_logLik = fit_gau1$log_l, order2_logLik = fit_gau2$log_l)
#> order1_logLik order2_logLik 
#>     -105.6720     -104.4205
bic_order_gau(y_gau, max_order = 2)$table
#>        order     log_l      bic selected
#> order0     0 -112.6549 249.2756    FALSE
#> order1     1 -105.6720 244.2971     TRUE
#> order2     2 -104.4205 247.7855    FALSE

# Example AD order test
test_order_gau(y_gau, p = 0, q = 1)$p_value
#> [1] 0.002952214

Missing-data AD fit

y_gau_miss <- y_gau
y_gau_miss[sample(length(y_gau_miss), 8)] <- NA

fit_gau_em <- fit_gau(y_gau_miss, order = 1, na_action = "em", em_max_iter = 10)
fit_gau_cc <- fit_gau(y_gau_miss, order = 1, na_action = "complete")
#> Warning: Only 13/20 subjects have complete data (65%).
#> Consider using na_action = 'em' for less information loss.

c(em_logLik = fit_gau_em$log_l, complete_case_logLik = fit_gau_cc$log_l)
#>            em_logLik complete_case_logLik 
#>            -94.00107            -63.11882
fit_gau_em$pct_missing
#> [1] 10

AD mean and covariance structure tests (complete data)

These AD inference tests currently require complete data.

# One-sample and two-sample mean-profile tests
mu0 <- colMeans(y_gau)
blocks_gau <- rep(1:2, each = nrow(y_gau) / 2)

test_one_sample_gau(y_gau, mu0 = mu0, p = 1)$p_value
#> [1] 1
test_two_sample_gau(y_gau, blocks = blocks_gau, p = 1)$p_value
#> [1] 0.01854549

# Wald contrast test: H0 that adjacent means are equal
C <- diff(diag(ncol(y_gau)))
test_contrast_gau(y_gau, C = C, p = 1)$p_value
#> [1] 0.8183341

# Covariance homogeneity across groups
test_homogeneity_gau(y_gau, blocks = blocks_gau, p = 1)$p_value
#>        g1 
#> 0.3237498

INAD Workflow (Count Outcomes)

Complete-data INAD fit

y_inad <- simulate_inad(
  n_subjects = 20,
  n_time = 4,
  order = 1,
  thinning = "binom",
  innovation = "pois",
  alpha = 0.4,
  theta = 3
)

fit_inad1 <- fit_inad(y_inad, order = 1, thinning = "binom", innovation = "pois")
fit_inad1$log_l
#> [1] -158.3541
bic_order_inad(y_inad, max_order = 2, thinning = "binom", innovation = "pois")$table
#>         order    logLik n_params      BIC
#> order_0     0 -164.6683        4 341.3196
#> order_1     1 -158.3541        7 337.6784
#> order_2     2 -158.3541        8 340.6741

Missing-data INAD fit

y_inad_miss <- y_inad
y_inad_miss[sample(length(y_inad_miss), 10)] <- NA

fit_inad_miss <- fit_inad(
  y_inad_miss,
  order = 1,
  thinning = "binom",
  innovation = "pois",
  na_action = "marginalize",
  max_iter = 10
)

fit_inad_miss$log_l
#> [1] -142.2786
fit_inad_miss$pct_missing
#> [1] 12.5

# Missing-data LRTs (observed-data likelihood)
blocks_inad <- rep(1:2, each = nrow(y_inad_miss) / 2)
test_order_inad(y_inad_miss, order_null = 0, order_alt = 1, blocks = blocks_inad)$p_value
#> [1] 0.08052965
test_homogeneity_inad(y_inad_miss, blocks = blocks_inad, order = 1, test = "mean")$p_value
#> [1] 0.7852657

CAT Workflow (Categorical Outcomes)

Complete-data CAT fit and inference

y_cat <- simulate_cat(n_subjects = 20, n_time = 4, order = 1, n_categories = 3)
fit_cat1 <- fit_cat(y_cat, order = 1)
fit_cat1$log_l
#> [1] -79.08119

# Wald CIs (complete data)
ci_cat1 <- ci_cat(fit_cat1, parameters = "marginal")
head(ci_cat1$marginal, 3)
#>        parameter time category estimate         se     lower     upper level
#> cat_1 pi_t1_cat1    1        1     0.25 0.09682458 0.0602273 0.4397727  0.95
#> cat_2 pi_t1_cat2    1        2     0.40 0.10954451 0.1852967 0.6147033  0.95
#> cat_3 pi_t1_cat3    1        3     0.35 0.10665365 0.1409627 0.5590373  0.95

# Order tests for CAT
run_order_tests_cat(y_cat, max_order = 2)$table
#>       comparison order_null order_alt method lrt_stat df    p_value significant
#> 1 AD(0) vs AD(1)          0         1    lrt 13.04437 12 0.36582405       FALSE
#> 2 AD(1) vs AD(2)          1         2    lrt 37.28660 24 0.04096144        TRUE

Missing-data CAT fit

y_cat_miss <- y_cat
y_cat_miss[sample(length(y_cat_miss), 12)] <- NA

fit_cat_miss <- fit_cat(y_cat_miss, order = 1, na_action = "marginalize")
fit_cat_miss$log_l
#> [1] -65.91133
fit_cat_miss$settings$na_action_effective
#> [1] "marginalize"

# EM alternative for CAT missing data (orders 0/1)
fit_cat_miss_em <- fit_cat(y_cat_miss, order = 1, na_action = "em", em_max_iter = 10)
#> Warning in em_cat(y = y, order = p, blocks = blocks_input, homogeneous =
#> homogeneous, : EM did not converge after 10 iterations (change = 0.000809).
fit_cat_miss_em$log_l
#> [1] -65.91256

# Missing-data order/homogeneity tests are supported
blocks_cat <- rep(1:2, each = nrow(y_cat_miss) / 2)
test_order_cat(y_cat_miss, order_null = 0, order_alt = 1)$p_value
#> [1] 0.2500927
test_homogeneity_cat(y_cat_miss, blocks = blocks_cat, order = 1)$p_value
#> [1] 0.3780152

Additional Inference Helpers (Complete Data)

# INAD homogeneity/stationarity tools
blocks <- rep(1:2, each = nrow(y_inad) / 2)
run_homogeneity_tests_inad(y_inad, blocks = blocks, order = 1)
run_stationarity_tests_inad(y_inad, order = 1, blocks = blocks)

# CAT stationarity/time-invariance tools
test_timeinvariance_cat(y_cat, order = 1)
test_stationarity_cat(y_cat, order = 1)

Known Limitations

EM entry points: em_gau (Gaussian), em_inad (INAD), and em_cat (CAT, orders 0/1) are available; for CAT order 2 with missing data, use fit_cat(na_action = "marginalize").
For CAT missingness, fit_cat(na_action = "marginalize") supports orders 0/1/2, while fit_cat(na_action = "em") (or em_cat) supports orders 0/1 with optional safeguard step-halving.
Missing-data confidence intervals are not implemented yet (ci_gau, ci_inad, ci_cat require complete-data fits).
AD missing-data LRT/mean/covariance tests are not implemented yet.
CAT missing-data time-invariance/stationarity tests (test_timeinvariance_cat, test_stationarity_cat, run_stationarity_tests_cat) are not implemented yet.
Current order support is up to order 2 for AD, INAD, and CAT.
CAT missing-data marginalization currently supports orders 0, 1, and 2.