Monotone missingness describes a study where, once a
subject drops out at some stage of a longitudinal or multi-stage design,
they stay missing at every later stage too – a common real-world pattern
(e.g. cohort attrition over repeated visits), as opposed to sporadic
missingness that comes and goes independently at each stage. A 6-stage
serial model, with each stage itself a 2-layer parallel submodel, is a
large, deeply-nested architecture: this tutorial exists to confirm that
the package’s serial fitting and missing-data handling actually hold up
at that scale and under a realistic, worsening missingness pattern – not
to teach a new API. Every function it calls
(estimate_lucid(), summary(),
boot_lucid()) is demonstrated in depth in the 3-model
tutorials; this file is a stress test of the same functions on a harder
topology.
This tutorial demonstrates a stress-test architecture that mirrors a real production pattern:
Rho_G = Rho_Z_Mu = Rho_Z_Cov = 0)Missing-data design in this tutorial:
s, it stays
missing at all later stages (monotone pattern)Goal: verify this design runs with the current missing-data mechanism and inspect stage-wise missingness summaries.
Key design choices:
G, CoG, CoY are
correlated.stage s
depends on stage s-1).Z is generated from latent stage
signal + exposures + shared component.Y is associated with final-stage latent structure and
exposure/covariates.make_serial_six_parallel_data <- function(n = 60, pG = 5, pZ = 3, seed = 5252) {
set.seed(seed)
# Exposure block
G <- matrix(rnorm(n * pG), nrow = n, ncol = pG)
colnames(G) <- paste0("G", seq_len(pG))
# Covariates linked to exposures (induced association)
CoG <- cbind(
cov1 = G[, 1] + rnorm(n, sd = 0.25),
cov2 = G[, 2] - 0.5 * G[, 3] + rnorm(n, sd = 0.25)
)
CoY <- CoG
# Serial latent signals
eta <- matrix(0, nrow = n, ncol = 6)
x <- matrix(0, nrow = n, ncol = 6)
eta[, 1] <- 0.9 * G[, 1] - 0.7 * G[, 2] + 0.4 * CoG[, 1] + rnorm(n, sd = 0.5)
x[, 1] <- as.numeric(eta[, 1] > median(eta[, 1]))
for (s in 2:6) {
eta[, s] <- 0.7 * as.numeric(scale(eta[, s - 1])) +
0.5 * G[, 1] - 0.4 * G[, 3] + 0.35 * x[, s - 1] + rnorm(n, sd = 0.6)
x[, s] <- as.numeric(eta[, s] > median(eta[, s]))
}
# 6 stages; each stage has 2 parallel layers
Z <- vector("list", 6)
names(Z) <- paste0("stage", seq_len(6))
for (s in seq_len(6)) {
shared <- rnorm(n, sd = 0.35)
layer1 <- cbind(
1.2 * x[, s] + 0.5 * G[, 1] + shared + rnorm(n, sd = 0.45),
0.9 * x[, s] - 0.3 * G[, 2] + shared + rnorm(n, sd = 0.45),
0.7 * x[, s] + 0.4 * G[, 4] + shared + rnorm(n, sd = 0.45)
)
layer2 <- cbind(
-1.0 * x[, s] + 0.45 * G[, 2] + shared + rnorm(n, sd = 0.45),
-0.8 * x[, s] - 0.35 * G[, 1] + shared + rnorm(n, sd = 0.45),
-0.6 * x[, s] + 0.30 * G[, 5] + shared + rnorm(n, sd = 0.45)
)
colnames(layer1) <- paste0("s", s, "_L1_f", seq_len(pZ))
colnames(layer2) <- paste0("s", s, "_L2_f", seq_len(pZ))
Z[[s]] <- list(layer1 = layer1, layer2 = layer2)
}
# Outcome associated with final latent stage + exposure/covariate terms
Y <- 0.8 * x[, 6] + 0.45 * G[, 1] - 0.25 * G[, 2] + 0.35 * CoY[, 2] + rnorm(n, sd = 0.7)
list(G = G, Z = Z, Y = as.numeric(Y), CoG = CoG, CoY = CoY)
}
d <- make_serial_six_parallel_data(seed = 5252)
str(d, max.level = 2)## List of 5
## $ G : num [1:60, 1:5] 3.026 0.713 1.496 -0.296 1.384 ...
## ..- attr(*, "dimnames")=List of 2
## $ Z :List of 6
## ..$ stage1:List of 2
## ..$ stage2:List of 2
## ..$ stage3:List of 2
## ..$ stage4:List of 2
## ..$ stage5:List of 2
## ..$ stage6:List of 2
## $ Y : num [1:60] 2.016 0.429 1.026 1.21 0.679 ...
## $ CoG: num [1:60, 1:2] 3.148 1.039 0.974 -0.544 1.125 ...
## ..- attr(*, "dimnames")=List of 2
## $ CoY: num [1:60, 1:2] 3.148 1.039 0.974 -0.544 1.125 ...
## ..- attr(*, "dimnames")=List of 2Policy encoded here:
0, 4, 8, 12, 16, 20i is listwise missing at stage
s, then subject i is also listwise missing at
all later stagesapply_monotone_missingness <- function(d, pZ = 3) {
listwise_n_by_stage <- c(0, 4, 8, 12, 16, 20)
for (s in seq_len(6)) {
if (listwise_n_by_stage[s] > 0) {
miss_rows <- seq_len(listwise_n_by_stage[s])
d$Z[[s]]$layer1[miss_rows, ] <- NA
d$Z[[s]]$layer2[miss_rows, ] <- NA
}
spor_rows <- seq_len(min(nrow(d$G), s + 1))
d$Z[[s]]$layer1[spor_rows, 1] <- NA
d$Z[[s]]$layer2[spor_rows, pZ] <- NA
}
d$listwise_n_by_stage <- listwise_n_by_stage
d
}
d_miss <- apply_monotone_missingness(d)
d_miss$listwise_n_by_stage## [1] 0 4 8 12 16 20Notes:
Rho_* = 0)list(list(2,2), ..., list(2,2)) with
length 6K6 <- replicate(6, list(2, 2), simplify = FALSE)
set.seed(5252)
serial_fit <- estimate_lucid(
lucid_model = "serial",
G = d_miss$G,
Z = d_miss$Z,
Y = d_miss$Y,
CoG = d_miss$CoG,
CoY = d_miss$CoY,
family = "normal",
K = K6,
Rho_G = 0,
Rho_Z_Mu = 0,
Rho_Z_Cov = 0,
max_itr = 6,
max_tot.itr = 36,
tol = 1e-2,
seed = 5252,
verbose = FALSE
)## Fitting LUCID serial model (6 stages)...## Stage 1/6 (parallel) finished: log-likelihood = -349.251.## Stage 2/6 (parallel) finished: log-likelihood = -323.580.## Stage 3/6 (parallel) finished: log-likelihood = -296.120.## Stage 4/6 (parallel) finished: log-likelihood = -281.957.## Stage 5/6 (parallel) finished: log-likelihood = -252.147.## Stage 6/6 (parallel) finished: log-likelihood = -298.761.
## Finished LUCID serial model.## [1] "lucid_serial"## [1] 6## [1] "lucid_parallel" "lucid_parallel" "lucid_parallel" "lucid_parallel"
## [5] "lucid_parallel" "lucid_parallel"verbose = TRUE)This small extra fit demonstrates detailed per-iteration logging behavior for serial mode.
K2 <- replicate(2, list(2, 2), simplify = FALSE)
# Smaller two-stage subset to keep verbose demo fast.
n_demo <- 30
d_demo <- list(
G = d_miss$G[1:n_demo, , drop = FALSE],
Z = lapply(d_miss$Z[1:2], function(stage) {
list(
layer1 = stage$layer1[1:n_demo, , drop = FALSE],
layer2 = stage$layer2[1:n_demo, , drop = FALSE]
)
}),
Y = d_miss$Y[1:n_demo],
CoG = d_miss$CoG[1:n_demo, , drop = FALSE],
CoY = d_miss$CoY[1:n_demo, , drop = FALSE]
)
set.seed(5251)
serial_fit_verbose <- estimate_lucid(
lucid_model = "serial",
G = d_demo$G,
Z = d_demo$Z,
Y = d_demo$Y,
CoG = d_demo$CoG,
CoY = d_demo$CoY,
family = "normal",
K = K2,
Rho_G = 0,
Rho_Z_Mu = 0,
Rho_Z_Cov = 0,
max_itr = 2,
max_tot.itr = 8,
tol = 1e-2,
seed = 5251,
verbose = TRUE
)## Fitting LUCID serial model (Stage 1/2)...
## Intializing imputation of missing values in 'Z' via LOD / sqrt(2)
##
## Intializing imputation of missing values in 'Z' via LOD / sqrt(2)
##
## Fitting LUCID in Parallel model (K = 2, Rho_G = 0, Rho_Z_Mu = 0, Rho_Z_Cov = 0) (K = 2, Rho_G = 0, Rho_Z_Mu = 0, Rho_Z_Cov = 0)
## iteration 1 : E-step finished.
## iteration 1: log-likelihood = -154.324
## iteration 2 : E-step finished.
## iteration 2: log-likelihood = -153.513## Finished LUCID parallel model: log-likelihood = -153.513.
##
## Fitting LUCID serial model (Stage 2/2)...
## Fitting LUCID in Parallel model (K = 2, Rho_G = 0, Rho_Z_Mu = 0, Rho_Z_Cov = 0) (K = 2, Rho_G = 0, Rho_Z_Mu = 0, Rho_Z_Cov = 0)
## iteration 1 : E-step finished.
## iteration 1: log-likelihood = -187.426
## iteration 2 : E-step finished.
## iteration 2: log-likelihood = -187.240## Finished LUCID parallel model: log-likelihood = -187.240.
##
## Success: LUCID serial model constructed!We check that recorded listwise row counts match the monotone design.
listwise_l1 <- vapply(serial_fit$missing_summary$stage, function(ms) {
as.integer(ms$layer_summary$listwise_rows[1])
}, integer(1))
listwise_l2 <- vapply(serial_fit$missing_summary$stage, function(ms) {
as.integer(ms$layer_summary$listwise_rows[2])
}, integer(1))
data.frame(
stage = 1:6,
expected_listwise = d_miss$listwise_n_by_stage,
observed_layer1 = listwise_l1,
observed_layer2 = listwise_l2
)## stage expected_listwise observed_layer1 observed_layer2
## 1 1 0 0 0
## 2 2 4 4 4
## 3 3 8 8 8
## 4 4 12 12 12
## 5 5 16 16 16
## 6 6 20 20 20Even with aggressive later-stage missingness, final-stage posterior probabilities should remain finite.
## [1] TRUE## [1] TRUEstopifnot(all(is.finite(last_stage$inclusion.p[[1]])))
stopifnot(all(is.finite(last_stage$inclusion.p[[2]])))By stage 6, 20 of nrow(d_miss$G) subjects have been
listwise-missing since stage 5 or earlier – carrying no direct omics
information into this stage’s own likelihood term. The check above
confirms that accumulated missingness alone doesn’t drive the posterior
to NaN/Inf, which is the failure mode this
section exists to rule out.
The full summary() report – the same one every other
vignette uses, unchanged by this model’s size – prints one
feature-selection overview and one set of coefficient tables per stage.
With 6 stages, each itself a 2-layer parallel submodel, this is the
single largest printed report any vignette in this package produces;
scanning it top to bottom confirms every stage’s missingness profile,
selection, and coefficients all look sane before trusting the fit for
anything downstream.
##
## ====================================================
## LUCID Serial: Model Summary
## ====================================================
##
## Model specification
## Family : normal
## Number of observations : 60
## Number of stages : 6
## Stage 1 : parallel (K = 2,2)
## Stage 2 : parallel (K = 2,2)
## Stage 3 : parallel (K = 2,2)
## Stage 4 : parallel (K = 2,2)
## Stage 5 : parallel (K = 2,2)
## Stage 6 : parallel (K = 2,2)
##
## Missing-data profile by stage
## Stage 1
## Layer 1 listwise/sporadic rows : 0 / 2
## Layer 2 listwise/sporadic rows : 0 / 2
## Stage 2
## Layer 1 listwise/sporadic rows : 4 / 0
## Layer 2 listwise/sporadic rows : 4 / 0
## Stage 3
## Layer 1 listwise/sporadic rows : 8 / 0
## Layer 2 listwise/sporadic rows : 8 / 0
## Stage 4
## Layer 1 listwise/sporadic rows : 12 / 0
## Layer 2 listwise/sporadic rows : 12 / 0
## Stage 5
## Layer 1 listwise/sporadic rows : 16 / 0
## Layer 2 listwise/sporadic rows : 16 / 0
## Stage 6
## Layer 1 listwise/sporadic rows : 20 / 0
## Layer 2 listwise/sporadic rows : 20 / 0
##
## Model fit statistics
## Log-likelihood : -1801.81
## BIC : 4700.91
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Stage-wise detailed parameter estimates
##
## --- Stage 1 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 0 / 60 (0.0%)
## Layer 1 sporadic rows : 2 / 60 (3.3%)
## Layer 1 missing cells : 2 / 180 (1.1%)
## Layer 2 listwise rows : 0 / 60 (0.0%)
## Layer 2 sporadic rows : 2 / 60 (3.3%)
## Layer 2 missing cells : 2 / 180 (1.1%)
##
## Feature selection overview
## G features selected : 5 / 5 (100.0%)
## G features by layer
## Layer 1 : 5 / 5 (100.0%)
## Layer 2 : 5 / 5 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -349.25
## BIC : 911.41
## Number of parameters : 52
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s1_L1_f1 -0.25923098 1.7766753
## s1_L1_f2 -0.07087825 1.0212576
## s1_L1_f3 0.02796816 0.8084774
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s1_L2_f1 -1.2140937 0.21626421
## s1_L2_f2 -1.1713477 0.15440970
## s1_L2_f3 -0.5157522 0.02402461
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each exposure for each layer
## Layer 1
##
## beta OR
## (Intercept).cluster2 -2.142589 0.1173506
## G1.cluster2 7.186028 1320.8462975
## G2.cluster2 3.353820 28.6118125
## G3.cluster2 -4.063713 0.0171851
## G4.cluster2 -1.752995 0.1732542
## G5.cluster2 3.789942 44.2538337
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 -0.47824432 6.198707e-01
## G1.cluster2 -7.23309223 7.222839e-04
## G2.cluster2 10.62829698 4.128675e+04
## G3.cluster2 -2.94054526 5.283691e-02
## G4.cluster2 0.03096535 1.031450e+00
## G5.cluster2 0.25659661 1.292524e+00
##
##
## --- Stage 2 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 4 / 60 (6.7%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 12 / 180 (6.7%)
## Layer 2 listwise rows : 4 / 60 (6.7%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 12 / 180 (6.7%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -323.58
## BIC : 819.12
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s2_L1_f1 -0.32476364 1.5770726
## s2_L1_f2 0.03621375 1.0082170
## s2_L1_f3 0.01434587 0.7739294
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s2_L2_f1 -0.9345513 0.1586644
## s2_L2_f2 -1.1641792 0.2081802
## s2_L2_f3 -0.6181080 0.1895868
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## beta OR
## (Intercept).cluster2 -0.2345533 0.79092411
## Stage1.Layer1.cluster2.cluster2 3.0061229 20.20889549
## Stage1.Layer2.cluster2.cluster2 -2.9934749 0.05011299
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 0.9763921 2.65486053
## Stage1.Layer1.cluster2.cluster2 -2.9861738 0.05048022
## Stage1.Layer2.cluster2.cluster2 1.5837012 4.87295814
##
##
## --- Stage 3 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 8 / 60 (13.3%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 24 / 180 (13.3%)
## Layer 2 listwise rows : 8 / 60 (13.3%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 24 / 180 (13.3%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -296.12
## BIC : 764.20
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s3_L1_f1 -0.3133371 1.5309424
## s3_L1_f2 -0.1356417 0.9311460
## s3_L1_f3 0.1989601 0.8251488
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s3_L2_f1 -0.6947063 0.36149336
## s3_L2_f2 -0.5201382 -0.04672601
## s3_L2_f3 -0.4876534 0.83015288
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## beta OR
## (Intercept).cluster2 0.3386909 1.403110e+00
## Stage2.Layer1.cluster2.cluster2 6.0688887 4.322001e+02
## Stage2.Layer2.cluster2.cluster2 -6.7814384 1.134642e-03
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 -4.1231203 0.01619391
## Stage2.Layer1.cluster2.cluster2 -0.1080911 0.89754586
## Stage2.Layer2.cluster2.cluster2 3.2698368 26.30704652
##
##
## --- Stage 4 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 12 / 60 (20.0%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 36 / 180 (20.0%)
## Layer 2 listwise rows : 12 / 60 (20.0%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 36 / 180 (20.0%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -281.96
## BIC : 735.88
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s4_L1_f1 -0.4247369 1.1626366
## s4_L1_f2 -0.2351415 0.6619763
## s4_L1_f3 -0.1777889 0.7520117
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s4_L2_f1 -0.8871681 0.3195956
## s4_L2_f2 -0.8313317 0.3952578
## s4_L2_f3 -0.6999865 0.3092289
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## beta OR
## (Intercept).cluster2 -0.8654305 0.4208703
## Stage3.Layer1.cluster2.cluster2 5.3281366 206.0536649
## Stage3.Layer2.cluster2.cluster2 -1.2556081 0.2849025
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 0.4462967 1.562515
## Stage3.Layer1.cluster2.cluster2 -2.0653098 0.126779
## Stage3.Layer2.cluster2.cluster2 1.8718092 6.500045
##
##
## --- Stage 5 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 16 / 60 (26.7%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 48 / 180 (26.7%)
## Layer 2 listwise rows : 16 / 60 (26.7%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 48 / 180 (26.7%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -252.15
## BIC : 676.26
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s5_L1_f1 -0.2996022 1.2611756
## s5_L1_f2 -0.1630761 0.5999957
## s5_L1_f3 0.1113482 0.5636818
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s5_L2_f1 -1.0062271 0.27218989
## s5_L2_f2 -1.1786110 0.07458108
## s5_L2_f3 -0.7027253 0.12793040
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## beta OR
## (Intercept).cluster2 -2.170905 1.140743e-01
## Stage4.Layer1.cluster2.cluster2 12.798914 3.618243e+05
## Stage4.Layer2.cluster2.cluster2 -10.681740 2.296040e-05
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 3.513576 3.356809e+01
## Stage4.Layer1.cluster2.cluster2 -7.218582 7.328406e-04
## Stage4.Layer2.cluster2.cluster2 5.643075 2.823295e+02
##
##
## --- Stage 6 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 20 / 60 (33.3%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 60 / 180 (33.3%)
## Layer 2 listwise rows : 20 / 60 (33.3%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 60 / 180 (33.3%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -298.76
## BIC : 794.05
## Number of parameters : 48
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Y (continuous outcome): intercept, effects of each non-reference latent cluster for each layer of Y (and effect of covariates if included)
## Gamma
## (Intercept) -0.05913686
## Layer1_LC2 0.06078451
## Layer2_LC2 1.05110540
## cov1 0.34504269
## cov2 0.25584470
##
## (2) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## mu_cluster1 mu_cluster2
## s6_L1_f1 1.5605963 -0.38155266
## s6_L1_f2 0.8935406 0.05500217
## s6_L1_f3 0.9361158 0.05836151
##
## Layer 2
##
## mu_cluster1 mu_cluster2
## s6_L2_f1 0.02787015 -0.8944043
## s6_L2_f2 0.07880488 -0.9214000
## s6_L2_f3 0.17140060 -0.7804256
##
## (3) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## beta OR
## (Intercept).cluster2 0.3766627 1.45741261
## Stage5.Layer1.cluster2.cluster2 -3.0656751 0.04662235
## Stage5.Layer2.cluster2.cluster2 2.5017497 12.20382830
##
## Layer 2
##
## beta OR
## (Intercept).cluster2 -0.04097893 0.9598494
## Stage5.Layer1.cluster2.cluster2 0.83420130 2.3029739
## Stage5.Layer2.cluster2.cluster2 -1.58901626 0.2041263Because this model is already fit with zero penalties, we can directly run bootstrap CI.
Practical note:
R in the tutorial for runtime.R for more stable
intervals.set.seed(5253)
serial_boot <- boot_lucid(
G = d_miss$G,
Z = d_miss$Z,
Y = d_miss$Y,
CoG = d_miss$CoG,
CoY = d_miss$CoY,
model = serial_fit,
R = 2,
conf = 0.90
)
# Stage-wise bootstrap objects are returned under $stage
length(serial_boot$stage)## [1] 6## [1] "beta" "mu" "gamma"length(serial_boot$stage) should read 6:
boot_lucid() resamples subjects once and refits the entire
6-stage chain on each resample, then reports one set of bootstrap
replicates per stage, mirroring the fit’s own submodel
structure.
This summary prints the same model tables plus CI columns for supported parameter blocks.
##
## ====================================================
## LUCID Serial: Model Summary
## ====================================================
##
## Model specification
## Family : normal
## Number of observations : 60
## Number of stages : 6
## Stage 1 : parallel (K = 2,2)
## Stage 2 : parallel (K = 2,2)
## Stage 3 : parallel (K = 2,2)
## Stage 4 : parallel (K = 2,2)
## Stage 5 : parallel (K = 2,2)
## Stage 6 : parallel (K = 2,2)
##
## Missing-data profile by stage
## Stage 1
## Layer 1 listwise/sporadic rows : 0 / 2
## Layer 2 listwise/sporadic rows : 0 / 2
## Stage 2
## Layer 1 listwise/sporadic rows : 4 / 0
## Layer 2 listwise/sporadic rows : 4 / 0
## Stage 3
## Layer 1 listwise/sporadic rows : 8 / 0
## Layer 2 listwise/sporadic rows : 8 / 0
## Stage 4
## Layer 1 listwise/sporadic rows : 12 / 0
## Layer 2 listwise/sporadic rows : 12 / 0
## Stage 5
## Layer 1 listwise/sporadic rows : 16 / 0
## Layer 2 listwise/sporadic rows : 16 / 0
## Stage 6
## Layer 1 listwise/sporadic rows : 20 / 0
## Layer 2 listwise/sporadic rows : 20 / 0
##
## Model fit statistics
## Log-likelihood : -1801.81
## BIC : 4700.91
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Stage-wise detailed parameter estimates
##
## --- Stage 1 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 0 / 60 (0.0%)
## Layer 1 sporadic rows : 2 / 60 (3.3%)
## Layer 1 missing cells : 2 / 180 (1.1%)
## Layer 2 listwise rows : 0 / 60 (0.0%)
## Layer 2 sporadic rows : 2 / 60 (3.3%)
## Layer 2 missing cells : 2 / 180 (1.1%)
##
## Feature selection overview
## G features selected : 5 / 5 (100.0%)
## G features by layer
## Layer 1 : 5 / 5 (100.0%)
## Layer 2 : 5 / 5 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -349.25
## BIC : 911.41
## Number of parameters : 52
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s1_L1_f1.cluster1 -0.25923098 -0.79361335 0.88693388
## Layer1.s1_L1_f2.cluster1 -0.07087825 -0.14553608 0.04977206
## Layer1.s1_L1_f3.cluster1 0.02796816 -0.02311424 0.18098680
## Layer1.s1_L1_f1.cluster2 1.77667527 1.58629484 2.12963448 *
## Layer1.s1_L1_f2.cluster2 1.02125760 0.99943648 1.37665268 *
## Layer1.s1_L1_f3.cluster2 0.80847737 0.62159663 1.18330380 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s1_L2_f1.cluster1 -1.21409366 -1.64451591 -0.96462446 *
## Layer2.s1_L2_f2.cluster1 -1.17134774 -1.86438089 -0.72311410 *
## Layer2.s1_L2_f3.cluster1 -0.51575219 -0.81882942 0.04689113
## Layer2.s1_L2_f1.cluster2 0.21626421 -0.01569531 0.61542538
## Layer2.s1_L2_f2.cluster2 0.15440970 -0.07734336 0.51817365
## Layer2.s1_L2_f3.cluster2 0.02402461 -0.53383939 0.20885447
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each exposure for each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -2.142589 -6.9850429 0.2053811
## G1.cluster2 7.186028 9.1883008 13.3802560 *
## G2.cluster2 3.353820 -0.1173109 7.6398951
## G3.cluster2 -4.063713 -8.1629158 -2.5783536 *
## G4.cluster2 -1.752995 -6.7730296 2.9787589
## G5.cluster2 3.789942 -3.5665146 11.9221808
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -0.47824432 -2.153376 8.945538
## G1.cluster2 -7.23309223 -52.418713 86.298505
## G2.cluster2 10.62829698 -56.492475 42.116627
## G3.cluster2 -2.94054526 -4.929223 6.362262
## G4.cluster2 0.03096535 -1.285787 2.389459
## G5.cluster2 0.25659661 -6.182917 11.589230
##
##
## --- Stage 2 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 4 / 60 (6.7%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 12 / 180 (6.7%)
## Layer 2 listwise rows : 4 / 60 (6.7%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 12 / 180 (6.7%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -323.58
## BIC : 819.12
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s2_L1_f1.cluster1 -0.32476364 -0.7426353 -0.36636475 *
## Layer1.s2_L1_f2.cluster1 0.03621375 -0.4114942 0.20647259
## Layer1.s2_L1_f3.cluster1 0.01434587 -0.4302874 -0.09155984 *
## Layer1.s2_L1_f1.cluster2 1.57707264 1.3378131 2.12564670 *
## Layer1.s2_L1_f2.cluster2 1.00821699 0.8852328 1.18515137 *
## Layer1.s2_L1_f3.cluster2 0.77392945 0.7544277 0.97289729 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s2_L2_f1.cluster1 -0.9345513 -1.18486439 -0.3299740 *
## Layer2.s2_L2_f2.cluster1 -1.1641792 -1.33395777 -1.1883889 *
## Layer2.s2_L2_f3.cluster1 -0.6181080 -0.52869893 -0.4672291 *
## Layer2.s2_L2_f1.cluster2 0.1586644 -0.02575317 0.1085187
## Layer2.s2_L2_f2.cluster2 0.2081802 0.36216746 0.3639570 *
## Layer2.s2_L2_f3.cluster2 0.1895868 -0.20071352 0.3496443
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -0.2345533 -0.5275514 2.287386
## Stage1.Layer1.cluster2.cluster2 3.0061229 2.4569013 3.421997 *
## Stage1.Layer2.cluster2.cluster2 -2.9934749 -4.6938575 -4.042293 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 0.9763921 0.3586997 0.8025441 *
## Stage1.Layer1.cluster2.cluster2 -2.9861738 -4.7768049 -1.4015125 *
## Stage1.Layer2.cluster2.cluster2 1.5837012 2.4207720 3.8864259 *
##
##
## --- Stage 3 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 8 / 60 (13.3%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 24 / 180 (13.3%)
## Layer 2 listwise rows : 8 / 60 (13.3%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 24 / 180 (13.3%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -296.12
## BIC : 764.20
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s3_L1_f1.cluster1 -0.3133371 -0.3909362 -0.2595396 *
## Layer1.s3_L1_f2.cluster1 -0.1356417 -0.2215396 -0.1122738 *
## Layer1.s3_L1_f3.cluster1 0.1989601 -0.3071382 0.4285289
## Layer1.s3_L1_f1.cluster2 1.5309424 1.2542982 1.7754245 *
## Layer1.s3_L1_f2.cluster2 0.9311460 0.5525322 1.2567254 *
## Layer1.s3_L1_f3.cluster2 0.8251488 0.8968467 0.9973711 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s3_L2_f1.cluster1 -0.69470634 -0.007620766 0.12246931
## Layer2.s3_L2_f2.cluster1 -0.52013817 -0.030556747 0.40226715
## Layer2.s3_L2_f3.cluster1 -0.48765339 -0.559267829 -0.01069365 *
## Layer2.s3_L2_f1.cluster2 0.36149336 0.531092947 1.25080102 *
## Layer2.s3_L2_f2.cluster2 -0.04672601 -0.247231088 0.41447547
## Layer2.s3_L2_f3.cluster2 0.83015288 1.520150904 2.22864465 *
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 0.3386909 -0.7106238 2.509950
## Stage2.Layer1.cluster2.cluster2 6.0688887 3.6377378 8.195110 *
## Stage2.Layer2.cluster2.cluster2 -6.7814384 -8.7273253 -7.451612 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -4.1231203 -12.348769 -9.032837 *
## Stage2.Layer1.cluster2.cluster2 -0.1080911 1.100694 6.079315 *
## Stage2.Layer2.cluster2.cluster2 3.2698368 4.267486 8.417789 *
##
##
## --- Stage 4 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 12 / 60 (20.0%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 36 / 180 (20.0%)
## Layer 2 listwise rows : 12 / 60 (20.0%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 36 / 180 (20.0%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -281.96
## BIC : 735.88
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s4_L1_f1.cluster1 -0.4247369 -0.9958713 -0.4661303 *
## Layer1.s4_L1_f2.cluster1 -0.2351415 -0.3815243 -0.1199789 *
## Layer1.s4_L1_f3.cluster1 -0.1777889 -0.8801466 0.3664514
## Layer1.s4_L1_f1.cluster2 1.1626366 1.1189991 1.1291377 *
## Layer1.s4_L1_f2.cluster2 0.6619763 0.4157009 0.7212194 *
## Layer1.s4_L1_f3.cluster2 0.7520117 0.4056094 0.7426555 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s4_L2_f1.cluster1 -0.8871681 -0.83999723 -0.7253571 *
## Layer2.s4_L2_f2.cluster1 -0.8313317 -1.40157111 -0.4104110 *
## Layer2.s4_L2_f3.cluster1 -0.6999865 -1.09210019 -0.6094454 *
## Layer2.s4_L2_f1.cluster2 0.3195956 0.13846992 0.2830234 *
## Layer2.s4_L2_f2.cluster2 0.3952578 0.05234972 0.7100608 *
## Layer2.s4_L2_f3.cluster2 0.3092289 0.20098883 0.4179397 *
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -0.8654305 -11.404738 -5.469946 *
## Stage3.Layer1.cluster2.cluster2 5.3281366 8.267649 10.224493 *
## Stage3.Layer2.cluster2.cluster2 -1.2556081 2.773614 8.790164 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 0.4462967 2.1628010 4.4102290 *
## Stage3.Layer1.cluster2.cluster2 -2.0653098 -4.7935742 -1.9579723 *
## Stage3.Layer2.cluster2.cluster2 1.8718092 0.3098809 0.8825582 *
##
##
## --- Stage 5 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 16 / 60 (26.7%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 48 / 180 (26.7%)
## Layer 2 listwise rows : 16 / 60 (26.7%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 48 / 180 (26.7%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -252.15
## BIC : 676.26
## Number of parameters : 42
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s5_L1_f1.cluster1 -0.2996022 -0.8882838 0.07489369
## Layer1.s5_L1_f2.cluster1 -0.1630761 -1.1629042 0.21029478
## Layer1.s5_L1_f3.cluster1 0.1113482 0.2590135 0.66042835 *
## Layer1.s5_L1_f1.cluster2 1.2611756 0.8747669 2.16118165 *
## Layer1.s5_L1_f2.cluster2 0.5999957 0.1880085 1.54315740 *
## Layer1.s5_L1_f3.cluster2 0.5636818 0.2781253 0.51088743 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s5_L2_f1.cluster1 -1.00622711 -1.0903533 -0.8796766 *
## Layer2.s5_L2_f2.cluster1 -1.17861099 -1.4072148 -0.9414385 *
## Layer2.s5_L2_f3.cluster1 -0.70272528 -0.6624194 -0.1962498 *
## Layer2.s5_L2_f1.cluster2 0.27218989 -0.2243491 0.9035287
## Layer2.s5_L2_f2.cluster2 0.07458108 -0.3429528 0.3628809
## Layer2.s5_L2_f3.cluster2 0.12793040 -0.4286360 0.4602318
##
## (2) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -2.170905 -6.258755 -2.90168 *
## Stage4.Layer1.cluster2.cluster2 12.798914 19.573464 26.98979 *
## Stage4.Layer2.cluster2.cluster2 -10.681740 -21.793861 -16.56249 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 3.513576 4.519565 7.655325 *
## Stage4.Layer1.cluster2.cluster2 -7.218582 -12.182219 -10.342349 *
## Stage4.Layer2.cluster2.cluster2 5.643075 6.245093 10.854133 *
##
##
## --- Stage 6 (parallel) ---
##
## ====================================================
## LUCID Parallel: Model Summary
## ====================================================
##
## Model specification
## Family : gaussian
## Number of observations : 60
## Clusters per layer : 2, 2
##
## Missing-data profile by layer
## Layer 1 listwise rows : 20 / 60 (33.3%)
## Layer 1 sporadic rows : 0 / 60 (0.0%)
## Layer 1 missing cells : 60 / 180 (33.3%)
## Layer 2 listwise rows : 20 / 60 (33.3%)
## Layer 2 sporadic rows : 0 / 60 (0.0%)
## Layer 2 missing cells : 60 / 180 (33.3%)
##
## Feature selection overview
## G features selected : 2 / 2 (100.0%)
## G features by layer
## Layer 1 : 2 / 2 (100.0%)
## Layer 2 : 2 / 2 (100.0%)
## Z features
## Layer 1 selected : 3 / 3 (100.0%)
## Layer 1 multi-cluster: 3
## Layer 2 selected : 3 / 3 (100.0%)
## Layer 2 multi-cluster: 3
##
## Model fit statistics
## Log-likelihood : -298.76
## BIC : 794.05
## Number of parameters : 48
##
## Regularization
## Rho_G : 0.000
## Rho_Z_Mu : 0.000
## Rho_Z_Cov : 0.000
##
## Detailed parameter estimates
## (1) Y (continuous outcome): intercept, effects of each non-reference latent cluster for each layer of Y (and effect of covariates if included)
## Gamma norm_lower norm_upper sig
## (Intercept) -0.05913686 -0.29501682 0.2502420
## Layer1_LC2 0.06078451 -0.19695520 0.2392204
## Layer2_LC2 1.05110540 0.63753139 1.5544808 *
## cov1 0.34504269 0.01954345 0.4241201 *
## cov2 0.25584470 0.12566303 0.5266616 *
##
## (2) Z: mean of omics data for each latent cluster of each layer
## Layer 1
##
## estimate norm_lower norm_upper sig
## Layer1.s6_L1_f1.cluster1 1.56059632 0.8366922 4.9034304 *
## Layer1.s6_L1_f2.cluster1 0.89354060 1.1651722 2.1268096 *
## Layer1.s6_L1_f3.cluster1 0.93611581 -0.6884367 3.0001803
## Layer1.s6_L1_f1.cluster2 -0.38155266 -2.9643424 -0.2248744 *
## Layer1.s6_L1_f2.cluster2 0.05500217 -0.5627217 -0.3004916 *
## Layer1.s6_L1_f3.cluster2 0.05836151 -1.2420110 0.5665753
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## Layer2.s6_L2_f1.cluster1 0.02787015 -0.6160551 1.09786091
## Layer2.s6_L2_f2.cluster1 0.07880488 -0.2418875 0.45295601
## Layer2.s6_L2_f3.cluster1 0.17140060 -0.1230959 0.77714140
## Layer2.s6_L2_f1.cluster2 -0.89440432 -1.0805042 -0.82878093 *
## Layer2.s6_L2_f2.cluster2 -0.92139998 -1.2668090 0.03064748
## Layer2.s6_L2_f3.cluster2 -0.78042556 -0.9207449 -0.75246468 *
##
## (3) E: intercept and odds ratio of being assigned to each latent cluster for each cluster from previous serial stage (for each layer)
## Layer 1
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 0.3766627 -3.334395 2.233794
## Stage5.Layer1.cluster2.cluster2 -3.0656751 -6.218274 -6.078432 *
## Stage5.Layer2.cluster2.cluster2 2.5017497 1.365089 11.008612 *
##
## Layer 2
##
## estimate norm_lower norm_upper sig
## (Intercept).cluster2 -0.04097893 0.6152230 1.4249365 *
## Stage5.Layer1.cluster2.cluster2 0.83420130 0.2542921 0.4418189 *
## Stage5.Layer2.cluster2.cluster2 -1.58901626 -3.2943156 -2.8372619 *Every coefficient table above now also carries the sig
column (see the 3-model tutorials for its exact definition); at
R = 2 replicates the resulting intervals are for
demonstrating the output format only, not for drawing conclusions about
which effects are real.
N or reduce
missingness severity if needed.## R version 4.4.0 (2024-04-24)
## Platform: aarch64-apple-darwin20
## Running under: macOS 26.6.2
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
##
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: America/Los_Angeles
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] plotly_4.11.0 ggplot2_4.0.2 LUCIDus_3.2.0
##
## loaded via a namespace (and not attached):
## [1] tidyr_1.3.1 sass_0.4.10 generics_0.1.4 shape_1.4.6.1
## [5] stringi_1.8.7 lattice_0.22-7 hms_1.1.4 digest_0.6.39
## [9] magrittr_2.0.4 evaluate_1.0.5 grid_4.4.0 RColorBrewer_1.1-3
## [13] iterators_1.0.14 fastmap_1.2.0 foreach_1.5.2 jsonlite_2.0.0
## [17] glmnet_4.1-10 Matrix_1.7-4 progress_1.2.3 nnet_7.3-20
## [21] survival_3.8-3 mclust_6.1.2 httr_1.4.7 purrr_1.2.0
## [25] crosstalk_1.2.2 viridisLite_0.4.2 scales_1.4.0 lazyeval_0.2.2
## [29] codetools_0.2-20 networkD3_0.4.1 jquerylib_0.1.4 cli_3.6.5
## [33] rlang_1.1.6 crayon_1.5.3 splines_4.4.0 withr_3.0.2
## [37] cachem_1.1.0 yaml_2.3.11 tools_4.4.0 dplyr_1.1.4
## [41] boot_1.3-32 vctrs_0.6.5 R6_2.6.1 lifecycle_1.0.4
## [45] htmlwidgets_1.6.4 pkgconfig_2.0.3 glasso_1.11 bslib_0.9.0
## [49] pillar_1.11.1 gtable_0.3.6 data.table_1.17.8 glue_1.8.0
## [53] Rcpp_1.1.0 tidyselect_1.2.1 xfun_0.54 tibble_3.3.0
## [57] data.tree_1.2.0 knitr_1.50 dichromat_2.0-0.1 farver_2.1.2
## [61] htmltools_0.5.9 igraph_2.2.1 labeling_0.4.3 rmarkdown_2.30
## [65] compiler_4.4.0 prettyunits_1.2.0 S7_0.2.1