Jointly estimates a Direct LiNGAM model from multiple datasets ("groups") that are assumed to share a common causal order but may have different structural coefficients (Shimizu 2012).
Usage
lingam_multi_group(
X_list,
prior_knowledge = NULL,
apply_prior_knowledge_softly = FALSE,
reg_method = "adaptive_lasso",
lambda = "BIC",
init_method = "ols"
)Arguments
- X_list
A list of numeric matrices or data frames (length >= 2), one per group. Each element must have
n_drows (sample size may differ by group) and the same number of columnspacross all groups.- prior_knowledge
Prior knowledge matrix (n_features x n_features) or NULL. Applied identically to every group. Same encoding as
lingam_direct(): 0: no directed path from x_i to x_j 1: directed path from x_i to x_j -1: unknown- apply_prior_knowledge_softly
Whether to apply prior knowledge softly (logical)
- reg_method
Regression method for adjacency matrix estimation. "ols": ordinary least squares, "lasso": LASSO regression, "adaptive_lasso": adaptive LASSO regression (default), "ridge": Ridge regression (robust to multicollinearity; does not perform sparse estimation).
- lambda
LASSO penalty (lambda) selection. Same choices as
lingam_direct().- init_method
Method for estimating the initial weights of adaptive LASSO regression ("ols" (default) or "ridge").
Value
A MultiGroupLingamResult object (list) containing:
adjacency_matrices: a named list of adjacency matrices, one per group (name = group name). Each follows the same convention aslingam_direct():B[i, j]is the causal coefficient from variable j to variable i (j -> i).causal_order: the causal order shared by all groups (integer vector of 1-based indices).
Details
Unlike lingam_direct(), this function has no measure argument: the
multi-group causal-order search only supports the pwling (pairwise
likelihood / entropy approximation) objective, matching the upstream
Python MultiGroupDirectLiNGAM, which does not offer a kernel-based
multi-group search.
For downstream analysis of a single group (total causal effects,
independence tests of residuals, plotting), extract that group as a plain
LingamResult with get_group_result() and pass it to the existing
single-group functions (estimate_total_effect(),
estimate_all_total_effects(), get_error_independence_p_values(),
plot_adjacency(), autoplot(), tidy()); no multi-group-specific
wrappers are provided for these.
References
S. Shimizu. Joint estimation of linear non-Gaussian acyclic models. Neurocomputing, 81: 104-107, 2012.
Examples
mg <- generate_multi_group_sample()
res <- lingam_multi_group(mg$data_list, reg_method = "ols")
print(res)
#> Multi-Group Direct LiNGAM Result
#> Groups : 2 (group1, group2)
#> Variables : 6
#> Causal order (common): x3 -> x0 -> x5 -> x2 -> x4 -> x1
#>
#> [group1] Adjacency matrix (row = to, col = from):
#> x0 x1 x2 x3 x4 x5
#> x0 0.000 0 0.000 3.033 0.000 0.000
#> x1 3.237 0 1.965 0.014 -0.034 0.006
#> x2 -0.236 0 0.000 6.112 0.000 0.049
#> x3 0.000 0 0.000 0.000 0.000 0.000
#> x4 7.921 0 -1.063 0.399 0.000 0.018
#> x5 4.016 0 0.000 -0.003 0.000 0.000
#>
#> [group2] Adjacency matrix (row = to, col = from):
#> x0 x1 x2 x3 x4 x5
#> x0 0.000 0 0.000 3.504 0.000 0.000
#> x1 2.732 0 2.568 0.083 0.034 0.093
#> x2 0.154 0 0.000 6.322 0.000 -0.024
#> x3 0.000 0 0.000 0.000 0.000 0.000
#> x4 8.483 0 -1.487 -0.110 0.000 0.006
#> x5 4.515 0 0.000 -0.045 0.000 0.000
# Analyze group 1 with the existing single-group tooling
g1 <- get_group_result(res, 1)
estimate_all_total_effects(mg$data_list[[1]], g1, method = "ols")
#> x0 x1 x2 x3 x4 x5
#> x0 0.00000000 0 0.000000 3.033460 0.00000000 0.00000000
#> x1 2.90911952 0 2.001580 21.058733 -0.03397056 0.10299386
#> x2 -0.03933572 0 0.000000 5.992677 0.00000000 0.04894766
#> x3 0.00000000 0 0.000000 0.000000 0.00000000 0.00000000
#> x4 8.03407606 0 -1.062516 18.276121 0.00000000 -0.03416285
#> x5 4.01586857 0 0.000000 12.179395 0.00000000 0.00000000