Choosing a Causal Discovery Method

lingamr implements eleven causal discovery estimators. They all share the same goal — recovering a directed causal structure from observational data — but each relaxes a different assumption of the basic LiNGAM model. This vignette helps you pick the right one.

The basic LiNGAM model assumes:

1. Linear causal relationships,
2. an acyclic causal graph (a DAG),
3. non-Gaussian, mutually independent error terms,
4. no latent confounder (every common cause is observed),
5. i.i.d. observations (no time structure, no group structure),
6. continuous variables and a complete (no NA) data matrix.

When all six hold, use lingam_direct(). Every other estimator in the package exists to relax one (or two) of these assumptions.

Decision Guide

Work through the questions in order; the first “yes” points to the method.

1. Are the observations a time series?
   • Yes, and temporal dependence is autoregressive → VAR-LiNGAM (lingam_var())
   • Yes, and the VAR residuals stay autocorrelated even with more lags (moving-average disturbances) → VARMA-LiNGAM (lingam_varma())
2. Are causal relationships plausibly nonlinear?
   • Yes, and all major common causes are observed → RESIT (lingam_resit())
   • Yes, and there may be unobserved variables → CAM-UV (lingam_camuv())
3. Might a latent confounder exist (linear case)?
   • You want to know which part of the causal order is still trustworthy → BottomUpParceLiNGAM (lingam_parce())
   • You want to know which specific pairs are confounded → RCD (lingam_rcd())
4. Does the data mix continuous and discrete variables? → LiM (lingam_lim(); binary by default, Poisson counts via is_poisson = TRUE)
5. Do you have several datasets that share a causal structure (multiple sites, periods, cohorts)? → MultiGroup Direct LiNGAM (lingam_multi_group())
6. Does the data contain missing values (NA)? → bootstrap_with_imputation() (bootstrap + multiple imputation)
7. Are there many variables (tens to hundreds), or even p > n? → HighDimDirectLiNGAM (lingam_high_dim())
8. None of the above → Direct LiNGAM (lingam_direct())

If several complications apply at once (say, a nonlinear time series), no single estimator handles both; you will have to prioritize the violation that matters most for your data, or transform the data (e.g. differencing a non-stationary series) so that fewer assumptions are violated.

Method Overview

Method	Function	Handles	Output notes	Bootstrap
Direct LiNGAM	lingam_direct()	The baseline: linear, acyclic, non-Gaussian, i.i.d.	Causal order + coefficient matrix	lingam_direct_bootstrap()
HighDimDirectLiNGAM	lingam_high_dim()	Many variables; p > n	Same object as lingam_direct()	—
VAR-LiNGAM	lingam_var()	Stationary time series (AR)	Instantaneous B0 + lagged matrices	lingam_var_bootstrap()
VARMA-LiNGAM	lingam_varma()	Time series with MA errors	AR (psi) + MA (omega) matrices	lingam_varma_bootstrap()
MultiGroup Direct LiNGAM	lingam_multi_group()	Multiple datasets, one shared order	Common order + per-group matrices	lingam_multi_group_bootstrap()
BottomUpParceLiNGAM	lingam_parce()	Latent confounders (linear)	Unresolved block; NA entries	lingam_parce_bootstrap()
RCD	lingam_rcd()	Latent confounders (linear)	Ancestor sets; confounded pairs NA	lingam_rcd_bootstrap()
RESIT	lingam_resit()	Nonlinear additive noise	0/1 edges (no coefficients)	lingam_resit_bootstrap()
CAM-UV	lingam_camuv()	Nonlinear + unobserved variables	Parents list; UCP/UBP pairs NA	—
LiM	lingam_lim()	Mixed continuous/discrete data	Coefficient matrix	—
Bootstrap with imputation	bootstrap_with_imputation()	Missing values (NA)	Aggregate via as_bootstrap_result()	(is itself a bootstrap)

Two practical cost notes:

• HSIC-based methods (ParceLiNGAM, RCD, RESIT, CAM-UV, and lingam_direct(measure = "kernel")) build $n \times n$ Gram matrices per test; they are not recommended for $n$ in the thousands — subsample first.
• Direct LiNGAM costs $O(p^3)$ in the number of variables; for large $p$ switch to lingam_high_dim().

Worked examples for every method are on the package website:

• Direct LiNGAM in depth
• Bootstrap and diagnostics
• Time series: VAR and VARMA
• Latent confounders: ParceLiNGAM and RCD
• Nonlinear methods: RESIT and CAM-UV
• Special data: LiM, MultiGroup, missing values

When LiNGAM Cannot Be Used

When the assumptions are not met, estimation either fails or systematically recovers an incorrect structure.

Assumption	When problems arise	Remedy / alternative
Non-Gaussian errors	When all errors follow a Gaussian distribution, the causal direction becomes unidentifiable	No LiNGAM variant can help; consider constraint-based methods (e.g. the PC algorithm in pcalg), which return an equivalence class instead of a unique direction
Acyclic graph (DAG)	When feedback loops (x -> y -> x) exist	Consider Cyclic LiNGAM (implemented in the Python lingam package)
No latent common causes	When unobserved common causes (hidden confounders) exist	lingam_parce(), lingam_rcd() (linear), lingam_camuv() (nonlinear)
Linear causal relationships	When the relationships among variables are nonlinear	lingam_resit(), lingam_camuv()
No measurement error (upstream variables)	When heavy measurement error is present on variables near the root, the direction is systematically reversed	See the measurement error paradox in the Direct LiNGAM article
Independent and identically distributed (i.i.d.)	Time-series data, or data pooled across heterogeneous sources	lingam_var() / lingam_varma() (time series), lingam_multi_group() (grouped data)
Sufficient sample size	When $n$ is extremely small relative to the number of variables $p$ (rule of thumb: $n < 10p$), estimation tends to be unstable	Reduce the number of variables; sparsify with reg_method = "adaptive_lasso"; for $p > n$ use lingam_high_dim()

A Checklist to Verify in Advance

Before starting an actual analysis, we recommend confirming the following.

1. Acyclicity of the graph – Can feedback loops be ruled out from domain expertise?
2. Absence of latent variables – Are the key observed variables all present? If not, prefer lingam_parce() / lingam_rcd() / lingam_camuv().
3. Non-Gaussianity of the errors – Can be checked with test_residual_normality() (though this is a post-estimation diagnostic). As a quick check beforehand, visually inspect each variable’s histogram and skewness.
4. Presence of measurement error – Is there measurement error on variables near the root? If so, interpret with care.
5. Sample size – Aim for $n \geq 10p$. If it falls short, do not over-trust the results.

Summary: LiNGAM is powerful when all assumptions – linear, acyclic, non-Gaussian, no latent variables, and i.i.d. – hold, and lingamr provides a dedicated estimator for the most common way each assumption breaks. Verifying the assumptions with domain knowledge and residual diagnostics before analysis is the first step toward reliable causal inference.