How to Choose a Conditional Independence Test

Choosing the right conditional independence (CI) test is crucial for the validity of your causal discovery or feature selection analysis. The appropriate test depends on the characteristics of your data and the underlying assumptions you are willing to make.

Key Considerations

Here are the primary factors to consider when selecting a test:

1. Data Type

• Continuous Data: If your variables are all continuous, you have several options:

  • fisherz_citk: Assumes linear relationships and multivariate normal data. It is very fast but may fail if these assumptions are violated.

  • spearman: A non-parametric alternative that works on ranked data. It is suitable for monotonic (but not necessarily linear) relationships.

  • kci: Optional R-backed KCIT (RCIT::KCIT) for complex, non-linear relationships.

  • rcot, rcit: Optional R-backed kernel/random-feature tests from the RCIT package.

  • cmiknn, cmiknn_mixed: Optional tigramite kNN-CMI tests.

  • mcmiknn: Optional mixed-type kNN CMI wrapper from local mCMIkNN repo.

  • regci: Optional tigramite parametric mixed-data regression CI.

  • rf, dml, crit, edml: Flexible ML-based options for non-linear structure.

• Discrete Data: If your variables are categorical:

  • gsq (G-Square) or chisq (Chi-Square): Classical tests based on contingency tables.

• Mixed Data: Current built-in options are limited; discretization is still a practical baseline for gsq/chisq.

  • disc_chisq, disc_gsq: Equal-frequency discretization adapters around classical discrete tests.

  • dummy_fisherz: One-hot encoding adapter with Fisher-Z aggregation.

  • hartemink_chisq: Information-preserving Hartemink discretization (via R bnlearn) + Chi-square.

  • dct: Optional DCT wrapper from local DCT repository.

2. Relationship Type

• Linear: If you believe the relationships between your variables are linear, fisherz is a computationally efficient choice.

• Monotonic: For relationships that are consistently increasing or decreasing but not necessarily linear, spearman is a robust option.

• Non-Linear / Complex: For arbitrary, complex relationships, machine learning-based tests like kci or rf are the most powerful and flexible choices, though they come at a higher computational cost.

Summary Table

Test Name	Data Type	Relationship Type	Key Assumption(s)
fisherz_citk	Continuous	Linear	Approximate Gaussianity
spearman	Continuous	Monotonic	Monotonicity
gsq / chisq	Discrete	Any	Adequate contingency support
kci	Continuous	Any	Requires rpy2 + R RCIT package
rcot / rcit	Continuous	Any	Requires rpy2 + R RCIT package
cmiknn / cmiknn_mixed / regci	Mixed or continuous	Any	Requires tigramite
mcmiknn	Mixed	Any	Requires local mCMIkNN repository
rf / dml / crit / edml	Continuous	Any	ML residualization quality
gcm_linear / gcm_rf / wgcm_rf	Continuous	Any	Residual covariance test
disc_chisq / disc_gsq	Mixed or continuous	Any	Discretization quality
dummy_fisherz	Mixed or discrete	Any	One-hot encoding fidelity
hartemink_chisq	Mixed or continuous	Any	Requires rpy2 + R bnlearn
dct	Mixed or discretized continuous	Any	Requires local DCT repository