conditional.independence.tests: Conditional independence tests
In bnlearn: Bayesian Network Structure Learning, Parameter Learning and Inference

independence-tests

R Documentation

Conditional independence tests

Description

Overview of the conditional independence tests implemented in bnlearn, with the respective reference publications.

Details

Unless otherwise noted, the reference publication for conditional independence tests is:

Edwards DI (2000). Introduction to Graphical Modelling. Springer, 2nd edition.

Additionally for continuous permutation tests:

Legendre P (2000). "Comparison of Permutation Methods for the Partial Correlation and Partial Mantel Tests." Journal of Statistical Computation and Simulation, 67:37–73.

and for semiparametric discrete tests:

Tsamardinos I, Borboudakis G (2010). "Permutation Testing Improves Bayesian Network Learning." Machine Learning and Knowledge Discovery in Databases, 322–337.

Available conditional independence tests (and the respective labels) for discrete Bayesian networks (categorical variables) are:

mutual information: an information-theoretic distance measure. It's proportional to the log-likelihood ratio (they differ by a 2n factor) and is related to the deviance of the tested models. The asymptotic \chi^2 test (mi and mi-adf), the Monte Carlo permutation test (mc-mi), the sequential Monte Carlo permutation test (smc-mi), and the semiparametric test (sp-mi) are implemented. Compared to mi, mi-adf adjusts the degrees of freedom for structural zeroes and automatically favours independence if there are fewer than 5 observations per parameter.
shrinkage estimator for the mutual information (mi-sh): an improved asymptotic \chi^2 test based on the James-Stein estimator for the mutual information.

Hausser J, Strimmer K (2009). "Entropy Inference and the James-Stein Estimator, with Application to Nonlinear Gene Association Networks." Statistical Applications in Genetics and Molecular Biology, 10:1469–1484.
Pearson's X^2: the classical Pearson's X^2 test for contingency tables. The asymptotic \chi^2 test (x2 and x2-adf, with adjusted degrees of freedom), the Monte Carlo permutation test (mc-x2), the sequential Monte Carlo permutation test (smc-x2) and semiparametric test (sp-x2) are implemented.

Available conditional independence tests (and the respective labels) for discrete Bayesian networks (ordered factors) are:

Jonckheere-Terpstra: a trend test for ordinal variables. The asymptotic normal test (jt), the Monte Carlo permutation test (mc-jt) and the sequential Monte Carlo permutation test (smc-jt) are implemented.

Available conditional independence tests (and the respective labels) for Gaussian Bayesian networks (normal variables) are:

linear correlation: Pearson's linear correlation. The exact Student's t test (cor), the Monte Carlo permutation test (mc-cor) and the sequential Monte Carlo permutation test (smc-cor) are implemented.

Hotelling H (1953). "New Light on the Correlation Coefficient and its Transforms." Journal of the Royal Statistical Society: Series B, 15(2):193–225.
Fisher's Z: a transformation of the linear correlation with asymptotic normal distribution. The asymptotic normal test (zf), the Monte Carlo permutation test (mc-zf) and the sequential Monte Carlo permutation test (smc-zf) are implemented.
mutual information: an information-theoretic distance measure. Again it is proportional to the log-likelihood ratio (they differ by a 2n factor). The asymptotic \chi^2 test (mi-g), the Monte Carlo permutation test (mc-mi-g) and the sequential Monte Carlo permutation test (smc-mi-g) are implemented.
shrinkage estimator for the mutual information (mi-g-sh): an improved asymptotic \chi^2 test based on the James-Stein estimator for the mutual information.

Ledoit O, Wolf M (2003). "Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection." Journal of Empirical Finance, 10:603–621.

Available conditional independence tests (and the respective labels) for conditional Gaussian Bayesian networks (mixed discrete and normal variables) are:

mutual information: an information-theoretic distance measure. Again it is proportional to the log-likelihood ratio (they differ by a 2n factor). Only the asymptotic \chi^2 test (mi-cg) is implemented.