independence-tests {bnlearn} | 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-square test (`mi` and `mi-adf`, with adjusted degrees of freedom), the Monte Carlo permutation test (`mc-mi`), the sequential Monte Carlo permutation test (`smc-mi`), and the semiparametric test (`sp-mi`) are implemented.

- shrinkage estimator for the mutual information (`mi-sh`): an improved asymptotic chi-square 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-square 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-square 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-square 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 hybrid 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-square test (`mi-cg`) is implemented.

[Package bnlearn version 4.7.1 Index]