FunChisq-package: Model-Free Functional Chi-Squared and Exact Tests

In FunChisq: Model-Free Functional Chi-Squared and Exact Tests

Model-Free Functional Chi-Squared and Exact Tests

Description

Statistical hypothesis testing methods for model-free functional dependency using asymptotic chi-squared or exact distributions. Functional chi-squared test statistics \insertCitezhang2013deciphering,zhang2014nonparametric,nguyen2018modelfree,zhong2019modelfree,zhong2019eft,Nguyen2020EFTFunChisq are asymmetric, functionally optimal, and model-free, unique from other related statistical measures.

Tests in this package reveal evidence for causality based on the causality-by-functionality principle \insertCiteSimon1966FunChisq. The tests require data from two or more variables be formatted as a contingency table. Continuous variables need to be discretized first, for example, using R packages Ckmeans.1d.dp or GridOnClusters.

The package implements an asymptotic functional chi-squared test \insertCitezhang2013deciphering,zhang2014nonparametricFunChisq, an adapted functional chi-squared test \insertCite@Kumar2022AFTFunChisq, and an exact functional test \insertCitenguyen2018modelfree,zhong2019modelfree,zhong2019eft,Nguyen2020EFTFunChisq. The normalized functional chi-squared test was used by Best Performer NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges \insertCiteHill:2016fkFunChisq.

A function index derived from the functional chi-squared offers a new effect size measure for the strength of function dependency. It is asymmetrically functionally optimal, different from the symmetric Cramer's V, also a better alternative to conditional entropy in many aspects.

A simulator is provided to generate functional, dependent non-functional, and independent patterns \insertCitesharma2017simulatingFunChisq.

For continuous data, these tests offer an advantage over regression analysis when a parametric form cannot be reliably assumed for the underlying function. For categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-squared test, G-test, or Fisher's exact test.

Details

Package:	FunChisq
Type:	Package
Current version:	2.5.3
Initial release version:	1.0
Initial release date:	2014-03-08
License:	LGPL (>= 3)

Author(s)

Yang Zhang, Hua Zhong, Hien Nguyen, Ruby Sharma, Sajal Kumar, Yiyi Li, and Joe Song

References

\insertAllCited

See Also

For data discretization, an option is optimal univariate clustering via package Ckmeans.1d.dp. A second option is joint multivariate discretization via package GridOnClusters.

For symmetric dependency tests on discrete data, see Pearson's chi-squared test (chisq.test), Fisher's exact test (fisher.test), mutual information (package entropy), and G-test, implemented in packages DescTools and RVAideMemoire.

FunChisq documentation built on May 31, 2023, 8:18 p.m.