Model-Free Functional Chi-Squared and Exact Tests.
Overview
The package provides statistical hypothesis testing methods for inferring model-free functional dependency. Functional test statistics are asymmetric and functionally optimal, unique from other related statistics. The test significance is based on either asymptotic chi-squared or exact distributions.
The tests include an asymptotic functional chi-squared test [@zhang2013deciphering], an adapted functional chi-squared test [@Kumar2022AFT], and an exact functional test [@zhong2019eft;@Nguyen2020EFT]. The normalized functional chi-squared test was used by Best Performer NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges (Hill et al., 2016) <10.1038/nmeth.3773>.
To measure the effect size, one can use the asymmetric function index [@Zhong2019FANTOM5;@KumarZSLS18]. Its value is minimized to 0 by perfectly independent patterns and maximized to 1 by perfect non-constant functions.
A simulator [@sharma2017simulating] can generate functional, non-functional, and independent patterns as contingency tables. The simulator provides options to control row and column marginal distributions and the noise level.
When to use the package
Tests in this package can be used to reveal evidence for causality based on the causality-by-functionality principle. They target model-free inference without assuming a parametric model. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed. Data can be first discretized, e.g., by R packages 'Ckmeans.1d.dp' or 'GridOnClusters'. For categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-squared or Fisher's exact tests. They are a better alternative to conditional entropy in many aspects.
To download and install the package
install.packages("FunChisq")