MINTsemiperm {semidist}

Mutual information independence test (categorical-continuous case)

Description

Implement the mutual information independence test (MINT) (Berrett and Samworth, 2019), but with some modification in estimating the mutual informaion (MI) between a categorical random variable and a continuous variable. The modification is based on the idea of Ross (2014).

MINTsemiperm() implements the permutation independence test via mutual information, but the parameter k should be pre-specified.

MINTsemiauto() automatically selects an appropriate k based on a data-driven procedure, and conducts MINTsemiperm() with the k chosen.

Usage

MINTsemiperm(X, y, k, B = 1000)

MINTsemiauto(X, y, kmax, B1 = 1000, B2 = 1000)

Arguments

X

Data of multivariate continuous variables, which should be an n-by-p matrix, or, a vector of length n (for univariate variable).

y

Data of categorical variables, which should be a factor of length n.

k

Number of nearest neighbor. See References for details.

B, B1, B2

Number of permutations to use. Defaults to 1000.

kmax

Maximum k in the automatic search for optimal k.

Value

A list with class "indtest" containing the following components

• method: name of the test;

• name_data: names of the X and y;

• n: sample size of the data;

• num_perm: number of replications in permutation test;

• stat: test statistic;

• pvalue: computed p-value.

For MINTsemiauto(), the list also contains

• kmax: maximum k in the automatic search for optimal k;

• kopt: optimal k chosen.

References

1. Berrett, Thomas B., and Richard J. Samworth. "Nonparametric independence testing via mutual information." Biometrika 106, no. 3 (2019): 547-566.

2. Ross, Brian C. "Mutual information between discrete and continuous data sets." PloS one 9, no. 2 (2014): e87357.

Examples

X <- mtcars[, c("mpg", "disp", "drat", "wt")]
y <- factor(mtcars[, "am"])

MINTsemiperm(X, y, 5)
MINTsemiauto(X, y, kmax = 32)