II.measure: A comprehensive function for evaluating interaction...

In Informeasure: R implementation of Information measures

Description

The II.measure function is used to calculate the amount information contained in a set of variables from the joint count table. The number of variables here is limited to three.

Usage

II.measure(
  XYZ,
  method = c("ML", "Jeffreys", "Laplace", "SG", "minimax", "shrink"),
  lambda.probs,
  unit = c("log", "log2", "log10"),
  verbose = TRUE
)

Arguments

XYZ	a joint count distribution table of three random variables.
method	six probability estimation algorithms are available, "ML" is the default.
lambda.probs	the shrinkage intensity, only called when the probability estimator is "shrink".
unit	the base of the logarithm. The default is natural logarithm, which is "log". For evaluating entropy in bits, it is suggested to set the unit to "log2".
verbose	a logic variable. if verbose is true, report the shrinkage intensity.

Details

Six probability estimation methods are available to evaluate the underlying bin probability from observed counts:
method = "ML": maximum likelihood estimator, also referred to empirical probability,
method = "Jeffreys": Dirichlet distribution estimator with prior a = 0.5,
method = "Laplace": Dirichlet distribution estimator with prior a = 1,
method = "SG": Dirichlet distribution estimator with prior a = 1/length(XY),
method = "minimax": Dirichlet distribution estimator with prior a = sqrt(sum(XY))/length(XY),
method = "shrink": shrinkage estimator.

Value

II.measure returns the interaction information.

References

Hausser, J., & Strimmer, K. (2009). Entropy Inference and the James-Stein Estimator, with Application to Nonlinear Gene Association Networks. Journal of Machine Learning Research, 1469-1484.

Mcgill, W. J. (1954). Multivariate information transmission. Psychometrika, 19(2), 97-116.

Examples

# three numeric vectors corresponding to three continuous random variables
x <- c(0.0, 0.2, 0.2, 0.7, 0.9, 0.9, 0.9, 0.9, 1.0)
y <- c(1.0, 2.0,  12, 8.0, 1.0, 9.0, 0.0, 3.0, 9.0)
z <- c(3.0, 7.0, 2.0,  11,  10,  10,  14, 2.0,  11)

# corresponding joint count table estimated by "uniform width" algorithm
XYZ <- discretize3D(x, y, z, "uniform_width")

# corresponding interaction information
II.measure(XYZ)

Informeasure documentation built on Nov. 8, 2020, 7:20 p.m.