mutualinf: Mutual information Based on Multivariate Distributions...

In genomaths/usefr: Utility Functions for Statistical Analyses

Mutual information Based on Multivariate Distributions Constructed from Copulas

Description

Computes the mutual information for pairwise x and y marginal values based on their multivariate distribution constructed from a copula.

Usage

mutualinf(
  x,
  y,
  copula = NULL,
  margins = NULL,
  paramMargins = NULL,
  method = "ml",
  ties.method = "max"
)

Arguments

x, y	marginal variates
copula	A copula object from class Mvdc or string specifying all the name for a copula from package copula-package.
margins	A character vector specifying all the parametric marginal distributions. See details below.
paramMargins	A list whose each component is a list (or numeric vectors) of named components, giving the parameter values of the marginal distributions. See details below.
method	A character string specifying the estimation method to be used to estimate the dependence parameter(s) (if the copula needs to be estimated) see fitCopula.

Details

The mutual information of a pairwise x and y marginal values is defined as:

I{x, y} = log(P(x,y)) - (log(P_1(x)) + log(P_2(y)))

where P(x,y) is the multivariate distribution constructed from a copula, and P_1(x) and P_2(y) are the marginal CDFs.

The values I{x, y} expresses a measurement of the relative dependece/independece of x and y at the specified point value.

Notice that the above definition expresses the differences between two uncertainty variations. So, for values I{x, y} > 0, we shall say that at point (x, y) there is a gain of information for the association of the subjacent stochastic processes generating x and y in respect to the independent processes. Otherwise, for values I{x, y} < 0 we shall say that at point (x, y) there is a loss of information for the association of the subjacent stochastic process generating x and y in respect to the independent processes. Or, equivallently, there is a gain of information for the independent processes in respect to their association.

Value

A list with a data frame carrying the estimated mutual information for each (x, y) pair, the joint and marginal probabilities, and the "mvdc" copula object.

See Also

ppCplot, bicopulaGOF, gofCopula, fitCDF, fitdistr, and fitMixDist.

Examples

require(stats)
set.seed(12) # set a seed for random number generation
## Random generation of a Normal distributed marginal variate
X <- rnorm(2000, mean = 1, sd = 0.2)

## Random generation of a Weibull-3P distributed marginal variate
Y <- X + rweibull3p(2000, shape = 2, scale = 0.85, mu = 1)

## Correlation test
cor.test(X, Y, method = "spearman")

## Non-linear model fit for 'Y' distribution values
fitY <- fitCDF(Y, distNames = 12) # 3P Weibull distribution model
coefs <- coef(fitY$bestfit) # model coefficients

## Goodness-of-fit test for the  Weibull-3P distribution model
mcgoftest(
    varobj = Y, distr = "weibull3p", pars = coefs, num.sampl = 99,
    sample.size = 1999, stat = "chisq", num.cores = 4, breaks = 200,
    seed = 123
)

## Settngs to estimate the Mutual information
margins <- c("norm", "weibull3p")
parMargins <- list(
    list(mean = 1, sd = 0.2),
    as.list(coefs)
) # Notice "as.list" is used here, not "list"

## Finally estimation of the mutual information
mutual.Inf <- mutualinf(
    x = X, y = Y, copula = "normalCopula",
    margins = margins, paramMargins = parMargins
)
head(mutual.Inf$stat)
## The fitted copula is also returned, so, it can be used in downstream
## analyses
mutual.Inf$copula@copula

genomaths/usefr documentation built on July 28, 2022, 12:31 p.m.