matie (version 1.2)

ma.nl: Calculates degree of nonlinearity for a particular association score.

Description

This function estimates nonlinear proportion of variance between one variable and a group of variables after linear association between the variable and the group has been removed.

Usage

ma.nl(Y, X)

Arguments

Y

A vector or a one column data frame.

X

a group of vectors or a data frame with the same number of samples as in Y

Value

Returns a list of real numbers:

Rsq

linear association, the value of R^2 due to the linear model Y ~ X.

A

total association (linear and nonlinear) between Y and the group X.

rA

the residual association (the association left in the residuals after the linear part has been regressed out of Y).

nl1

A - Rsq, the nonlinear part of the association.

nl2

(A - Rsq) / A, the nonlinear proportion of the association.

nl3

(A - Rsq) / (1 - Rsq), the proportion of total variance that is not explained by a linear model but is explained by A.

Details

A linear model, Y ~ X, is constructed and ma is used to compute R^2 between Y and X.

References

Discovering general multidimensional associations, http://arxiv.org/abs/1303.1828

See Also

ma agram

Examples

    X1 = runif(1000)
    X2 = runif(1000)
    Y = sin(0.5*pi*X1) + sin(0.5*pi*X2) + rnorm(1000)*0.000001
    ma.nl(Y,cbind(X1,X2))
    #
    # in the case of bivariate associations all these measures
    # are symmetric apart from rA, the residual association
    X = runif(1000)
    Y = sin(0.5*pi*X) + rnorm(1000)*0.01
    ma.nl(Y,X)$rA
    ma.nl(X,Y)$rA