Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 | ```
ma.nl(Y, X)
``` |

`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 |

A linear model, `Y ~ X`

, is constructed and `ma`

is used to compute R^2 between Y and X.

Returns a list of real numbers:

`Rsq` |
linear association, the value of R^2 due to the linear model |

`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. |

Ben Murrell, Dan Murrell & Hugh Murrell.

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

1 2 3 4 5 6 7 8 9 10 11 | ```
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
``` |

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