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

A non-parametric measure of association between variables.
The association score *A* ranges from 0 (when the variables are independent)
to 1 (when they are perfectly associated).
*A* is a kind of *R^2* estimate,
and can be thought of as the proportion of variance in one variable
explained by another
(or explained by a number of other variables -
*A* works for multivariate associations as well).

1 | ```
ma(d,partition,ht,hp,hs,ufp)
``` |

`d` |
the |

`partition` |
a list of column indices specifying variable groupings. Defaults to |

`ht` |
tangent for the hyperbolic correction, default |

`hp` |
power for the hyperbolic correction, default |

`hs` |
scale for the hyperbolic correction, default |

`ufp` |
for debugging purposes, default |

An estimate of association (possibly nonlinear) is computed
using a ratio of
maximum likelihoods for the *marginal distribution* and
maximum weighted likelihoods for the *joint distribution*.

Before the computation is carried out the data is ranked using the
`rwt`

function from the `matie`

package.
This estimate is usually conservative (ie low) and a small-samples hyperbolic
correction is applied by adding an offset, `os`

,
to the joint likelihood given by:

`os = ( 1 - 1 / (1 + A * ht) ) * ( n ^ (hp) / hs ) `

before the likelihood ratio is re-computed.

As the dimension of the data set increases so does the under-estimation of A even with the hyperbolic correction.

Returns a list of values ...

`A ` |
a score (including hyperbolic correction) estimating association for the data |

`rawA` |
the association score before hyperbolic correction |

`jointKW ` |
the optimal kernel width for the joint distribution |

`altLL ` |
the optimal weighted log likelihood for the alternate distribution |

`nullLL ` |
the optimal log likelihood for the marginal distribution |

`marginalKW ` |
the optimal kernel width for the marginal distribution |

`weight` |
the optimal weight used for the mixture |

`LRstat` |
the |

`nRows` |
n, the number of complete samples in the data set |

`mCols` |
m, the number of variables in the data set |

`partition` |
user supplied partition for the variables in the data set |

`ufp` |
user supplied debugging flag |

The data set can be of any dimension.

Ben Murrell, Dan Murrell & Hugh Murrell.

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

1 2 3 4 5 6 7 8 | ```
# bivariate association
d <- shpd(n=1000,m=2,Rsq=0.9)
ma(d)$A
#
# multivariate association (the proportion of variance in "Salary"
# explained by "Hits" and "Years")
data(baseballData)
ma(baseballData,partition=list(11,c(2,7)))$A
``` |

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