### Abstract

In first place a decomposition of the l.r.t. (likelihood ratio test) statistic to test the independence between a set of variables and a given number of other sets of variables into a number of independent l.r.t. statistics is presented. This decomposition induces a decomposition of the null hypothesis for this test, which allows for a different view over the test. Then, based on this decomposition, a double decomposition of the l.r.t. statistic to test the independence of m sets of variables is presented which itself induces a double decomposition of the null hypothesis of independence among m sets of variables which in turn allows for a different view and interpretation of this test. These decompositions are much useful in helping us to relate these tests and interpret them under a modeling point of view.

Original language | Unknown |
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Title of host publication | Mathematics and Computers in Science and Engineering Series |

Pages | 13-19 |

Publication status | Published - 1 Jan 2014 |

Event | 16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems - Duration: 1 Jan 2014 → … |

### Conference

Conference | 16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems |
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Period | 1/01/14 → … |

## Cite this

Coelho, C. M. A., & Marques, F. J. G. P. (2014). A double decomposition of the test of independence of sets of variables that allows for a modeling view of this test. In

*Mathematics and Computers in Science and Engineering Series*(pp. 13-19)