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Communication Dans Un Congrès Année : 2009

Collinearity measures and effective sample sizes: links and comparison.

Résumé

There are many statistical problems connected with (almost) collinearity among multivariate data or random multivariate variables. Many statistical methods have been developed to tackle the problem of multicollinearity. A part of them is connected with the notion of linear dimensionnality. It appears that dimensionnality is generally not sufficient to have a good insight of the problem. The quantification of collinearity is still an interesting issue though it has not led to many investigations. Some very specific proposals have been made, and among them the attempt to deal with the multicollinearity in linear regression models [Kovacs and al. 05]. The measure they proposed can fortunately be used in a rather large framework. It appears that this approach can be related with a far older attempt to quantify the redundancy due to covariance between random variables. The problem is known as the ``equivalent number of repetitions” in the sens that a number of independant variables equivalent to a number of correlated variables is searched. This paradigm was probably initiated by Bartels in 1943 and reached some rather pertinent solutions with Тер Мкртчян in 1969, though some works on the topic were found later. The purpose of the presentation is first to recall the problem of redundancy. Then the theory of ``equivalent number of repetitions” is fully detailed from the very beginning to the most recent contributions. The link with the multicollinearity is highlighted that enables the comparison of both approaches. This comparison is viewed through the examination of classical chronological models. Finally, a model of increasing collinearity is proposed and a numerical study that helps to better understand the response of the different measures to this increasing collinearity.
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Dates et versions

hal-00486827 , version 1 (26-05-2010)

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  • HAL Id : hal-00486827 , version 1

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Thierry Dhorne. Collinearity measures and effective sample sizes: links and comparison.. Challenges for the Analysis of the Economy, the Business ans Social Progress., Nov 2009, Szeged, Hungary. pp.221. ⟨hal-00486827⟩
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