Re: [R] O/T -2 Log Lambda and Chi Square

From: Spencer Graves <>
Date: Mon 11 Jul 2005 - 09:55:09 EST

          There is a huge and growing literature on this, including Crainiceanu, Ruppert and Vogelsang (2003) "some properties of likelihood ratio tests in linear mixed models"
( The nlme package includes a function "simulate.lme" to evalute the adequacy of alternative distributions for 2*log(likelihood ratio) for the results of lme.

          Much of the careful work on this rests on asymptotic normality of the maximum likelihood estimates, and this is the same for 2*log(likelihood ratio) as the standard quadratic form in the MLEs. However, the latter is affected by parameter effects, whereas the likelihood ratio statistic is only impacted by the intrinsic curvature of the manifold upon which the log(likelihood) vector is projected to obtain the MLEs. For nonlinear regression, Bates and Watts (1988) Nonlinear Regression and Its Applications (Wiley) computed measures of intrinsic and parameter effects curvature for a number of published nonlinear regression examples. In nearly all their examples, the intrinsic curvature was in negligible, especially when compared to the parameter effects.

          If this does not answer your question (or lead you to an answer), please try a more specific question.

          spencer graves

Laura Holt wrote:

> Hi R People:
> Sorry about the off topic question. Does anyone know the reference
> for "-2 Log Lambda is approx dist. Chi square", please?
> It may be Bartlett, but I'm not sure....
> thanks in advance!
> Sincerely,
> Laura Holt
> mailto:
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> PLEASE do read the posting guide!

Spencer Graves, PhD
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Received on Mon Jul 11 10:43:33 2005

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