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

[Spencer Graves]

	  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" 
(http://www.orie.cornell.edu/~davidr/papers/zeroprob_rev01.pdf).  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: holtlaura at gmail.com
> 
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