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"
(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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