[R-sig-ME] Likelihood ratios

[Mike Lawrence]

By "complexity-corrected", I simply meant a likelihood ratio that
takes into account potential differences in the number of parameters
between models, penalizing the more complex model. In the Glover &
Dixon paper I cited in my original post, they compute a likelihood
ratio based on ANOVA sums of squares, then apply a complexity
correction factor (they show formulae for both AIC and BIC) to yield a
final ratio that I've been calling a "complexity-corrected likelihood
ratio". Sorry for causing confusion by using my idiosyncratic
nomenclature!

On Tue, Jun 1, 2010 at 8:25 PM, Ben Bolker <bolker at ufl.edu> wrote:
>  Yes, or
>
> exp(logLik(fit2,REML=FALSE)-logLik(fit1,REML=FALSE))
>
>
>   What is a "complexity-corrected" likelihood ratio?
>   I'm very nervous about mixing in the AIC penalty terms with the rest
> of the likelihood ratio -- and, as I think has been pointed out, you
> have to be careful to set REML=FALSE ...
>
> fengsj at mail.utexas.edu wrote:
>> Is there someting similar for glmer models?
>> Thanks!
>>
>>
>> Quoting Mike Lawrence <Mike.Lawrence at dal.ca>:
>>
>>> After posting this, I thought to contact Pete Dixon himself and indeed
>>> it seems he already coded the functions to obtain a likelihood ratio
>>> comparing two lmer models:
>>>
>>> AIC_lmer = function(x){
>>>      require(lme4)
>>>      print(formula(attr(x,"call")))
>>>      summary(x)@AICtab
>>> }
>>>
>>> LR_lmer = function(m0,m1){
>>>      exp((AIC_lmer(m0)[[1]]-AIC_lmer(m1)[[1]])/2)
>>> }
>>>
>>> #example usage:
>>> LR_lmer( my_fit1 , my_fit2 )
>>>
>>>
>>>
>>> On Tue, Jun 1, 2010 at 1:50 PM, Mike Lawrence <Mike.Lawrence at dal.ca> wrote:
>>>> oops, I guess that should be:
>>>>
>>>> LR = exp( anova( fit1 , fit2 )$Chisq[2] / -2 )
>>>>
>>>>
>>>> On Tue, Jun 1, 2010 at 1:28 PM, Mike Lawrence <Mike.Lawrence at dal.ca> wrote:
>>>>> Hi folks,
>>>>>
>>>>> I have 2 lmer fits, one (fit1) nested in the other (fit2), and I'd
>>>>> like to compute the likelihood ratio comparing the models so I can say
>>>>> something like "there is X times more evidence for fit1 than for fit2"
>>>>> (as in Glover & Dixon, 2004, www.ncbi.nlm.nih.gov/pubmed/15732688).
>>>>>
>>>>> I know I can use anova(fit1,fit2) to obtain a null-hypothesis
>>>>> significance test of the fits, and I suspect the output also contains
>>>>> the information I need to make my evidentiary statement, but I'm not
>>>>> confident of what I'm doing here. Is it correct that the reported
>>>>> value of chi-square from anova() is simply the D of the likelihood
>>>>> ratio test (http://en.wikipedia.org/wiki/Likelihood_ratio_test)? If
>>>>> so, does it sound right that I can simply derive the
>>>>> complexity-corrected likelihood ratio as:
>>>>>
>>>>> LR = exp( -2 * anova( fit1 , fit2 )$Chisq[2] )
>>>>>
>>>>> ?
>>>>>
>>>>>
>>>>> Mike
>>>>>
>>>>> --
>>>>> Mike Lawrence
>>>>> Graduate Student
>>>>> Department of Psychology
>>>>> Dalhousie University
>>>>>
>>>>> Looking to arrange a meeting? Check my public calendar:
>>>>> http://tr.im/mikes_public_calendar
>>>>>
>>>>> ~ Certainty is folly... I think. ~
>>>>>
>>>>
>>>>
>>>> --
>>>> Mike Lawrence
>>>> Graduate Student
>>>> Department of Psychology
>>>> Dalhousie University
>>>>
>>>> Looking to arrange a meeting? Check my public calendar:
>>>> http://tr.im/mikes_public_calendar
>>>>
>>>> ~ Certainty is folly... I think. ~
>>>>
>>>
>>>
>>> --
>>> Mike Lawrence
>>> Graduate Student
>>> Department of Psychology
>>> Dalhousie University
>>>
>>> Looking to arrange a meeting? Check my public calendar:
>>> http://tr.im/mikes_public_calendar
>>>
>>> ~ Certainty is folly... I think. ~
>>>
>>> _______________________________________________
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>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>> _______________________________________________
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>
>
> --
> Ben Bolker
> Associate professor, Biology Dep't, Univ. of Florida
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-- 
Mike Lawrence
Graduate Student
Department of Psychology
Dalhousie University

Looking to arrange a meeting? Check my public calendar:
http://tr.im/mikes_public_calendar

~ Certainty is folly... I think. ~