[R-sig-eco] Are likelihood approaches frequentist?

[Rubén Roa-Ureta]

Ben Bolker wrote:
> Farrar.David at epamail.epa.gov wrote:
>   
>> I'm a little surpised not to see A.W.F. Edwards book on Likelihood cited 
>> in connection 
>> with the possibility of a distinctive "likelihoodist" viewpoint, as I 
>> think the book was influential, 
>> including for some biologists.  (The first edition of the book was 
>> sometimes known as 
>> "Little Red Likelihood.") 
>>     
>
>   I did cite it ...
>
>   Ruben: can you give a central Lindsey citation?
Hi Ben,
I just posted a reference to his general ideas on model selection to the 
list.

>   I like
> "Statistical Heresies" (1999, The Statistician), although
> I'm bothered by the following passage (bottom of p. 15),
> on the subject of calibrating differences in deviance
> for models of differing complexity:
>
>   With a fairly large set of 6215 observations, a=0.22
> might be chosen as a reasonable value for the height
> of the normed likelihood determining the interval of
> precision for one parameter; this implies the deviance
> must be penalized by adding three (equal to -2 log(0.22))
> times the number of parameters. (This a is smaller than
> that from the AIC: a = 1/e = 0.37 so twice the number
> of parameters would be added to the deviance.  It is larger
> than that from a $\chi^2$-test at 5% with 1 degree of
> freedom, a=0.14, or adding 3.84 times the number of
> parameters, but, with p parameters, this does not change
> to 0.14^p.)
>
>   So ... one just gets to pick the penalty term based
> on common sense (calibrated from decades of statistical
> practice)?
>
>   Ben Bolker
>
>   
I agree with Paulo's answer. If you want a cutoff value from the normed 
likelihood to make an interval of precision for one parameter, then a 
socialized reference cutoff value will have to be agreed, like the 
p-value=0.05 of sampling-distribution inference. But that is not 
absolutely necessary I believe. If you refrain from making intervals, 
then you can report your parameter estimate and its precision by means 
of the curvature of the likelihood around the maximum w.r.t. to that 
parameter (the formation concept of Edwards, akin to the estimation 
variance but without the asymptotics, fully conditional on the observed 
sample), and that's it.
If you want to make an interval, then I prefer Royall's proposal of a 
canonical experiment. I think it appeals well to intuition.
Regards
Rubén