Are likelihood approaches frequentist?
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 Rub?n