Reconciling Near Identical AIC Values and Highly Significant P Value

Hi,

I may completely misunderstand your problem, but if you replace a
predictor variable by another one with the same number of parameters
(let's say, for instance, ? length ? by ? surface ? in a linear
regression), then

 1) comparing AIC and likelihoods value is the same since the number
    of parameters does not change ;
    hence same AIC <=> predictors give equally good fits

 2) chi-square tests is meaningless, since models are not nested.
    Here, I guess you have the very low p because the function uses a
    0-degrees of freedom [same number of parameters...]  khi-square,
    that is the constant 0, and any value other than 0 as a null
    probability, hence p = 0 < whatever you want...

From 2), it results than comparing AIC is, between your two options,

the only one valid when models are not nested.

For the second point, I don't know.

Hope this helps,

? Hi all,
? 
? When comparing identical models (only difference in predictor variable;
? same d.f.) in lme4' using anova(model2,model), sometime I see nearly
? identical AIC values like model2=1479.6 and model=1479.5 and a very low chi
? sq. value like 0.1062, yet an extremely low p-value of <0.0001.  How would
? you reconcile this?  Should we be more concerned with looking for
? differences in AIC values of >3 when determing a better fit model, rather
? than looking at a p-value?
? 
? Secondly, I read on the glmm.wikidot.com/faq page that when testing for the
? significance of random effects, p values are conservative and are roughly
? half what is returned when performing LRTs.  Do you find that what Pinheiro
? and Bates (2000) states is sufficient to justify reporting the significance
? of random effects when reported p values are between 0.05 and 0.10?  And is
? it enough to convince you that is the case, especially when examining the
? raw data with this in mind?
? 
? Thank you,
? Jacob
? 
? 	[[alternative HTML version deleted]]
? 
? _______________________________________________
? R-sig-mixed-models at r-project.org mailing list
? https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html