[R] AIC and anova, lme

[Patrick Giraudoux]

Dear listers,

Here we have a strange result we can hardly cope with. We want to 
compare a null mixed model with a mixed model with one independent 
variable.

 > lmmedt1<-lme(mediane~1, random=~1|site, na.action=na.omit, data=bdd2)
 > lmmedt9<-lme(mediane~log(0.0001+transat), random=~1|site, 
na.action=na.omit, data=bdd2)

Using the Akaike Criterion and selMod of the package pgirmess gives the 
following output:

 > selMod(list(lmmedt1,lmmedt9))
                 model       LL K  N2K       AIC  deltAIC  w_i      AICc 
deltAICc w_ic
2 log(1e-04 + transat) 44.63758 4  7.5 -81.27516 0.000000 0.65 -79.67516 
0.000000 0.57
1                    1 43.02205 3 10.0 -80.04410 1.231069 0.35 -79.12102 
0.554146 0.43

The usual conclusion would be that the two models are equivalent and to 
keep the null model for parsimony (!).

However, an anova shows that the variable 'log(1e-04 + transat)' is 
significantly different from 0 in model 2 (lmmedt9)

 > anova(lmmedt9)
                     numDF denDF   F-value p-value
(Intercept)              1    20 289.43109  <.0001
log(1e-04 + transat)     1    20  31.18446  <.0001

Has anyone an opinion about what looks like a paradox here ?

Patrick