[R-sig-ME] effect of adding a constant to predictor

[Don Cohen]

Ben Bolker writes:

 >    On first glance this is indeed a bit surprising. However, I believe
 > the reason is that you've specified group and input2 as separate
 > (independent) random effects, without allowing a correlation between
 > them, which means that the random-effects model is no longer invariant
 > to shifts in the parameters.  If you had used (1+input2|group) as your
 > random effect instead, I believe you would get the same
 > log-likelihood/AIC either way.

Well, when I make that change I do get the same answer.
Thanks for the explanation.  Not being invariant to additive 
shifts makes me wonder whether this is a reasonable model at all.

This raises another question.  I've been using drop1 to compute
P values.  I expected that I could compute the P values at 
different values of interacting inputs by using these additive
shifts, but evidently that's not going to work.
Is there some other way to compute a p values for input1 at some 
non-zero value of input2 ?

Given that the shifted model seems to make as much sense as the
original, perhaps it's reasonable to just use one model for one 
value of input2 and the other model for the other value?