[R-sig-ME] how to test interaction correctly

[Norman Forschack]

Hello,

I modeled the relationship of two electrophysiological brain signals for two separate cognitive conditions from a balanced empirical dataset.
The formula was 
f = formula(PA ~ I(OsciPow^2) + OsciPow + (OsciPow + I(OsciPow^2) | Subject) )
where PA is a potential amplitude and OsciPow is oscillation power, the random effect term is grouped by individual participant.

The separate models are these:
mdlPA_att <- lmer(f,data=data[ data2Attention=="attend",],REML=F) and
mdlPA_ign <- lmer(f,data=data[ data2Attention=="ignore",],REML=F)
Both of them I tested with the pbkrtest toolbox against an intercept only model and a linear relationship only model.

As the quadratic (negative for the first model, positive for the second) and linear term (positive for the first model and negative for the second) for the fixed effects differ descriptively, I tried to model the interaction between the cognitive conditions and wonder whether this is the correct way and how to test it, i.e. against which reduced model.

So here's the interaction model:
mdlPA_ia = lmer(PA ~ 1 + OsciPow*Attention + I(OsciPow^2)*Attention + (1 + OsciPow + I(OsciPow^2) + Attention | Subject), data=data,REML=F)

and the reduced model I want to compare it to:
mdlPA_reduced = lmer(PA ~ 1 + OsciPow + I(OsciPow^2) + Attention + (1 + OsciPow + I(OsciPow^2) | Subject) + (1 + Attention | Subject), data=data,REML=F)

Do think this is reasonable? Especially for the reduced model, I'm unsure about the two uncorrelated random effect terms and whether it's necessary to have two random intercepts grouped by subject. When I leave out one Intercept, the model does not converge.
What about having just one random effects term with correlated predictors?

Thank you for you're time!
Norman
___________________________________________________________
Norman Forschack, Dipl.-Psych.
Max-Planck Institute for Human Cognitive and Brain Sciences
Stephanstraße 1a
04103 Leipzig

mail: forschack at cbs.mpg.de
phone: +49341 9940171
web: http://www.cbs.mpg.de/~forschack