post for likelihood ration tests

Hi there, 

I was wondering if i could get some advice regarding the model comparison when interaction is included. please see some details below


Info

DV: Metaphoricity (continuous)

Fixed effects (within subjects manipulation): Hand Free (Left v. Right)

                                                                        Gesture (Absence vs. Presence)

Random effects: Participants

                        Items

 

Maximal model (driven by our research question)

Model1 = lmer(Metaphoricity ~ HandFree*Gesture + (1 + HandFree*Gesture|Participants) + (1 + HandFree*Gesture|Items)

 

 

Reduced model with main effects only

Model2 = lmer(Metaphoricity ~ HandFree + Gesture + (1 + HandFree + Gesture|Participants) + (1 + HandFree + Gesture|Items)

 

 

Null model

Model3 = lmer(Metaphoricity ~ 1 + (1 + HandFree*Gesture|Participants) + (1 + HandFree*Gesture|Items)

 

 

 

Question:

1.     What will be the correct reduced/null model to compare the maximal one with in a likelihood ratio test as a means to obtain p-values?

a.     If I use the reduced model with main effects only the random effect structure would have to change contrary to Barr et al.?s (2013) suggestion to keep the same random effect structure.

b.     If I use the null model with no fixed effect I am not sure I understand why we keep the by subjects and by items slope for the interaction when the interaction is not in the model.