[R-sig-ME] Related fixed and random factors and planned comparisons in a 2x2 design

[paul]

Dear All,

I am trying to use mixed-effect modeling to analyze brain wave data from
two groups of participants when they were presented with two distinct
stimulus. The data points (scalp voltage) were gathered from the same set
of 9 nearby channels from each participant. And so I have the following
factors:

   - voltage: the dependent variable
   - group: the between-participant/within-item variable for groups A and B
   - item: the within-participant variable (note there are exactly only 2
   items, P and Q)
   - participant: identifying each participant across the two groups
   - channel: identifying each channel (note that data from these channels
   in a nearby region tend to display similar, thus correlated, patterns in
   the same participant)

The hypothesis is that only group B will show difference between P and Q
(i.e., there should be an interaction effect). So I established a
mixed-effect model using the lme4 package in R:

model <- lmer(voltage~1+group+item+(group:item)+(1|participant)+(1|channel),
              data=data, REML=FALSE)

Questions:

   1.

   I'm not sure if it is reasonable to add in participant as a random
   effect, because it is related to group and seems to weaken the effects of
   group. Would it be all right if I don't add it in?
   2.

   Because the data from nearby channels of the same participant tend to be
   correlated, I'm not sure if modeling participant and channel as crossed
   random effects is all right. But meanwhile it seems also strange if I treat
   channel as nested within participant, because they are the same set of
   channels across participants.
   3.

   The interaction term is significant. But how should planned comparisons
   be done (e.g., differences between groups A and B for P) or is it even
   necessary to run planned comparisons? I saw suggestions for t-tests,
   lsmeans, glht, or for more complicated methods such as breaking down the
   model and subsetting the data:

   data[, P_True:=(item=="P")]
   posthoc<-lmer(voltage~1+group
       +(1|participant)+1|channel)
       , data=data[item=="P"]
       , subset=data$P_True
       , REML=FALSE)

   But especially here comparing only between two groups while modeling
   participant as a random effect seems detrimental to the group effects. And
   I'm not sure if it is really OK to do so. On the other hand, because the
   data still contain non-independent data points (from nearby channels), I'm
   not sure if simply using t-tests is all right. Will non-parametric tests
   (e.g., Wilcoxon tests) do in such cases?
   4.

   I suppose I don't need to model item as a random effect because there
   are only two of them, one for each level, right?

I would really appreciate your help!!

Best regards,

Paul

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