Hi all,

I am having trouble formulating the best way to analyze a dataset. The data
description is as follows, with a header of the data below:

> str(post)
'data.frame': 8256 obs. of  6 variables:
 $ Subject         : int  124 124 124 124 124 124 124 124 124 124 ...
 $ GROUP           : chr  "PI" "PI" "PI" "PI" ...
 $ response.corr   : int  1 1 1 1 1 0 1 1 1 1 ...
 $ proc            : chr  "GoProc" "GoProc" "GoProc" "NogoProc" ...
 $ response.emotion: chr  "H" "H" "H" "F" ...
 $ SubTrial        : int  2 3 4 5 6 7 8 9 10 11 ...

> head(post)
   Subject GROUP response.corr     proc      response.emotion SubTrial
        124    PI             1                GoProc                H
           2
        124    PI             1                GoProc                H
           3
        124    PI             1                GoProc                H
           4
        124    PI             1                NogoProc             F
         5
        124    PI             1                GoProc                H
           6
        124    PI             0                NogoProc             F
         7

It is of interest to understand how GROUP membership effects response.corr.
Each subject responds 96 times by pressing a button or not pressing the
button under 2 crossed conditions: proc and response.emotion. SubTrial is
not a variable of interest, but is simply presented to show repetitions in
measurement.

My attempt at answering this was to use the following 2 models:

model1 <- lmer(response.corr ~ GROUP * proc * response.emotion + (1 |
Subject),family=binomial,data=post)
model2 <- lmer(response.corr ~ GROUP * proc * response.emotion + (proc *
response.emotion | Subject),family=binomial,data=post)

While the second model fits the data better, I find it strange to fit a
random slope by proc and response.emotion since they are variables of
interest. Is this idea misfounded?

Furthermore, I think that these models fit things such that GROUP, proc &
response.emotion are crossed at level 1 and nested under Subject, which is
a random variable at level 2. Is that correct? Logically, it seemed to me
that proc and response.emotion should be crossed at level 1 and nested
under Subject which is random at level 2, which is nested under GROUP at
level 3, since each subject belongs to one of 2 different groups. But I had
no idea how to fit such a model, nor whether or not this was the right idea.

I have read through Bates' book on lme4 and plenty of other materials
online, but am still having trouble. Normally I would simply fit a model
whereby I'd average response.corr by subject and then feed the ratio scores
I have (4 per subject; one for each level of proc * response.emotion) into
a model like such:

model3 <- lmer(response.corr.ratio ~ GROUP * proc * response.emotion  + (1
| Subject), data=post.ratio)


But I believe that this approach is limited as these are binary data with
several subjects having ratios that are near floors or ceilings by
condition, which may bias the estimated error. That is why I turned to the
raw data and a multi-level modeling approach.


Any insight would be much appreciated.


Thanks in advance,

Matthew

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