Hi,
I'd like to run a 2x4 repeated measures ANOVA and test specific contrasts within this
design, but I can't seem to find any examples of how to code 2 factors when one has >2
levels or of repeated measures designs with >1 factor.
Here are the details of my design:
-Both factors are repeated measures, such that every subject performs every condition.
In other words, Factor A has 2 levels and Factor B has 4 levels, so each subject performs
A1B1 A1B2 A1B3 A1B4 A2B1 A2B2 A2B3 A2B4.
-Each subject does 4 runs, though all conditions are included in each run.
I also have a rest condition that follows each of the experimental conditions.
Here is how I've set up my analysis:
1) At the 1st level, for each run, I am contrasting each condition vs. the rest condition,
which gives me 8 copes.
2) At the 2nd level, for each subject, I combine these 8 copes across the 4 runs.
Then, here are the 3rd level analyses that seem to make sense to me, though I'm new at
this.
3A) Set up the design matrix with an EV for each of the 8 conditions + EVs for each
subject. Here is an example with only 2 subjects included for simplicity:
1 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 1 0
0 0 0 0 1 0 0 0 1 0
0 0 0 0 0 1 0 0 1 0
0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 1 1 0
1 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 1
0 0 0 1 0 0 0 0 0 1
0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 1 0 0 0 1
0 0 0 0 0 0 1 0 0 1
0 0 0 0 0 0 0 1 0 1
and some example contrasts:
A1-A2 1 1 1 1 -1 -1 -1 -1 0 0
B1-rest 1 0 0 0 1 0 0 0 0 0
B2-B1 -1 1 0 0 -1 1 0 0 0 0
and the 3 F-tests:
A1-2 1 1 1 1 -1 -1 -1 -1 0 0
B1-4 3 -1 -1 -1 3 -1 -1 -1 0 0
B2-4 -1 3 -1 -1 -1 3 -1 -1 0 0
B3-4 -1 -1 3 -1 -1 -1 3 -1 0 0
A1-2*B1-4 3 -1 -1 -1 -3 1 1 1 0 0
A1-2*B2-4 -1 3 -1 -1 1 -3 1 1 0 0
A1-2*B3-4 -1 -1 3 -1 1 1 -3 1 0 0
When I run it this way, I get a rank deficient/singular matrix error. It runs fine without
the subject EVs included, but then I'm not able to remove the subject mean variability
from the residuals. Should I perhaps be doing this at the 1st level instead and then using
the multi-session, multi-subject example to average across runs and subjects? If so, how
can I contrast each condition vs. rest beforehand, and still do this?
3B) I also attempted to code it with 7 predictors instead. Here is the design matrix that I
generated for testing individual contrasts with the following coding scheme (following
your tripled two-group difference example):
A1B1 = a + b + c + d + e + f + g
A1B2 = -a
A1B3 = -b
A1B4 = -c
A2B1 = -d
A2B2 = -e
A2B3 = -f
A2B4 = -g
1 1 1 1 1 1 1
-1 0 0 0 0 0 0
0 -1 0 0 0 0 0
0 0 -1 0 0 0 0
0 0 0 -1 0 0 0
0 0 0 0 -1 0 0
0 0 0 0 0 -1 0
0 0 0 0 0 0 -1
and some example contrasts:
A1-A2 0 0 0 2 2 2 2
A2-A1 0 0 0 -2 -2 -2 -2
B1-0 1 1 1 0 1 1 1
B2-0 -1 0 0 0 -1 0 0
B2-B1 -2 -1 -1 -2 -2 -1 -1
B4-B3 0 1 -1 0 0 1 -1
B2-B4 -1 0 1 0 -1 0 1
and the design matrix I created for the F-test (1st column codes A, 2nd-4th columns code
B, and 5-7th columns code interactions)
(roughly following the ANOVA: 1-factor 4-levels (Repeated Measures) example):
1 -1 -1 -1 -1 -1 -1
1 1 0 0 1 0 0
1 0 1 0 0 1 0
1 0 0 1 0 0 1
-1 -1 -1 -1 1 1 1
-1 1 0 0 -1 0 0
-1 0 1 0 0 -1 0
-1 0 0 1 0 0 -1
along with the F-test matrix:
A1-2 1 0 0 0 0 0 0
B2-1 0 1 0 0 0 0 0
B3-1 0 0 1 0 0 0 0
B4-1 0 0 0 1 0 0 0
A1-2*B2-1 0 0 0 0 1 0 0
A1-2*B3-1 0 0 0 0 0 1 0
A1-2*B4-1 0 0 0 0 0 0 1
For all of these, I also have N additional columns (one for each subject) in order to
remove the subject mean variability.
Any advice or comments would be greatly appreciated.
Thanks!
Kristen
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