Hi all,

I am trying to build a fMRI FEAT analysis that would analyze 2x2 factorial
ANOVA interactions as a first-level analysis in a single subject. In the FSL
archives this was mainly discussed as a second-level analysis, but I hope
this can be done as a first-level analysis as well (the FEAT manual
suggested this possibility but did not describe it much further). A major
concern in this type of analysis is that the interaction is typically much
smaller than the main effects. Thus any confounding effects or mistakes in
the analysis can easily modify or become the whole outcome of a interaction
study. Any advice how to set this analysis up _really_ correctly in FEAT
would be much appreciated.

In the stimuli, there are 2 factors (A and B) at 2 levels (ON and OFF). Thus
there are 4 types of stimuli: A0B0 = REST, A1B0 = A, A0B1 = B, and A1B1 =
AB. Physically, the "AB" condition corresponds to a stimulus where both A
and B are presented simultaneously. Stimulus duration is 0.3 seconds for all
stimuli A/B/AB.

We use a sparse sampling design (clustered volume acquisition) with one full
volume EPI every 10 seconds (taking one full volume of 24 slices takes 1.2
seconds, which is followed by a pause of 8.8 seconds when no EPI data is
collected). Each EPI is preceded by a single stimulus (one of the four
categories REST/A/B/AB) at 4 seconds before EPI onset. The stimuli are
presented in a random order. We collect about 50 full EPI volumes for each
of the 4 stimulus categories (hence this is a repeated measures ANOVA with
50 values for each cell, for each voxel separately).

In all the considerations below, EV1=stimulus A, EV2=stimulus B, and
EV3=stimulus AB (_not_ the interaction). REST is defined implicitly by
exclusion (as time periods when none of the paradigm files suggest there
would have been a stimulus) and thus there is no separate paradigm file for
REST.

The FEAT manual (Appendix A) describes "how to model nonlinear interactions
between two EVs" (factors). I here assume that the "interaction" discussed
in the FEAT manual at Appendix A is the 2x2 factorial ANOVA interaction,
please correct me if I am wrong. Below I have three suggestions; Suggestion
1 is what the manual would seem to indicate but that does not work.




*** Suggestion 1. The manual suggests "setting up two original EVs"
(corresponding to stimuli A and B when presented alone?), and then "an
interaction term, which will will only be up when both the original EVs are
up, and down otherwise" (corresponding to stimulus AB?). However for
Interaction, it is not possible to assign a paradigm file, and paradigm
files can only be assigned to EV1 and EV2 (A and B). Since calculation of
interaction requires values from all 4 cells (REST, A, B, and AB), there
must be some way of telling FEAT how to distinguish between AB and REST
events. The logical conclusion would be to construct two paradigm files, one
that is "1" always when stimulus A is present (thus, for A and AB stimuli),
and another that is "1" always when the stimulus B is present (thus, for B
and AB stimuli) - thus the AB stimuli occur when both of the two paradigm
files show "1". Then one would simply generate a third EV (EV3) and select
that as Interaction between EV1 and EV2. Then one would build the following
4 contrasts:

OC1 [1 0 0] ; for main effect A
OC2 [0 1 0] ; for main effect B
OC3 [0 0 1] ; for Interaction (positive)
OC4 [0 0 -1] ; for Interaction (negative)

However this leads to that EV1 and EV2 are overlapping (for AB stimuli, both
are "1" at the same time), and thus they are NOT independent of each other.
This violates the basic requirement of the GLM that all events be
independent of each other. Attempts to set up the analysis this way result
in an error of the type "Problem with processing the model: At least one EV
is (close to) a linear combination of the others. You should probably alter
your design. (Design matrix is rand deficient - ratio of min:max eigenvalues
in SVD matrix is 1.283201e-06)".




*** Suggestion 2. Given the failure of Suggestion 1, the only way to tell
all the 4 cells apart (REST, A, B, and AB) would be to have at least 3
paradigm files (for A, B, and AB; REST would be implicit from the other
three files).

Then, then to analyze the interaction, one should have three paradigm files
(all in 3-column format).
Paradigm file 1 has "1" every time only the stimulus A is on,
Paradigm file 2 has "1" every time only the stimulus B is on, and
Paradigm file 3 has "1" every time the AB stimulus is on.
Now the three paradigm files are completely non-overlapping and thus
independent of each other, and GLM should be happy.

Then I should set the number of original EVs as 4, assign the Custom (3
column format) paradigm files for EV1 (A), EV2 (B), EV3 (AB), and set
"Interaction" for EV4, Between EVs [1 2 3] (all three buttons 1-3 selected
for choosing the interaction components).

In the contrasts I should select 5 contrasts (for original EVs?) with
OC1 [1 0 0 0] ;A vs. REST
OC2 [0 1 0 0] ;B vs. REST
OC3 [0 0 1 0] ;AB vs. REST
OC4 [0 0 0 1] ;Interaction (+)
OC5 [0 0 0 -1] ; Interaction (-)

No F-tests are selected in this approach.

With this approach, there is again an error of the type "Problem with
processing the model: At least one EV is (close to) a linear combination of
the others. You should probably alter your design. (Design matrix is rand
deficient - ratio of min:max eigenvalues in SVD matrix is 1.283201e-06)".
Also according to the FEAT manual [regarding
Stats/First-level/EVs/Interaction], "this EV [interaction] is produced by
multiplying together selected EVs". Is this different from a 2x2 factorial
ANOVA interaction?




*** Suggestion 3. This is exactly the same as Suggestion 2 (including the
above settings for EVs and contrasts), but now I add four F-tests in the
General Linear Model/Contrasts & F-tests:

           F F F F
           1 2 3 4
OC1 [X - - -]
OC2 [- X - -]
OC3 [- - X -]
OC4 [- - - X]
OC5 [- - - X]

The OC4 and OC5 F-tests should give the 2x2 factorial ANOVA interactions
(for positive and negative interactions, respectively).

*****************

Which one, if any, of the above would be the correct FEAT setting for
first-level 2x2 factorial ANOVA w/ repeated measures ?

Thanks in advance,

Tommi

--
Tommi Raij, M.D., Ph.D.
Research Fellow
MGH/MIT/HMS Athinoula A. Martinos Center for Biomedical Imaging
Building 149, 13th Street, Mailcode 149-2301
Charlestown, MA 02129 U.S.A.

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