Dear Dr. Henson,
We are reading the
SPM archives and find that you have answered some questions about covarying out
RT as in the email attached at the very end. We have three questions and would
really hope you can kindly give us some hint. Please bear with me since I need
to make an example to be sure things are clear. Sorry to write so
long.
Suppose we have
two conditions A and B and let us suppose A occurs at time 10 20 30 and the
RTs are 1 sec 2 sec 3 sec each; B occurs at time 40 50 60 and the
RTs are 4 sec 5 sec 6 sec each.
Following
your suggestion, to covary out common RT, we first key in a regressor
of task (A+B) with onset time (10, 20, 30, 40, 50,
60) and duration (1,2,3,4,5,6), then incorporate two modulations for
this regressor. The first one is RT and we key in (1,2,3,4,5,6) and the second
one is a categorical modulation and we key in,
say (2,2,2, 1,1,1).
Now
our questions are
(1) Is it true that SPM will remove
the mean of these modulations? That is,
the RT modulation (1,2,3,4,5,6) has the mean of (1+2+3+4+5+6)/6=3.5 so in fact,
the RT regressor in the design matrix will be (-2.5,-1.5,-0.5,0.5,1.5,2.5) and
the categorical modulation has the mean of (2+2+2+1+1+1)/6=1.5, so the
categorical regressor in the design matrix will be (0.5,0.5,0.5,-0.5,-0.5,-0.5)?
Since we are basically running a linear model of
signal=beta1*[task]+beta2*[RT]+beta3[category],
then is it true beta1 gives us the area which
has on average 3.5 sec RT and is more activated in task than in the
baseline? Our reasoning is that if RT has an effect and if mean is
indeed removed by SPM, then whether the mean RT effect is incorporated
into beta1? If that is the case, is there any choice in SPM that
we can do to shut off this mean removal so that we can have a pure
task effect and a pure RT effect (so that the average RT effect won't get
incorporated into beta1)?
(2) Related to question (1), does the order of
keying in modulations matter? Since there are RT and categorical
modulations, suppose instead we key in the categorical modulation first and then
the RT modulation, would we get the same result as in (1) where RT is
modulated first and then category is modulated the next? We are curious about
what exactly you mean by "the resulting regressor is orthogonal to that for
the condition effect itself," and worry whether orders will matter as far as
orthogonality is concerned.
(3) In fact, in our experiment there are
scores on how well a subject has done A and scores on how well a subject has
done B. And we would like to see whether when a subject has a higher
score on A may have different brain activations than when he has a
lower score on A. It seems that in the model above, we cannot feed in the
score in any way since only A-B or B-A can be tested. So if we want to covary
out common RT, but still we want to know for only A, having a higher score would
bring in different brain activations, could you please give us some hint on how
to build a model? We thought about running
(#)
signal=beta1*[A]+beta2*[RT_A]+beta3[score_A]+beta4*[B]+beta5*[RT_B]+beta6[score_B]
(that is, we feed in a regressor for A,
another for B, and each regressor is modulated by its RT and its score
respectively), but this will have the problem that you mentioned below that only
covarying out RT within conditions, not across conditions. We thought if we can
shut off the mean-corrected function of SPM, then running (#) would look
perfectly fine, but if we cannot, then (#) has the problem of not covarying
out common RT across A and B.
Thank you so much for answering
these questions. We simply cannot find answers anywhere and greatly
greatly appreciate your help.
Best,
Nissen
----------------------------------------------------------------------
Andreas -
> I would like to covary out reaction time in one of my
experiments (using
> SPM99). The experiment contained two conditions (and
not explicitly
> modelled null events as a baseline condition). I entered
the reaction
> times as a parametric modulation of each
trial.
>
> Intuitively, I thought that e.g. the contrast [1 0 -1 0]
identifies
> brain regions differentially activated by the two tasks
(having covaried
> out common RT effects), and that e.g. the contrast [0 1
0 1] identifies
> the main effect of reaction time.
>
> In one
of your recent e-mails I found the following:
>
> "(...) The slight
complication comes if you have more than one
> trial-type. You could enter
a separate parametric modulation of each
> trial-type by the RTs for that
trial-type, but that will only covary out
> trial-specific RT effects. You
probably want to covary out common RT
> effects. The way to do this is to
collapse all your trials into one
> trial-type, then enter two parametric
modulations. One modulation would
> be RTs, as above. The other would be a
"categorical" modulation that
> indicates whether each trial is of type1
or type2. A contrast of [1] on
> the column for this "categorical"
modulation will identify regions that
> show a difference between your
trial-types, having covaried out common
> RT effects
(...)"
>
> Is there something wrong with the way I have built my
design matrix?
Your design matrix will "covary out" RT differences across
trials
WITHIN an condition. However, it will not covary out RT
differences
BETWEEN conditions. This is because the parametric modulations
(RTs
in your case) are always mean-corrected (so the resulting regressor
is
orthogonal to that for the condition effect itself). Thus any
difference
in mean RT between your two conditions will not be "covaried out",
and
could possibly* still contribute to any BOLD differences you
find
between your two conditions (in your [1 0 -1 0] contrast). If you
want
to covary out RTs that differ across conditions, you need to create
the
alternative design matrix that I described above.
*Or
alternatively, you may want to ask: "why am I covarying out RTs
if they are
simply another consequence of the same underlying cause
that generates my
BOLD differences?", ie are they really a "confound"
or simply another
correlated dependent
variable?...
Rik
--
---------------------------------------------------------
DR
RICHARD HENSON
Institute of Cognitive Neuroscience
& Wellcome
Department of Imaging Neuroscience
University College London
17 Queen
Square
London, WC1N 3AR
England
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