Dear Dr Clark,

Since noone else has piped up yet, I thought that I would give this one a go.

>I'm trying to track down a problem with my experiment design where
>occasionally I get a grey bar (actually, 2 grey bars adjacent to one another,
>one corresponding to the hrf and one to the derivative) in the parameter
>estimability bar.  I know this usually results from specifying the same onset
>for two conditions, but I have verified multiple times that this is not what
>is happening (and moreover, I am generating the design matrices automatically
>and most of these matrices have given me no grief at all).

So, it sounds as though you are doing an event-related analysis in 
fMRI.  Usually it's pretty hard to get two covariates co-linear in an 
event-related design matrix (unless they are identical), so to see 
grey bars in the parameter estimability bar is indeed a bit of a 
surprise.  By contrast, in a block design it would be very easy to 
accidentally over-specify the model, resulting in grey bars (there's 
an example of this later in this message).

>So, I have one theory.  In my experiment, bins are determined partly by a
>subsequent behavioral (memory) task.  This unfortunately results in bins with
>very few (sometimes 0 or 1) members.  The grey bars have only appeared twice,
>and each time they have corresponded to a condition with only one member
>(those with 0 are tossed out by the program generating the design matrix).
>
>Could small bins be preventing the SPM package from deconvolving the
>hemodynamics?  And could this be why I'm seeing the grey bars?

SPM doesn't attempt to deconvolve the data (as one might do if one 
wanted to get back to the original neural responses starting from the 
BOLD signal).  It simply uses multiple regression to try to fit the 
data with a series of covariates, which often consist of the train of 
expected neural responses convolved with a standard hrf to try to 
model the expected haemodynamic response.

However, if you have only one event, which occurs within a couple of 
seconds of the end of the experiment, then this might generate a 
covariate which in fact is just a column of zeros for the whole 
experiment, and a 1st temporal derivative which is therefore also a 
column of zeros (appearing in mid-grey).  This is because although 
the event occurs before the end of the experiment, the response lags 
sufficiently that there is no response at all in the modelled 
covariate, which assumes a delay of a couple of seconds before the 
response starts to rise.  A quick glance at your design matrix should 
tell you if this is the problem.

Obviously a column of zeros will have a parameter estimate which 
cannot be estimated - any parameter estimate from minus infinity to 
plus infinity would model the data equally well (i.e. it would 
contribute nothing to the model).

>I'm usually just going to throw out these conditions for subjects that have so
>few trials anyway, but I want to make sure that I'm not letting something
>slide by.

If you are throwing out columns of zeros, then clearly you lose 
nothing - they contribute nothing to the model anyway.

>Also, there are some cases where out of 4 scans, only one has this problem
>with parameter estimability, and the rest of the scans have sizable bins.  So,
>although scan 1 might only have 1 exemplar, the rest might have a total of 20.
>  Should I be averaging in that 1 exemplar from the first scan, or should I
>toss it?

What you decide to do probably won't make much difference.  However, 
one possibility would be to assume that the size of the response in a 
given subject doesn't change from one session to the next.  If you 
were prepared to do this, then you could model the events from all 
four sessions in one column of the design matrix.  This way you 
needn't lose the contribution made by sessions in which very few 
events occurred.  You certainly wouldn't expect to run into any 
problems with parameter estimability if you did this.  Also you may 
make your analysis more sensitive (if this assumption turns out to be 
a reasonable one) by reducing the degrees of freedom.

However, if you want to do this, you probably won't want to assume 
that there is no change in baseline between session since this is 
unlikely to be true.   It would therefore be sensible to add, for 
each subject, three user-specified covariates consisting of columns 
looking like this (for an example in which there are only five scans 
in each of the sessions): 3 3 3 3 3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
-1 -1 -1 -1
and -1 -1 -1 -1 -1 3 3 3 3 3  -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 and -1 -1 
-1 -1 -1 -1 -1 -1 -1 -1 3 3 3 3 3 -1 -1 -1 -1 -1.  (In fact the 3s 
should be 1s, and the -1s should be minus 1/3, but it would have 
taken too long to write it out like that!).

Note that you don't want to add a 4th column like this: -1 -1 -1 -1 
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 3 3 3 3 3, because if you did, then 
these 4 columns would sum to zero, and you would end up with even 
more unwanted grey in your parameter estimability bar!  Note also 
that if you ask SPM to high-pass filter the data, it will also 
high-pass filter the design matrix, so your user-specified columns 
won't come out looking quite like the ones that you entered.

>  Thanks!
>Dav Clark

No problem.  Hope it has at least given you some food for thought,

Best wishes,

Richard.


-- 
from: Dr Richard Perry,
Clinical Lecturer, Wellcome Department of Cognitive Neurology, 
Institute of Neurology, Darwin Building, University College London, 
Gower Street, London WC1E 6BT.
Tel: 0207 679 2187;  e mail: [log in to unmask]


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